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William Stanley Jevons, The Theory of Political
Economy [1871]
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LIBERTY FUND, INC.
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Edition Used:
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
Author: William Stanley Jevons
About This Title:
One of three seminal works published in 1871 (along with Walras and Menger) which
introduced the idea of the marginal theory of utility and thus a revolution in economic
thinking.
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About Liberty Fund:
Liberty Fund, Inc. is a private, educational foundation established to encourage the
study of the ideal of a society of free and responsible individuals.
Copyright Information:
The text is in the public domain.
Fair Use Statement:
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Table Of Contents
Preface to the First Edition (1871)
Preface to the Second Edition (1879)
Preface to the Third Edition By Harriet Jevons
Errata
Chapter I: Introduction
Mathematical Character of the Science.
Confusion Between Mathematical and Exact Sciences.
Capability of Exact Measurement.
Measurement of Feeling and Motives.
Logical Method of Economics.
Relation of Economics to Ethics.
Chapter II: Theory of Pleasure and Pain
Pleasure and Pain As Quantities.
Pain the Negative of Pleasure.
Anticipated Feeling.
Uncertainty of Future Events.
Chapter III: Theory of Utility
Definition of Terms.
The Laws of Human Want.
Utility Is Not an Intrinsic Quality.
Law of the Variation of Utility.
Total Utility and Degree of Utility.
Variation of the Final Degree of Utility.
Disutility and Discommodity.
Distribution of Commodity In Different Uses.
Theory of Dimensions of Economic Quantities.
Actual, Prospective, and Potential Utility.
Distribution of a Commodity In Time.
Chapter IV: Theory of Exchange
Importance of Exchange In Economics.
Ambiguity of the Term Value.
Value Expresses Ratio of Exchange.
Popular Use of the Term Value.
Dimension of Value.
Definition of Market.
Definition of Trading Body.
The Law of Indifference.
The Theory of Exchange.
Symbolic Statement of the Theory.
Analogy to the Theory of the Lever.
Impediments to Exchange.
Illustrations of the Theory of Exchange.
Problems In the Theory of Exchange.
Complex Cases of the Theory.
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Competition In Exchange.
Failure of the Equations of Exchange.
Negative and Zero Value.
Equivalence of Commodities.
Acquired Utility of Commodities.
The Gain By Exchange.
Numerical Determination of the Laws of Utility.
Opinions As to the Variation of Price.
Variation of the Price of Corn.
The Origin of Value.
Chapter V: Theory of Labour
Definition of Labour.
Quantitative Notions of Labour.
Symbolic Statement of the Theory.
Dimensions of Labour.
Balance Between Need and Labour.
Distribution of Labour.
Relation of the Theories of Labour and Exchange.
Relations of Economic Quantities.
Various Cases of the Theory.
Joint Production.
Over-production.
Limits to the Intensity of Labour.
Chapter VI: Theory of Rent
Accepted Opinions Concerning Rent.
Symbolic Statement of the Theory.
Illustrations of the Theory.
Chapter VII: Theory of Capital
The Function of Capital.
Capital Is Concerned With Time.
Quantitative Notions Concerning Capital.
Expression For Amount of Investment.
Dimensions of Capital, Credit and Debit.
Effect of the Duration of Work.
Illustrations of the Investment of Capital.
Fixed and Circulating Capital.
Free and Invested Capital.
Uniformity of the Rate of Interest.
General Expression For the Rate of Interest.
Dimension of Interest.
Peacock On the Dimensions of Interest.
Tendency of Profits to a Minimum.
Advantage of Capital to Industry.
Are Articles In the Consumers' Hands Capital?
Chapter VIII: Concluding Remarks
The Doctrine of Population.
Relation of Wages and Profit.
Professor Hearn's Views.
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[Back to Table of Contents]
PREFACE TO THE FIRST EDITION
(1871)
THE contents of the following pages can hardly meet with ready acceptance among
those who regard the Science of Political Economy as having already acquired a
nearly perfect form. I believe it is generally supposed that Adam Smith laid the
foundations of this science; that Malthus, Anderson, and Senior added important
doctrines; that Ricardo systematised the whole; and, finally, that Mr. J. S. Mill filled
in the details and completely expounded this branch of knowledge. Mr. Mill appears
to have had a similar notion; for he distinctly asserts that there was nothing; in the
Laws of Value which remained for himself or any future writer to clear up. Doubtless
it is difficult to help feeling that opinions adopted and confirmed by such eminent
men have much weight of probability in their favour. Yet, in the other sciences this
weight of authority has not been allowed to restrict the free examination of new
opinions and theories; and it has often been ultimately proved that authority was on
the wrong side.
There are many portions of Economical doctrine which appear to me as scientific in
form as they are consonant with facts. I would especially mention the Theories of
Population and Rent, the latter a theory of a distinctly mathematical character, which
seems to give a clue to the correct mode of treating the whole science. Had Mr. Mill
contented himself with asserting the unquestionable truth of the Laws of Supply and
Demand, I should have agreed with him. As founded upon facts, those laws cannot be
shaken by any theory; but it does not therefore follow, that our conception of Value is
perfect and final. Other generally accepted doctrines have always appeared to me
purely delusive, especially the so-called Wage Fund Theory. This theory pretends to
give a solution of the main problem of the science—to determine the wages of labour;
yet, on close examination, its conclusion is found to be a mere truism, namely, that
the average rate of wages is found by dividing the whole amount appropriated to the
payment of wages by the number of those between whom it is divided. Some other
supposed conclusions of the science are of a less harmless character, as, for instance,
those regarding the advantage of exchange (see the section on "The Gain by
Exchange," p. 141).
In this work I have attempted to treat Economy as a Calculus of Pleasure and Pain,
and have sketched out, almost irrespective of previous opinions, the form which the
science, as it seems to me, must ultimately take. I have long thought that as it deals
throughout with quantities, it must be a mathematical science in matter if not in
language. I have endeavoured to arrive at accurate quantitative notions concerning
Utility, Value, Labour, Capital, etc., and I have often been surprised to find how
clearly some of the most difficult notions, especially that most puzzling of notions
Value, admit of mathematical analysis and expression. The Theory of Economy thus
treated presents a close analogy to the science of Statical Mechanics, and the Laws of
Exchange are found to resemble the Laws of Equilibrium of a lever as determined by
the principle of virtual velocities. The nature of Wealth and Value is explained by the
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consideration of indefinitely small amounts of pleasure and pain, just as the Theory of
Statics is made to rest upon the equality of indefinitely small amounts of energy. But I
believe that dynamical branches of the Science of Economy may remain to be
developed, on the consideration of which I have not at all entered.
Mathematical readers may perhaps think that I have explained some elementary
notions, that of the Degree of Utility for instance, with unnecessary prolixity. But it is
to the neglect of Economists to obtain clear and accurate notions of quantity and
degree of utility that I venture to attribute the present difficulties and imperfections of
the science; and I have purposely dwelt upon the point at full length. Other readers
will perhaps think that the occasional introduction of mathematical symbols obscures
instead of illustrating the subject. But I must request all readers to remember that, as
Mathematicians and Political Economists have hitherto been two nearly distinct
classes of persons, there is no slight difficulty in preparing a mathematical work on
Economy with which both classes of readers may not have some grounds of
complaint.
It is very likely that I have fallen into errors of more or less importance, which I shall
be glad to have pointed out; and I may say that the cardinal difficulty of the whole
theory is alluded to in the section of Chapter IV. upon the "Ratio of Exchange,"
beginning at p. 84 (p. 90 of this edition). So able a mathematician as my friend
Professor Barker, of Owens College, has had the kindness to examine some of the
proof sheets carefully; but he is not, therefore, to be held responsible for the
correctness of any part of the work.
My enumeration of the previous attempts to apply mathematical language to Political
Economy does not pretend to completeness even as regards English writers; and I find
that I forgot to mention a remarkable pamphlet "On Currency" published
anonymously in 1840 (London, Charles Knight and Co.) in which a mathematical
analysis of the operations of the Money Market is attempted. The method of treatment
is not unlike that adopted by Dr. Whewell, to whose Memoirs a reference is made; but
finite or occasionally infinitesimal differences are introduced. On the success of this
anonymous theory I have not formed an opinion; but the subject is one which must
some day be solved by mathematical analysis. Garnier, in his treatise on Political
Economy, mentions several continental mathematicians who have written on the
subject of Political Economy; but I have not been able to discover even the titles of
their Memoirs.
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[Back to Table of Contents]
PREFACE TO THE SECOND EDITION
(1879)
IN preparing this second edition certain new sections have been added, the most
important of which are those treating of the dimensions of economic quantities (pp.
61-69, 83-84, 178-179, 232-234). The subject, of course, is one which lies at the basis
of all clear thought about economic science. It cannot be surprising that many debates
end in logomachy, when it is still uncertain how many meanings the word value has,
or what kind of a quantity utility itself is. Imagine the mental state of astronomers if
they could not agree among themselves whether Right Ascension was the name of a
heavenly body, or a force or an angular magnitude. Yet this would not be worse than
failing to ascertain clearly whether by value we mean a numerical ratio, or a mental
state, or a mass of commodity. John Stuart Mill tells us explicitly1 that "The value of
a thing means the quantity of some other thing, or of things in general, which it
exchanges for." It might of course be explained that Mill did not intend what he said;
but as the statement stands it makes value into a thing, and is just as philosophic as if
one were to say, "Right Ascension means the planet Mars, or planets in general."
These sections upon the dimensions of economic quantities have caused me great
perplexity, especially as regards the relation between utility and time (pp. 64-69). The
theory of capital and interest also involves some subtleties. I hope that my solutions of
the questions raised will be found generally correct; but where they do not settle a
question, they may sometimes suggest one which other writers may answer. A
correspondent, Captain Charles Christie, R.E., to whom I have shown these sections
after they were printed, objects reasonably enough that commodity should not have
been represented by M, or Mass, but by some symbol, for instance Q, which would
include quantity of space or time or force, in fact almost any kind of quantity.
Services often involve time, or force exerted, or space passed over, as well as mass. In
this objection I quite concur, and I must therefore request the reader either to interpret
M with a wider meaning than is given to it in p. 64, or else mentally to substitute
another symbol.
In treating the dimensions of interest, I point out the curious fact that so profound a
mathematician as the late Dean Peacock went quite astray upon the subject (pp.
249-252). Other new sections are those in which I introduce the idea of negative and
approximately zero value, showing that negative value may be brought under the
forms of the equations of exchange without any important modification. Readers of
Mr. Macleod's works are of course familiar with the idea of negative value; but it was
desirable for me to show how important it really is, and how naturally it falls in with
the principles of the theory. I may also draw attention to the section (pp. 102-106) in
which I illustrate the mathematical character of the equations of exchange by drawing
an exact analogy between them and the equations applying to the equilibrium of the
lever.
Two or three correspondents, especially Herr Harald Westergaard of Copenhagen,
have pointed out that a little manipulation of the symbols, in accordance with the
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simple rules of the differential calculus, would often give results which I have
laboriously argued out. The whole question is one of maxima and minima, the
mathematical conditions of which are familiar to mathematicians. But, even if I were
capable of presenting the subject in the concise symbolic style satisfactory to the taste
of a practised mathematician, I should prefer in an essay of this kind to attain my
results by a course of argument which is not only fundamentally true, but is clear and
convincing to many readers who, like myself, are not skilful and professional
mathematicians. In short, I do not write for mathematicians, nor as a mathematician,
but as an economist wishing to convince other economists that their science can only
be satisfactorily treated on an explicitly mathematical basis. When mathematicians
recognise the subject as one with which they may usefully deal, I shall gladly resign it
into their hands. I have expressed a feeling in more than one place that the whole
theory might probably have been put in a more general form by treating labour as
negative utility, and thus bringing it under the ordinary equations of exchange. But the
fact is there is endless occupation for an economist in developing and improving his
science, and I have found it requisite to reissue this essay, as the bibliopoles say,
"with all faults." I have, however, carefully revised every page of the book, and have
reason to hope that little or no real error remains in the doctrines stated. The faults are
in the form rather than the matter.
Among minor alterations, I may mention the substitution for the name Political
Economy of the single convenient term Economics. I cannot help thinking that it
would be well to discard, as quickly as possible, the old troublesome double-worded
name of our Science. Several authors have tried to introduce totally new names, such
as Plutology, Chrematistics, Catallactics, etc. But why do we need anything better
than Economics? This term, besides being more familiar and closely related to the old
term, is perfectly analogous in form to Mathematics, Ethics, Æsthetics, and the names
of various other branches of knowledge, and it has moreover the authority of usage
from the time of Aristotle. Mr. Macleod is, so far as I know, the re-introducer of the
name in recent years, but it appears to have been adopted also by Mr. Alfred Marshall
at Cambridge. It is thus to be hoped that Economics will become the recognised name
of a science, which nearly a century ago was known to the French Economists as la
science économique. Though employing the new name in the text, it was obviously
undesirable to alter the title-page of the book.
When publishing a new edition of this work, eight years after its first appearance, it
seems natural that I should make some remarks upon the changes of opinion about
economic science which have taken place in the interval. A remarkable discussion has
been lately going on in the reviews and journals concerning the logical method of the
science, touching even the question whether there exists any such science at all.
Attention was drawn to the matter by Mr. T. E. Cliffe Leslie's remarkable article1 "On
the Philosophical Method of Political Economy," in which he endeavours to dissipate
altogether the deductive science of Ricardo. Mr. W. T. Thornton's writings have a
somewhat similar tendency. The question has been further stirred up by the admirable
criticism to which it was subjected in the masterly address of Professor J. K. Ingram,
at the last meeting of the British Association. This Address has been reprinted in
several publications1 in England, and has been translated into the chief languages of
Western Europe. It is evident, then, that a spirit of very active criticism is spreading,
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which can hardly fail to overcome in the end the prestige of the false old doctrines.
But what is to be put in place of them? At the best it must be allowed that the fall of
the old orthodox creed will leave a chaos of diverse opinions. Many would be glad if
the supposed science collapsed altogether, and became a matter of history, like
astrology, alchemy, and the occult sciences generally. Mr. Cliffe Leslie would not go
quite so far as this, but would reconstruct the science in a purely inductive or
empirical manner. Either it would then be a congeries of miscellaneous disconnected
facts, or else it must fall in as one branch of Mr. Spencer's Sociology. In any case, I
hold that there must arise a science of the development of economic forms and
relations.
But as regards the fate of the deductive method, I disagree altogether with my friend
Mr. Leslie; he is in favour of simple deletion; I am for thorough reform and
reconstruction. As I have previously explained, 2 the present chaotic state of
Economics arises from the confusing together of several branches of knowledge.
Subdivision is the remedy. We must distinguish the empirical element from the
abstract theory, from the applied theory, and from the more detailed art of finance and
administration. Thus will arise various sciences, such as commercial statistics, the
mathematical theory of economics, systematic and descriptive economics, economic
sociology, and fiscal science. There may even be a kind of cross subdivision of the
sciences; that is to say, there will be division into branches as regards the subject, and
division according to the manner of treating the branch of the subject. The manner
may be theoretical, empirical, historical, or practical; the subject may be capital and
labour, currency, banking, taxation, land tenure, etc.—not to speak of the more
fundamental division of the science as it treats of consumption, production, exchange,
and distribution of wealth. In fact, the whole subject is so extensive, intricate, and
diverse, that it is absurd to suppose it can be treated in any single book or in any
single manner. It is no more one science than statics, dynamics, the theory of heat,
optics, magnetoelectricity, telegraphy, navigation, and photographic chemistry are one
science. But as all the physical sciences have their basis more or less obviously in the
general principles of mechanics, so all branches and divisions of economic science
must be pervaded by certain general principles. It is to the investigation of such
principles—to the tracing out of the mechanics of self-interest and utility, that this
essay has been devoted. The establishment of such a theory is a necessary preliminary
to any definitive drafting of the superstructure of the aggregate science.
Turning now to the theory itself, the question is not so much whether the theory given
in this volume is true, but whether there is really any novelty in it. The exclusive
importance attributed in England to the Ricardian School of Economists, has
prevented almost all English readers from learning the existence of a series of French,
as well as a few English, German, or Italian economists, who had from time to time
treated the science in a more or less strictly mathematical manner. In the first edition
(pp. 14-18), I gave a brief account of such writings of the kind as I was then
acquainted with; it is from the works there mentioned, if from any, that I derived the
idea of investigating Economics mathematically. To Lardner's Railway Economy I
was probably most indebted, having been well acquainted with that work since the
year 1857. Lardner's book has always struck me as containing a very able
investigation, the scientific value of which has not been sufficiently estimated; and in
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chapter xiii. (pp. 286-296, etc.) we find the Laws of Supply and Demand treated
mathematically and illustrated graphically.
In the preface to the first edition (p. xi),1 I remarked that in his treatise on Political
Economy, M. Joseph Garnier mentioned several continental mathematicians who had
written on the subject of Economics, and I added that I had not been able to discover
even the titles of their memoirs. This, however, must have been the result of careless
reading or faulty memory, for it will be found that Garnier himself1 mentions the
titles of several books and memoirs. The fact is that, writing as I did then at a distance
from any large library, I made no attempt to acquaint myself with the literature of the
subject, little thinking that it was so copious and in some cases so excellent as is now
found to be the case. With the progress of years, however, my knowledge of the
literature of political economy has been much widened, and the hints of friends and
correspondents have made me aware of the existence of many remarkable works
which more or less anticipate the views stated in this book. While preparing this new
edition, it occurred to me to attempt the discovery of all existing writings of the kind.
With this view I drew up a chronological list of all the mathematico-economic works
known to me, already about seventy in number, which list, by the kindness of the
editor, Mr. Giffen, was printed in the Journal of the London Statistical Society for
June 1878 (vol. xli. pp. 398-401), separate copies being forwarded to the leading
economists, with a request for additions and corrections. My friend, M. Léon Walras,
Rector of the Academy of Lausanne, after himself making considerable additions to
the list, communicated it to the Journal des Économistes (December 1878), to the
editor of which we are much indebted for its publication. Copies of the list were also
sent to German and Italian economical journals. For the completion of the
bibliographical list I am under obligations to Professor W. B. Hodgson, Professor
Adamson, Mr. W. H. Brewer, M.A., H.M. Inspector of Schools, the Baron d'Aulnis de
Bourouill, Professor of Political Economy at Utrecht, M. N. G. Pierson of
Amsterdam, M. Vissering of Leiden, Professor Luigi Cossa of Pavia, and others.
All reasonable exertions have thus been made to render complete and exhaustive the
list of mathematico-economic works and papers, which is now printed in the first
Appendix to this book (pp. 277-291). It is hardly likely that many additions can be
made to the earlier parts of the lists, but I shall be much obliged to any readers who
can suggest corrections or additions. I shall also be glad to be informed of any new
publications suitable for insertion in the list. On the other hand, it is possible that
some of the books mentioned in the list ought not to be there. I have not been able in
all cases to examine the publications myself, so that some works inserted at the
suggestion of correspondents may have been named under misconception of the
precise purpose of the list. Economic works, for instance, containing numerical
illustrations and statistical facts numerically expressed, however abundantly, have not
been intentionally included, unless there was also mathematical method in the
reasoning. Without this condition the whole literature of numerical commercial
statistics would have been imported into my list. In other cases only a small portion of
a book named can be called mathematico-economic; but this fact is generally noted by
the quotation of the chapters or pages in question. The tendency, however, has been to
include rather than to exclude, so that the reader might have before him the whole
field of literature requiring investigation.
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To avoid misapprehension it may be well to explain that the ground for inserting any
publication or part of a publication in this list, is its containing an explicit recognition
of the mathematical character of economics, or the advantage to be attained by its
symbolical treatment. I contend that all economic writers must be mathematical so far
as they are scientific at all, because they treat of economic quantities, and the relations
of such quantities, and all quantities and relations of quantities come within the scope
of the mathematics. Even those who have most strongly and clearly protested against
the recognition of their own method, continually betray in their language the
quantitative character of their reasonings. What, for instance, can be more clearly
mathematical in matter than the following quotation from Cairnes's chief work:1
—"We can have no difficulty in seeing how cost in its principal elements is to be
computed. In the case of labour, the cost of producing a given commodity will be
represented by the number of average labourers employed in its production—regard at
the same time being had to the severity of the work and the degree of risk it
involves—multiplied by the duration of their labours. In that of abstinence, the
principle is analogous: the sacrifice will be measured by the quantity of wealth
abstained from, taken in connection with the risk incurred, and multiplied by the
duration of the abstinence." Here we deal with computation, multiplication, degree of
severity, degree of risk, quantity of wealth, duration, etc., all essentially mathematical
things, ideas, or operations. Although my esteemed friend and predecessor has in his
preliminary chapter expressly abjured my doctrines, he has unconsciously adopted the
mathematical method in all but appearance.
We might easily go further back, and discover that even the father of the science, as
he is often considered, is thoroughly mathematical. In the fifth chapter of the First
Book of the Wealth of Nations, for instance, we find Adam Smith continually arguing
about "quantities of labour," "measures of value," "measures of hardship,"
"proportion," "equality," etc.; the whole of the ideas in fact are mathematical. The
same might be said of almost any other passages from the scientific parts of the
treatise, as distinguished from the historical parts. In the first chapter of the Second
Book (29th paragraph), we read—"The produce of land, mines, and fisheries, when
their natural fertility is equal, is in proportion to the extent and proper application of
the capitals employed about them. When the capitals are equal, and equally well
applied, it is in proportion to their natural fertility." Now every use of the word equal
or equality implies the existence of a mathematical equation; an equation is simply an
equality; and every use of the word proportion implies a ratio expressible in the form
of an equation.
I hold, then, that to argue mathematically, whether correctly or incorrectly, constitutes
no real differentia as regards writers on the theory of economics. But it is one thing to
argue and another thing to understand and to recognise explicitly the method of the
argument. As there are so many who talk prose without knowing it, or, again, who
syllogise without having the least idea what a syllogism is, so economists have long
been mathematicians without being aware of the fact. The unfortunate result is that
they have generally been bad mathematicians, and their works must fall. Hence the
explicit recognition of the mathematical character of the science was an almost
necessary condition of any real improvement of the theory. It does not follow, of
course, that to be explicitly mathematical is to ensure the attainment of truth, and in
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such writings as those of Canard and Whewell, we find plenty of symbols and
equations with no result of value, owing to the fact that they simply translated into
symbols the doctrines obtained, and erroneously obtained, without their use. Such
writers misunderstood and inverted altogether the function of mathematical symbols,
which is to guide our thoughts in the slippery and complicated processes of reasoning.
Ordinary language can usually express the first axioms of a science, and often also the
matured results; but only in the most lame, obscure, and tedious way can it lead us
through the mazes of inference.
The bibliographical list, of which I am speaking, is no doubt a very heterogeneous
one, and may readily be decomposed into several distinct classes of economical
works. In a first class may be placed the writings of those economists who have not at
all attempted mathematical treatment in an express or systematic manner, but who
have only incidentally acknowledged its value by introducing symbolic or graphical
statements. Among such writers may be mentioned especially Rau (1868), Hagen
(1844), J. S. Mill (1848), and Courcelle-Seneuil (1867). Many readers may be
surprised to hear that John Stuart Mill has used mathematical symbols; but, on turning
to Book III., chapters xvii. and xviii., of the Principles of Political Economy, those
difficult and tedious chapters in which Mill leads the reader through the Theory of
International Trade and International Values, by means of yards of linen and cloth, the
reader will find that Mill at last yields, and expresses himself concisely and clearly1
by means of equations between m,n,p, and q. His mathematics are very crude; still
there is some approach to a correct mathematical treatment, and the result is that these
chapters, however tedious and difficult, will probably be found the truest and most
enduring parts of the whole treatise.
A second class of economists contains those who have abundantly employed
mathematical apparatus, but, misunderstanding its true use, or being otherwise
diverted from a true theory, have built upon the sand. Misfortunes of this kind are not
confined to the science of economics, and in the most exact branches of physical
science, such as mechanics, molecular physics, astronomy, etc., it would be possible
to adduce almost innumerable mathematical treatises, which must be pronounced
nonsense. In the same category must be placed the mathematical writings of such
economists as Canard (1801), Whewell (1829, 1831, and 1850), Esmenard du Mazet
(1849 and 1851), and perhaps Du Mesnil-Marigny (1860).
The third class forms an antithesis with the second, for it contains those authors who,
without any parade of mathematical language or method, have nevertheless carefully
attempted to reach precision in their treatment of quantitative ideas, and have thus
been led to a more or less complete comprehension of the true theory of utility and
wealth. Among such writers Francis Hutcheson, the Irish founder of the great Scotch
School, and the predecessor of Adam Smith at Glasgow, probably stands first. His
employment of mathematical symbols1 seems rather crude and premature, but the
precision of his ideas about the estimation of quantities of good and evil is beyond
praise. He thoroughly anticipates the foundations of Bentham's moral system,
showing that the Moment of Good or Evil is, in a compound proportion of the
Duration and Intenseness, affected also by the Hazard or uncertainty of our
existence.1 As to Bentham's ideas, they are adopted as the starting-point of the theory
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given in this work, and are quoted at the beginning of chapter ii. (pp. 28, 29).
Bentham has repeated his statement as to the mode of measuring happiness in several
different works and pamphlets, as for instance in that remarkable one called "A Table
of the Springs of Action" (London, 1817, p. 3); and also in the "Codification Proposal,
addressed by Jeremy Bentham to all Nations professing Liberal Opinions" (London,
1822, pp. 7-11). He here speaks explicitly of the application of arithmetic to questions
of utility, meaning no doubt the application of mathematical methods. He even
describes (p. 11) the four circumstances governing the value of a pleasure or pain as
the dimensions of its value, though he is incorrect in treating propinquity and certainty
as dimensions.
It is worthy of notice that Destutt de Tracy, one of the most philosophic of all
economists, has in a few words recognised the true method of treatment, though he
has not followed up his own idea. Referring to the circumstances which, in his
opinion, render all economic and moral calculations very delicate, he says,1 "On ne
peut guère employer dans ces matières que des considérations tirées de la théorie des
limites." So well known an English economist as Malthus has also shown in a few
lines his complete appreciation of the mathematical nature of economic questions. In
one of his excellent pamphlets2 he remarks, "Many of the questions, both in morals
and politics, seem to be of the nature of the problems de maximis et minimis in
Fluxions; in which there is always a point where a certain effect is the greatest, while
on either side of this point it gradually diminishes." But I have not thought it desirable
to swell the bibliographical list by including all the works in which there are to be
found brief or casual remarks of the kind.
I may here remark that all the writings of Mr. Henry Dunning Macleod exhibit a
strong tendency to mathematical treatment. Some of his works or papers in which this
mathematical spirit is most strongly manifested have been placed in the list. It is not
my business to criticise his ingenious views, or to determine how far he really has
created a mathematical system. While I certainly differ from him on many important
points, I am bound to acknowledge the assistance which I derive from the use of
several of his works.
In the fourth and most important class of mathematico-economic writers must be
placed those who have consciously and avowedly attempted to frame a mathematical
theory of the subject, and have, if my judgment is correct, succeeded in reaching a
true view of the Science. In this class certain distinguished French philosophers take
precedence and priority. One might perhaps go back with propriety to Condillac's
work, Le Commerce et le Gouvernement, first published in the year 1776, the same
year in which the Wealth of Nations appeared. In the first few chapters of this
charming philosophic work we meet perhaps the earliest distinct statement of the true
connection between value and utility. The book, however, is not included in the list
because there is no explicit attempt at mathematical treatment. It is the French
engineer Dupuit who must probably be credited with the earliest perfect
comprehension of the theory of utility. In attempting to frame a precise measure of the
utility of public works, he observed that the utility of a commodity not only varies
immensely from one individual to another, but that it is also widely different for the
same person according to circumstances. He says, "nous verrions que l'utilité du
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morceau de pain peut croitre pour le meme individu depuis zéro jusqu'au chiffre de sa
fortune entière" (1849, Dupuit, De l'influence des Péages, etc., p. 185). He
establishes, in fact, a theory of the gradation of utility, beautifully and perfectly
expounded by means of geometrical diagrams, and this theory is undoubtedly
coincident in essence with that contained in this book. He does not, however, follow
his ideas out in an algebraic form. Dupuit's theory was the subject of some
controversy in the pages of the Annales des Ponts et Chaussées, but did not receive
much attention elsewhere, and I am not aware that any English economist ever knew
anything about these remarkable memoirs.
The earlier treatise of Cournot, his admirable Recherches sur les Principes
Mathématiques de la Théorie des Richesses (Paris, 1838), resembles Dupuit's
memoirs in being, until within the last few years, quite unknown to English
economists. In other respects Cournot's method is contrasted to Dupuit's. Cournot did
not frame any ultimate theory of the ground and nature of utility and value, but, taking
the palpable facts known concerning the relations of price, production and
consumption of commodities, he investigated these relations analytically and
diagraphically with a power and felicity which leaves little to be desired. This work
must occupy a remarkable position in the history of the subject. It is strange that it
should have remained for me among Englishmen to discover its value. Some years
since (1875) Mr. Todhunter wrote to me as follows: "I have sometimes wondered
whether there is anything of importance in a book published many years since. by M.
A. A. Cournot, entitled Recherches sur les Principes Mathématiques de la Théorie
des Richesses. I never saw it, and when I have mentioned the title, I never found any
person who had read the book. Yet Cournot was eminent for mathematics and
metaphysics, and so there may be some merit in this book." I procured a copy of the
work as far back as 1872, but have only recently studied it with sufficient care to form
any definite opinion upon its value. Even now I have by no means mastered all parts
of it, my mathematical power being insufficient to enable me to follow Cournot in all
parts of his analysis. My impression is that the first chapter of the work is not
remarkable; that the second chapter contains an important anticipation of discussions
concerning the proper method of treating prices, including an anticipation (p. 21) of
my logarithmic method of ascertaining variations in the value of gold; that the third
chapter, treating of the conditions of the foreign exchanges, is highly ingenious if not
particularly useful; but that by far the most important part of the book commences
with the fourth chapter upon the "Loi du débit." The remainder of the book, in fact,
contains a wonderful analysis of the laws of supply and demand, and of the relations
of prices, production, consumption, expenses and profits. Cournot starts from the
assumption that the débit or demand for a commodity is a function of the price, or D =
F (p); and then, after laying down empirically a few conditions of this function, he
proceeds to work out with surprising power the consequences which follow from
those conditions. Even apart from its economic importance, this investigation, so far
as I can venture to judge it, presents a beautiful example of mathematical reasoning,
in which knowledge is apparently evolved out of ignorance. In reality the method
consists in assuming certain simple conditions of the functions as conformable to
experience, and then disclosing by symbolic inference the implicit results of these
conditions. But I am quite convinced that the investigation is of high economic
importance, and that, when the parts of political economy to which the theory relates
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come to be adequately treated, as they never have yet been, the treatment must be
based upon the analysis of Cournot, or at least must follow his general method. It
should be added that his investigation has little relation to the contents of this work,
because Cournot does not recede to any theory of utility, but commences with the
phenomenal laws of supply and demand.
Discouraged apparently by the small amount of attention paid to his mathematical
treatise, Cournot in a later year (1863) produced a more popular non-symbolic work
on Economics; but this later work does not compare favourably in interest and
importance with his first treatise.
English economists can hardly be blamed for their ignorance of Cournot's economic
works when we find French writers equally bad. Thus the authors of Guillaumin's
excellent Dictionnaire de l'EconomiePolitique, which is on the whole the best work of
reference in the literature of the science, ignore Cournot and his works altogether, and
so likewise does Sandelin in his copious Répertoire Général d'Economie Politique.
M. Joseph Garnier in his otherwise admirable text-book1 mixes up Cournot with far
inferior mathematicians, saying: "Dans ces derniers temps M. Esmenard du Mazet, et
M. du Mesnil-Marigny ont aussi fait abus, ce nous semble, des formules algébriques;
les Recherches sur les Principes Mathématiques des Richesses de M. Cournot, ne
nous ont fourni aucun moyen d'élucidation." Mac-Culloch of course knows nothing of
Cournot. Mr. H. D. Macleod has the merit at least of mentioning Cournot's work, but
he misspells the name of the author, and gives only the title of the book, which he had
probably never seen.
We now come to a truly remarkable discovery in the history of this branch of
literature. Some years since my friend Professor Adamson had noticed in one of
Kautz's works on Political Economy2 a brief reference to a book said to contain a
theory of pleasure and pain, written by a German author named Hermann Heinrich
Gossen. Although he had advertised for it, Professor Adamson was unable to obtain a
sight of this book until August 1878, when he fortunately discovered it in a German
bookseller's catalogue, and succeeded in purchasing it. The book was published at
Brunswick in 1854; it consists of 278 well-filled pages, and is entitled, Entwickelung
der Gesetze des menschlichen Verkehrs, und der daraus fliessenden Regeln für
menschliches Handeln, which may be translated—"Development of the laws of
human Commerce, and of the consequent Rules of Human Action." I will describe the
contents of this remarkable volume as they are reported to me by Professor Adamson.
Gossen evidently held the highest possible opinion of the importance of his own
theory, for he commences by claiming honours in economic science equal to those of
Copernicus in astronomy. He then at once insists that mathematical treatment, being
the only sound one, must be applied throughout; but, out of consideration for the
reader, the higher analysis will be explicitly introduced only when it is requisite to
determine maxima and minima. The treatise then opens with the consideration of
Economics as the theory of pleasure and pain, that is as the theory of the procedure by
which the individual and the aggregate of individuals constituting society, may realise
the maximum of pleasure with the minimum of painful effort. The natural law of
pleasure is then clearly stated, somewhat as follows: Increase of the same kind of
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consumption yields pleasure continuously diminishing up to the point of satiety. This
law he illustrates geometrically, and then proceeds to investigate the conditions under
which the total pleasure from one or more objects may be raised to a maximum.
The term Werth is next introduced, which may, Professor Adamson thinks, be
rendered with strict accuracy as utility, and Gossen points out that the quantity of
utility, material or immaterial, is measured by the quantity of pleasure which it
affords. He classifies useful objects as: (1) those which possess pleasure-giving
powers in themselves; (2) those which only possess such powers when in combination
with other objects; (3) those which only serve as means towards the production of
pleasure-giving objects. He is careful to point out that there is no such thing as
absolute utility, utility being purely a relation between a thing and a person. He next
proceeds to give the derivative laws of utility somewhat in the following
manner:—That separate portions of the same pleasure-giving object have very
different degrees of utility, and that in general for each person only a limited number
of such portions has utility; any addition beyond this limit is useless, but the point of
uselessness is only reached after the utility has gone through all the stages or degrees
of intensity. Hence he draws the practical conclusion that each person should so
distribute his resources as to render the final increments of each pleasure-giving
commodity of equal utility for him.
In the next place Gossen deals with labour, starting from the proposition that the
utility of any product must be estimated after deduction of the pains of labour required
to produce it. He describes the variation of the pain of labour much as I have done,
exhibiting it graphically, and inferring that we must carry on labour to the point at
which the utility of the product equals the pain of production. In treating the theory of
exchange he shows how barter gives rise to an immense increase of utility, and he
infers that exchange will proceed up to the point at which the utilities of the portions
next to be given and received are equal. A complicated geometrical representation of
the theory of exchange is given. The theory of rent is investigated in a most general
manner, and the work concludes with somewhat vague social speculations, which, in
Professor Adamson's opinion, are of inferior merit compared with the earlier portions
of the treatise.
From this statement it is quite apparent that Gossen has completely anticipated me as
regards the general principles and method of the theory of Economics. So far as I can
gather, his treatment of the fundamental theory is even more general and thorough
than what I was able to scheme out. In discussing the book, I lie under the serious
difficulty of not being able to read it; but, judging from what Professor Adamson has
written or read to me, and from an examination of the diagrams and symbolic parts of
the work, I should infer that Gossen has been unfortunate in the development of his
theory. Instead of dealing, as Cournot and myself have done, with undetermined
functions, and introducing the least possible amount of assumption, Gossen assumed,
for the sake of simplicity, that economic functions follow a linear law, so that his
curves of utility are generally taken as straight lines. This assumption enables him to
work out a great quantity of precise formulas and tabular results, which fill many
pages of the book. But, inasmuch as the functions of economic science are seldom or
never really linear, and usually diverge very far from the straight line, I think that the
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symbolic and geometric illustrations and developments introduced by Gossen must
for the most part be put down among the many products of misplaced in-genuity. I
may add, in my own behalf, that he does not seem really to reach the equations of
exchange as established in this book; that the theory of capital and interest is wanting;
and that there is a total absence of any resemblance between the working out of the
matter, except such as arises from a common basis of truth.
The coincidence, however, between the essential ideas of Gossen's system and my
own is so striking, that I desire to state distinctly, in the first place, that I never saw
nor so much as heard any hint of the existence of Gossen's book before August 1878,
and to explain, in the second place, how it was that I did not do so. My unfortunate
want of linguistic power has prevented me, in spite of many attempts, from ever
becoming familiar enough with German to read a German book. I once managed to
spell out with assistance part of the logical lecture notes of Kant; but that is my sole
achievement in German literature. Now this work of Gossen has remained unknown
even to most of the great readers of Germany. Professor Adamson remarks that the
work seems to have attracted no attention in Germany. The eminent and learned
economist of Amsterdam, Professor N. G. Pierson, writes to me: "Gossen's book is
totally unknown to me. Roscher does not mention it in his very laborious History of
Political Economy in Germany. I never saw it quoted; but I will try to get it. It is very
curious that such a remarkable work has remained totally unknown even to a man like
Professor Roscher, who has read everything." Mr. Cliffe Leslie, also, who has made
the German Economists his special study, informs me that he was quite unaware of
the existence of the book.1 Under such circumstances it would have been far more
probable that I should discover the theory of pleasure and pain, than that I should
discover Gossen's book, and I have carefully pointed out, both in the first edition and
in this, certain passages of Bentham, Senior, Jennings, and other authors, from which
my system was, more or less consciously, developed. I cannot claim to be totally
indifferent to the rights of priority; and from the year 1862, when my theory was first
published in brief outline, I have often pleased myself with the thought that it was at
once a novel and an important theory. From what I have now stated in this preface it
is evident that novelty can no longer be attributed to the leading features of the theory.
Much is clearly due to Dupuit, and of the rest a great share must be assigned to
Gossen. Regret may easily be swallowed up in satisfaction if I succeed eventually in
making that understood and valued which has been so sadly neglected.
Almost nothing is known to me concerning Gossen; it is uncertain whether he is
living or not. On the title-page he describes himself as Königlich preussischem
Regierungs - Assessor ausser Dienst, which may be translated "Royal Prussian
Government Assessor, retired;" but the tone of his remarks here and there seems to
indicate that he was a disappointed if not an injured man. The reception of his one
work can have lent no relief to these feelings; rather it must much have deepened
them. The book seems to have contained his one cherished theory; for I can find under
the name of Gossen no trace of any other publication or scientific memoir whatever.
The history of these forgotten works is, indeed, a strange and discouraging one; but
the day must come when the eyes of those who cannot see will be opened. Then will
due honour be given to all who like Cournot and Gossen have laboured in a thankless
field of human knowledge, and have met with the neglect or ridicule they might well
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have expected. Not indeed that such men do really work for the sake of honour; they
bring forth a theory as the tree brings forth its fruit.
It remains for me to refer to the mathematico-economic writings of M. Léon Walras,
the Rector of the Academy of Lausanne. It is curious that Lausanne, already
distinguished by the early work of Isnard (1781), should recently have furnished such
important additions to the science as the Memoirs of Walras. For important they are,
not only because they complete and prove that which was before published elsewhere
in the works described above, but because they contain a third or fourth independent
discovery of the principles of the theory. If we are to trace out "the filiation of ideas"
by which M. Walras was led to his theory, we should naturally look back to the work
of his father, Auguste Walras, published at Paris in 1831, and entitled De la Nature de
la Richesse, et de l'origine de la Valeur. In this work we find, it is true, no distinct
recognition of the mathematical method, but the analysis of value is often acute and
philosophic. The principal point of the work moreover is true, that value depends
upon rarity—"La valeur," says Auguste Walras, "dérive de la rareté." Now it is
precisely upon this idea of the degree of rarity of commodities that Léon Walras bases
his system. The fact that some four or more independent writers such as Dupuit,
Gossen, Walras, and myself, should in such different ways have reached substantially
the same views of the fundamental ideas of economic science, cannot but lend great
probability, not to say approximate certainty, to those views. I am glad to hear that M.
Walras intends to bring out a new edition of his Mathematico-Economic Memoirs, to
which the attention of my readers is invited. The titles of his publications will be
found in the Appendix I.
The works of Von Thünen and of several other German economists contain
mathematical investigations of much interest and importance. A considerable number
of such works will be found noted in the list, which, however, is especially defective
as regards German literature. I regret that I am not able to treat this branch of the
subject in an adequate manner.
My bibliographical list shows that in recent years, that is to say since the year 1873,
there has been a great increase in the number of mathematico-economic writings. The
names of Fontaneau, Walras, Avigdor, Lefèvre, Petersen, Boccardo, recur time after
time. In such periodicals as the Journal des Actuaires Français, or the National -
Oekonomisk Tidsskrift—a journal so creditable to the energy and talent of the Danish
Economic School—the mathematical theory of Economics is treated as one of
established interest and truth, with which readers would naturally be acquainted. In
England we have absolutely no periodical in which such discussions could be
conducted. The reader will not fail to remark that it is into the hands of French,
Italian, Danish, or Dutch writers that this most important subject is rapidly passing.
They will develop that science which only excites ridicule and incredulity among the
followers of Mill and Ricardo. There are just a few English mathematicians, such as
Fleeming Jenkin, George Darwin, Alfred Marshall, or H. D. Macleod, and one or two
Americans like Professor Simon Newcomb, who venture to write upon the obnoxious
subject of mathematico-economic science. I ought to add, however, that at Cambridge
(England) the mathematical treatment of Economics is becoming gradually
recognised owing to the former influence of Mr. Alfred Marshall, now the principal of
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University College, Bristol, whose ingenious mathematico - economic problems,
expounded more geometrico, have just been privately printed at Cambridge.
If we overlook Hutcheson, who did not expressly write on Economics, the earliest
mathematico - economic author seems to be the Italian Ceva, whose works have just
been brought to notice in the Giornale degli Economisti (see 1878, Nicolini). Ceva
wrote in the early part of the eighteenth century, but I have as yet no further
information about him. The next author in the list is the celebrated Beccaria, who
printed a very small, but distinctly mathematical, tract on Taxation as early as 1765.
Italians were thus first in the field. The earliest English work of the kind yet
discovered is an anonymous Essay on the Theory of Money, published in London in
1771, five years before the era of the Wealth of Nations. Though crude and absurd in
some parts, it is not devoid of interest and ability, and contains a distinct and partially
valid attempt to establish a mathematical theory of currency. This remarkable Essay
is, so far as I know, wholly forgotten and almost lost in England. Neither MacCulloch
nor any other English economist known to me, mentions the work. I discovered its
existence a few months ago by accidentally finding a copy on a bookseller's stall. But
it shames an Englishman to learn that English works thus unknown in their own
country are known abroad, and I owe to Professor Luigi Cossa, of the University of
Pavia, the information that the Essay was written by Major-General Henry Lloyd, an
author of some merit in other branches of literature. Signor Cossa's excellent Guido
alla Studio di Economia Politica, a concise but judiciously written text-book, is well
qualified to open our eyes as to the insular narrowness of our economic learning. It is
a book of a kind much needed by our students of Economics, and I wish that it could
be published in an English dress.
From this bibliographical survey emerges the wholly unexpected result, that the
mathematical treatment of Economics is coeval with the science itself. The notion that
there is any novelty or originality in the application of mathematical methods or
symbols must be dismissed altogether. While there have been political economists
there has always been a certain number who with various success have struck into the
unpopular but right path. The unfortunate and discouraging aspect of the matter is the
complete oblivion into which this part of the literature of Economics has always
fallen, oblivion so complete that each mathematico-economic writer has been obliged
to begin almost de novo. It is with the purpose of preventing for the future as far as I
can such ignorance of previous exertions, that I have spent so much pains upon this
list of books.
I should add that in arranging the list I have followed, very imperfectly, the excellent
example set by Professor Mansfield Merriman, of the Sheffield Scientific School of
Yale College, in his "List of Writings relating to the Method of Least Squares."1 Such
bibliographies are of immense utility, and I hope that the time is nearly come when
each student of a special branch of science or literature will feel bound to work out its
bibliography, unless, of course, the task shall have been already accomplished. The
reader will see that, in Appendix II., I have taken the liberty of working out also a part
of the bibliography of my own writings.
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Looking now to the eventual results of the theory, I must beg the reader to bear in
mind that this book was never put forward as containing a systematic view of
Economics. It treats only of the theory, and is but an elementary sketch of elementary
principles. The working out of a complete system based on these lines must be a
matter of time and labour, and I know not when, if ever, I shall be able to attempt it.
In the last chapter, I have, however, indicated the manner in which the theory of
wages will be affected. This chapter is reprinted almost as it was written in 1871;
since then the wage-fund theory has been abandoned by most English Economists,
owing to the attacks of Mr. Cliffe Leslie, Mr. Shadwell, Professor Cairnes, Professor
Francis Walker, and some others. Quite recently more extensive reading and more
careful cogitation have led to a certain change in my ideas concerning the
superstructure of Economics—in this wise:
Firstly, I am convinced that the doctrine of wages, which I adopted in 1871, under the
impression that it was somewhat novel, is not really novel at all, except to those
whose view is bounded by the maze of the Ricardian Economics. The true doctrine
may be more or less clearly traced through the writings of a succession of great
French Economists, from Condillac, Baudeau, and Le Trosne, through J.-B. Say,
Destutt de Tracy, Storch, and others, down to Bastiat and Courcelle-Seneuil. The
conclusion to which I am ever more clearly coming is that the only hope of attaining a
true system of Economics is to fling aside, once and for ever, the mazy and
preposterous assumptions of the Ricardian School. Our English Economists have been
living in a fool's paradise. The truth is with the French School, and the sooner we
recognise the fact, the better it will be for all the world, except perhaps the few writers
who are too far committed to the old erroneous doctrines to allow of renunciation.
Although, as I have said, the true theory of wages is not new as regards the French
School, it is new, or at any rate renewed, as regards our English Schools of
Economics. One of the first to treat the subject from the right point of view was Mr.
Cliffe Leslie, in an article first published in Fraser's Magazine for July 1868, and
subsequently reprinted in a collection of Essays.1 Some years afterwards Mr. J. L.
Shadwell independently worked out the same theory of wages which he has fully
expounded in his admirable System of Political Economy.2 In Hearn's Plutology,
however, as pointed out in the text of this book (pp. 271 - 273), we find the same
general idea that wages are the share of the produce which the laws of supply and
demand enable the labourer to secure. It is probable that like ideas might be traced in
other works were this the place to attempt a history of the subject.
Secondly, I feel sure that when, casting ourselves free from the Wage-Fund Theory,
The Cost of Production doctrine of Value, the Natural Rate of Wages, and other
misleading or false Ricardian doctrines, we begin to trace out clearly and simply the
results of a correct theory, it will not be difficult to arrive at a true doctrine of wages.
This will probably be reached somewhat in the following way:—We must regard
labour, land, knowledge, and capital as conjoint conditions of the whole produce, not
as causes each of a certain portion of the produce. Thus in an elementary state of
society, when each labourer owns all the three or four requisites of production, there
would really be no such thing as wages, rent, or interest at all. Distribution does not
arise even in idea, and the produce is simply the aggregate effect of the aggregate
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conditions. It is only when separate owners of the elements of production join their
properties, and traffic with each other, that distribution begins, and then it is entirely
subject to the principles of value and the laws of supply and demand. Each labourer
must be regarded, like each landowner and each capitalist, as bringing into the
common stock one part of the component elements, bargaining for the best share of
the produce which the conditions of the market allow him to claim successfully. In
theory the labourer has a monopoly of labour of each particular kind, as much as the
landowner of land, and the capitalist of other requisite articles. Property is only
another name for monopoly. But when different persons own property of exactly the
same kind, they become subject to the important Law of Indifference, as I have called
it (pp. 90-93), namely, that in the same open market, at any one moment, there cannot
be two prices for the same kind of article. Thus monopoly is limited by competition,
and no owner, whether of labour, land, or capital, can, theoretically speaking, obtain a
larger share of produce for it than what other owners of exactly the same kind of
property are willing to accept.
So far there may seem to be nothing novel in this view; it is hardly more than will be
found stated in a good many economic works. But as soon as we begin to follow out
this simple view, the consequences are rather startling. We are forced, for instance, to
admit that rates of wages are governed by the same formal laws as rents. This view is
not new to the readers of Storch, who in the third book of his excellent Cours
d'Economie Politique has a chapter1 "De la Rente des talens et des qualités morales."
But it is a very new doctrine to one whose economic horizon is formed by Mill and
Faweett, Ricardo and Adam Smith. Even Storch has not followed out the doctrine
thoroughly; for he applies the idea of rent only to cases of eminent talent. It must be
evident, however, that talent and capacity of all kinds are only a question of degree, so
that, according to the Law of Continuity, the same principle must apply to all
labourers.
A still more startling result is that, so far as cost of production regulates the values of
commodities, wages must enter into the calculation on exactly the same footing as
rent. Now it is a prime point of the Ricardian doctrines that rent does not enter into
cost of production. As J. S. Mill says,2 "Rent, therefore, forms no part of the cost of
production which determines the value of agricultural produce." And again,1 "Rent is
not an element in the cost of production of the commodity which yields it; except in
the cases," etc. Rent in fact is represented as the effect not the cause of high value;
wages on the contrary are treated as the cause, not the effect. But if rent and wages be
really phenomena subject to the same formal laws, this opposite relation to value must
involve error. The way out of the difficulty is furnished by the second sentence of the
paragraph from which the last quotation was taken. Mill goes on to say: "But when
land capable of yielding rent in agriculture is applied to some other purpose, the rent
which it would have yielded is an element in the cost of production of the commodity
which it is employed to produce." Here Mill edges in as an exceptional case that
which proves to be the rule, reminding one of other exceptional cases described as
"Some peculiar cases of value" (see p. 197 below), which I have shown to include
almost all commodities.
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Now Mill allows that when land capable of yielding rent in agriculture is applied to
some other purpose, the rent which would have been produced in agriculture is an
element in the cost of production of other commodities. But wherefore this distinction
between agriculture and other branches of industry? Why does not the same principle
apply between two different modes of agricultural employment? If land which has
been yielding £2 per acre rent as pasture be ploughed up and used for raising wheat,
must not the £2 per acre be debited against the expenses of the production of wheat?
Suppose that somebody introduced the beetroot culture into England with a view to
making sugar; this new branch of industry could not be said to pay unless it yielded,
besides all other expenses, the full rents of the lands turned from other kinds of
culture. But if this be conceded, the same principle must apply generally; a potato-
field should pay as well as a clover-field, and a clover-field as a turnip-field; and so
on. The market prices of the produce must adjust themselves so that this shall in the
long run be possible. The rotation of crops, no doubt, introduces complication into the
matter, but does not modify the general reasoning. The principle which emerges is
that each portion of land should be applied to that culture or use which yields the
largest total of utility, as measured by the value of the produce; if otherwise applied
there will be loss. Thus the rent of land is determined by the excess of produce in the
most profitable employment.
But when the matter is fully thought out, it will be seen that exactly the same principle
applies to wages. A man who can earn six shillings a day in one employment will not
turn to another kind of work unless he expects to get six shillings a day or more from
it. There is no such thing as absolute cost of labour; it is all matter of comparison.
Every one gets the most which he can for his exertions; some can get little or nothing,
because they have not sufficient strength, knowledge, or ingenuity; others get much,
because they have, comparatively speaking, a monopoly of certain powers. Each
seeks the work in which his peculiar faculties are most productive of utility, as
measured by what other people are willing to pay for the produce. Thus wages are
clearly the effect not the cause of the value of the produce. But when labour is turned
from one employment to another, the wages it would otherwise have yielded must be
debited to the expenses of the new product. Thus the parallelism between the theories
of rent and wages is seen to be perfect in theory, however different it may appear to
be in the details of application. Precisely the same view may be applied, mutatis
mutandis, to the rent yielded by fixed capital, and to the interest of free capital. In the
last case, the Law of Indifference peculiarly applies, because free capital, loanable for
a certain interval, is equally available for all branches of industry; hence, at any
moment and place, the interest of such capital must be the same in all branches of
trade.
I ought to say that Mill, as pointed out to me by Professor Adamson, has a remarkable
section at the end of chapter v. of Book III. of the Principles, in which he explains
that all inequalities, artificial or natural, give rise to extra gains of the nature of Rent.
This section is a very satisfactory one inasmuch as it tends to support the view on
which I am now insisting, a view, however, which, when properly followed out, will
overthrow many of the principal doctrines of the Ricardo-Mill Economics. Those who
have studied Mill's philosophic character as long and minutely as I have done, will not
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for a moment suppose that the occurrence of this section in Mill's book tends to
establish its consistency with other portions of the same treatise.
But of course I cannot follow out the discussion of this matter in a mere preface. The
results to be expected are partly indicated in my Primer of Political Economy, but in
that little treatise my remarks upon the Origin of Rent (p. 94), as originally printed in
the first edition, were erroneous, and the section altogether needs to be rewritten.
When at length a true system of Economics comes to be established, it will be seen
that that able but wrong-headed man, David Ricardo, shunted the car of Economic
science on to a wrong line, a line, however, on which it was further urged towards
confusion by his equally able and wrong-headed admirer, John Stuart Mill. There
were Economists, such as Malthus and Senior, who had a far better comprehension of
the true doctrines (though not free from the Ricardian errors), but they were driven
out of the field by the unity and influence of the Ricardo-Mill school. It will be a work
of labour to pick up the fragments of a shattered science and to start anew, but it is a
work from which they must not shrink who wish to see any advance of Economic
Science.
THE CHESTNUTS,
HAMPSTEAD HEATH, N.W.
May 1879.
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PREFACE TO THE THIRD EDITION
By Harriet Jevons
THE present edition of the Theory of Political Economy is an exact reprint of the
second edition, with the exception of the first Appendix containing the bibliographical
list of mathematico-economic books. I desired to add to that list several books which
it had been my husband's intention to include in the next edition, and when I
consulted my friend, Mr. H. S. Foxwell, he advised me to continue it up to the present
date. I am greatly indebted to the kindness of those friends who have enabled me to
accomplish this; and amongst others my thanks are especially due to the Rev. P. H.
Wicksteed, Professor F. Y. Edgeworth, and Professor Harald Westergaard of
Copenhagen, for the trouble they have taken in revising proofs for me, as well as in
supplying me with the titles of those books which ought to be included. We have
endeavoured to follow the rules which Mr. Jevons has laid down in the preface to the
second edition, and though the list is probably not complete, I hope that no work of
importance has been omitted.
A few books published during my husband's lifetime, but which were, I believe,
unknown to him, are now included, but I have enclosed them within brackets. I have
also marked the place at which the additional list prepared by himself ends.
HARRIET A. JEVONS.
August 1888.
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ERRATA
[Note from Econlib Editor: The error on page 108, covering the last pair of equations
in paragraph IV.50, appears to have been corrected in the third edition. The error on
page 201, covering the last few sentences of paragraph V.27 remains in this edition,
but we have noted it in a footnote for the paragraph.]
P. 108, for f
1
(a - y), read f
1
(a - x).
P. 201, for "in this respect be taken negatively," read "in this respect be taken
positively."
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CHAPTER I
INTRODUCTION
THE science of Political Economy rests upon a few notions of an apparently simple
character. Utility, wealth, value, commodity, labour, land, capital, are the elements of
the subject; and whoever has a thorough comprehension of their nature must possess
or be soon able to acquire a knowledge of the whole science. As almost every
economical writer has remarked, it is in treating the simple elements that we require
the most care and precision, since the least error of conception must vitiate all our
deductions. Accordingly, I have devoted the following pages to an investigation of the
conditions and relations of the above-named notions.
Repeated reflection and inquiry have led me to the somewhat novel opinion, that
value depends entirely upon utility. Prevailing opinions make labour rather than utility
the origin of value; and there are even those who distinctly assert that labour is the
cause of value. I show, on the contrary, that we have only to trace out carefully the
natural laws of the variation of utility, as depending upon the quantity of commodity
in our possession, in order to arrive at a satisfactory theory of exchange, of which the
ordinary laws of supply and demand are a necessary consequence. This theory is in
harmony with facts; and, whenever there is any apparent reason for the belief that
labour is the cause of value, we obtain an explanation of the reason. Labour is found
often to determine value, but only in an indirect manner, by varying the degree of
utility of the commodity through an increase or limitation of the supply.
These views are not put forward in a hasty or ill-considered manner. All the chief
points of the theory were sketched out seventeen years ago; but they were then
published only in the form of a brief paper communicated to the Statistical or
Economic Section of the British Association at the Cambridge Meeting, which took
place in the year 1862. A still briefer abstract of that paper was inserted in the Report
of the Meeting,2 and the paper itself was not printed until June 1866.23 Since writing
that paper, I have, over and over again, questioned the truth of my own notions, but
without ever finding any reason to doubt their substantial correctness.
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Mathematical Character Of The Science.
It is clear that Economics, if it is to be a science at all, must be a mathematical
science. There exists much prejudice against attempts to introduce the methods and
language of mathematics into any branch of the moral sciences. Many persons seem
to think that the physical sciences form the proper sphere of mathematical method,
and that the moral sciences demand some other method,—I know not what. My
theory of Economics, however, is purely mathematical in character. Nay, believing
that the quantities with which we deal must be subject to continuous variation, I do
not hesitate to use the appropriate branch of mathematical science, involving though it
does the fearless consideration of infinitely small quantities. The theory consists in
applying the differential calculus to the familiar notions of wealth, utility, value,
demand, supply, capital, interest, labour, and all the other quantitative notions
belonging to the daily operations of industry. As the complete theory of almost every
other science involves the use of that calculus, so we cannot have a true theory of
Economics without its aid.
To me it seems that our science must be mathematical, simply because it deals with
quantities. Wherever the things treated are capable of being greater or less, there the
laws and relations must be mathematical in nature. The ordinary laws of supply and
demand treat entirely of quantities of commodity demanded or supplied, and express
the manner in which the quantities vary in connection with the price. In consequence
of this fact the laws are mathematical. Economists cannot alter their nature by denying
them the name; they might as well try to alter red light by calling it blue. Whether the
mathematical laws of Economics are stated in words, or in the usual symbols,
x,y,z,p,q, etc., is an accident, or a matter of mere convenience. If we had no regard to
trouble and prolixity, the most complicated mathematical problems might be stated in
ordinary language, and their solution might be traced out by words. In fact, some
distinguished mathematicians have shown a liking for getting rid of their symbols,
and expressing their arguments and results in language as nearly as possible
approximating to that in common use. In his Système du Monde, Laplace attempted to
describe the truths of physical astronomy in common language; and Thomson and
Tait interweave their great Treatise on Natural Philosophy with an interpretation in
ordinary words, supposed to be within the comprehension of general readers.4
These attempts, however distinguished and ingenious their authors, soon disclose the
inherent defects of the grammar and dictionary for expressing complicated relations.
The symbols of mathematical books are not different in nature from language; they
form a perfected system of language, adapted to the notions and relations which we
need to express. They do not constitute the mode of reasoning they embody; they
merely facilitate its exhibition and comprehension. If, then, in Economics, we have to
deal with quantities and complicated relations of quantities, we must reason
mathematically; we do not render the science less mathematical by avoiding the
symbols of algebra,—we merely refuse to employ, in a very imperfect science, much
needing every kind of assistance, that apparatus of appropriate signs which is found
indispensable in other sciences.
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Confusion Between Mathematical And Exact Sciences.
Many persons entertain a prejudice against mathematical language, arising out of a
confusion between the ideas of a mathematical science and an exact science. They
think that we must not pretend to calculate unless we have the precise data which will
enable us to obtain a precise answer to our calculations; but, in reality, there is no
such thing as an exact science, except in a comparative sense. Astronomy is more
exact than other sciences, because the position of a planet or star admits of close
measurement; but, if we examine the methods of physical astronomy, we find that
they are all approximate. Every solution involves hypotheses which are not really
true: as, for instance, that the earth is a smooth, homogeneous spheroid. Even the
apparently simpler problems in statics or dynamics are only hypothetical
approximations to the truth.1
We can calculate the effect of a crowbar, provided it be perfectly inflexible and have a
perfectly hard fulcrum,—which is never the case.2 The data are almost wholly
deficient for the complete solution of any one problem in natural science. Had
physicists waited until their data were perfectly precise before they brought in the aid
of mathematics, we should have still been in the age of science which terminated at
the time of Galileo.
When we examine the less precise physical sciences, we find that physicists are, of all
men, most bold in developing their mathematical theories in advance of their data. Let
any one who doubts this examine Airy's "Theory of the Tides," as given in the
Encyclopædia Metropolitana; he will there find a wonderfully complex mathematical
theory which is confessed by its author to be incapable of exact or even approximate
application, because the results of the various and often unknown contours of the seas
do not admit of numerical verification. In this and many other cases we have
mathematical theory without the data requisite for precise calculation.
The greater or less accuracy attainable in a mathematical science is a matter of
accident, and does not affect the fundamental character of the science. There can be
but two classes of sciences—those which are simply logical, and those which, besides
being logical, are also mathematical. If there be any science which determines merely
whether a thing be or be not—whether an event will happen, or will not happen—it
must be a purely logical science; but if the thing may be greater or less, or the event
may happen sooner or later, nearer or farther, then quantitative notions enter, and the
science must be mathematical in nature, by whatever name we call it.
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Capability Of Exact Measurement.
Many will object, no doubt, that the notions which we treat in this science are
incapable of any measurement. We cannot weigh, nor gauge, nor test the feelings of
the mind; there is no unit of labour, or suffering, or enjoyment. It might thus seem as
if a mathematical theory of Economics would be necessarily deprived for ever of
numerical data.
I answer, in the first place, that nothing is less warranted in science than an
uninquiring and unhoping spirit. In matters of this kind, those who despair are almost
invariably those who have never tried to succeed. A man might be despondent had he
spent a lifetime on a difficult task without a gleam of encouragement; but the popular
opinions on the extension of mathematical theory tend to deter any man from
attempting tasks which, however difficult, ought, some day, to be achieved.
If we trace the history of other sciences, we gather no lessons of discouragement. In
the case of almost everything which is now exactly measured, we can go back to the
age when the vaguest notions prevailed. Previous to the time of Pascal, who would
have thought of measuring doubt and belief? Who could have conceived that the
investigation of petty games of chance would have led to the creation of perhaps the
most sublime branch of mathematical science—the theory of probabilities? There are
sciences which, even within the memory of men now living, have become exactly
quantitative. While Quesnay and Baudeau and Le Trosne and Condillac were
founding Political Economy in France, and Adam Smith in England, electricity was a
vague phenomenon, which was known, indeed, to be capable of becoming greater or
less, but was not measured nor calculated: it is within the last forty or fifty years that a
mathematical theory of electricity, founded on exact data, has been established. We
now enjoy precise quantitative notions concerning heat, and can measure the
temperature of a body to less than part of a degree Centigrade. Compare this
precision with that of the earliest makers of thermometers, the Academicians del
Cimento, who used to graduate their instruments by placing them in the sun's rays to
obtain a point of fixed temperature.1
De Morgan excellently said,1 "As to some magnitudes, the clear idea of measurement
comes soon: in the case of length, for example. But let us take a more difficult one,
and trace the steps by which we acquire and fix the idea: say weight. What weight is,
we need not know.... We know it as a magnitude before we give it a name: any child
can discover the more that there is in a bullet, and the less that there is in a cork of
twice its size. Had it not been for the simple contrivance of the balance, which we are
well assured (how, it matters not here) enables us to poise equal weights against one
another, that is, to detect equality and inequality, and thence to ascertain how many
times the greater contains the less, we might not to this day have had much clearer
ideas on the subject of weight, as a magnitude, than we have on those of talent,
prudence, or self-denial, looked at in the same light. All who are ever so little of
geometers will remember the time when their notions of an angle, as a magnitude,
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were as vague as, perhaps more so than, those of a moral quality; and they will also
remember the steps by which this vagueness became clearness and precision."
Now there can be no doubt that pleasure, pain, labour, utility, value, wealth, money,
capital, etc., are all notions admitting of quantity; nay, the whole of our actions in
industry and trade certainly depend upon comparing quantities of advantage or
disadvantage. Even the theories of moralists have recognised the quantitative
character of the subject. Bentham's Introduction to the Principles of Morals and
Legislation is thoroughly mathematical in the character of the method. He tells us1 to
estimate the tendency of an action thus: "Sum up all the values of all the pleasures on
the one side, and those of all the pains on the other. The balance, if it be on the side of
pleasure, will give the good tendency of the act upon the whole, with respect to the
interests of that individual person; if on the side of pain, the bad tendency of it upon
the whole." The mathematical character of Bentham's treatment of moral science is
also well exemplified in his remarkable tract entitled, "A Table of the Springs of
Action," printed in 1817, as in p. 3, and elsewhere.
"But where," the reader will perhaps ask, "are your numerical data for estimating
pleasures and pains in Political Economy?" I answer, that my numerical data are more
abundant and precise than those possessed by any other science, but that we have not
yet known how to employ them. The very abundance of our data is perplexing. There
is not a clerk nor book-keeper in the country who is not engaged in recording
numerical facts for the economist. The private-account books, the great ledgers of
merchants and bankers and public offices, the share lists, price lists, bank returns,
monetary intelligence, Custom-house and other Government returns, are all full of the
kind of numerical data required to render 5Economics an exact mathematical science.
Thousands of folio volumes of statistical, parliamentary, or other publications await
the labour of the investigator. It is partly the very extent and complexity of the
information which deters us from its proper use. But it is chiefly a want of method
and completeness in this vast mass of information which prevents our employing it in
the scientific investigation of the natural laws of Economics.
I hesitate to say that men will ever have the means of measuring directly the feelings
of the human heart. A unit of pleasure or of pain is difficult even to conceive; but it is
the amount of these feelings which is continually prompting us to buying and selling,
borrowing and lending, labouring and resting, producing and consuming; and it is
from the quantitative effects of the feelings that we must estimate their comparative
amounts. We can no more know nor measure gravity in its own nature than we can
measure a feeling; but, just as we measure gravity by its effects in the motion of a
pendulum, so we may estimate the equality or inequality of feelings by the decisions
of the human mind. The will is our pendulum, and its oscillations are minutely
registered in the price lists of the markets. I know not when we shall have a perfect
system of statistics, but the want of it is the only insuperable obstacle in the way of
making Economics an exact science. In the absence of complete statistics, the science
will not be less mathematical, though it will be immensely less useful than if it were,
comparatively speaking, exact. A correct theory is the first step towards improvement,
by showing what we need and what we might accomplish.
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Measurement Of Feeling And Motives.
Many readers may, even after reading the preceding remarks, consider it quite
impossible to create such a calculus as is here contemplated, because we have no
means of defining and measuring quantities of feeling, like we can measure a mile, or
a right angle, or any other physical quantity. I have granted that we can hardly form
the conception of a unit of pleasure or pain, so that the numerical expression of
quantities of feeling seems to be out of the question. But we only employ units of
measurement in other things to facilitate the comparison of quantities; and if we can
compare the quantities directly, we do not need the units. Now the mind of an
individual is the balance which makes its own comparisons, and is the final judge of
quantities of feeling. As Mr. Bain says,1 "It is only an identical proposition to affirm
that the greatest of two pleasures, or what appears such, sways the resulting action; for
it is this resulting action that alone determines which is the greater."
Pleasures, in short, are, for the time being, as the mind estimates them; so that we
cannot make a choice, or manifest the will in any way, without indicating thereby an
excess of pleasure in some direction. It is true that the mind often hesitates and is
perplexed in making a choice of great importance: this indicates either varying
estimates of the motives, or a feeling of incapacity to grasp the quantities concerned. I
should not think of claiming for the mind any accurate power of measuring and
adding and subtracting feelings, so as to get an exact balance. We can seldom or never
affirm that one pleasure is an exact multiple of another; but the reader who carefully
criticises the following theory will find that it seldom involves the comparison of
quantities of feeling differing much in amount. The theory turns upon those critical
points where pleasures are nearly, if not quite, equal. I never attempt to estimate the
whole pleasure gained by purchasing a commodity; the theory merely expresses that,
when a man has purchased enough, he would derive equal pleasure from the
possession of a small quantity more as he would from the money price of it. Similarly,
the whole amount of pleasure that a man gains by a day's labour hardly enters into the
question; it is when a man is doubtful whether to increase his hours of labour or not,
that we discover an equality between the pain of that extension and the pleasure of the
increase of possessions derived from it.
The reader will find, again, that there is never, in any single instance, an attempt made
to compare the amount of feeling in one mind with that in another. I see no means by
which such comparison can be accomplished. The susceptibility of one mind may, for
what we know, be a thousand times greater than that of another. But, provided that the
susceptibility was different in a like ratio in all directions, we should never be able to
discover the difference. Every mind is thus inscrutable to every other mind, and no
common denominator of feeling seems to be possible. But even if we could compare
the feelings of different minds, we should not need to do so; for one mind only affects
another indirectly. Every event in the outward world is represented in the mind by a
corresponding motive, and it is by the balance of these that the will is swayed. But the
motive in one mind is weighed only against other motives in the same mind, never
against the motives in other minds. Each person is to other persons a portion of the
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outward world—the non-ego as the meta-physicians call it. Thus motives in the mind
of A may give rise to phenomena which may be represented by motives in the mind of
B; but between A and B there is a gulf. Hence the weighing of motives must always
be confined to the bosom of the individual.
I must here point out that, though the theory presumes to investigate the condition of a
mind, and bases upon this investigation the whole of Economics, practically it is an
aggregate of individuals which will be treated. The general forms of the laws of
Economics are the same in the case of individuals and nations; and, in reality, it is a
law operating in the case of multitudes of individuals which gives rise to the
aggregate represented in the transactions of a nation. Practically, however, it is quite
impossible to detect the operation of general laws of this kind in the actions of one or
a few individuals. The motives and conditions are so numerous and complicated, that
the resulting actions have the appearance of caprice, and are beyond the analytic
powers of science. With every increase in the price of such a commodity as sugar, we
ought, theoretically speaking, to find every person reducing his consumption by a
small amount, and according to some regular law. In reality, many persons would
make no change at all; a few, probably, would go to the extent of dispensing with the
use of sugar altogether so long as its cost continued to be excessive. It would be by
examining the average consumption of sugar in a large population that we might
detect a continuous variation, connected with the variation of price by a constant law.
It would not, of necessity, happen that the law would be exactly the same in the case
of aggregates and individuals, unless all those individuals were of the same character
and position as regards wealth and habits; but there would be a more or less regular
law to which the same kind of formulæ would apply. The use of an average, or, what
is the same, an aggregate result, depends upon the high probability that accidental and
disturbing causes will operate, in the long run, as often in one direction as the other,
so as to neutralise each other. Provided that we have a sufficient number of
independent cases, we may then detect the effect of any tendency, however slight.
Accordingly, questions which appear, and perhaps are, quite indeterminate as regards
individuals, may be capable of exact investigation and solution in regard to great
masses and wide averages.1
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Logical Method Of Economics.
The logical method of Economics as a branch of the social sciences is a subject on
which much might be written, and on which very diverse opinions are held at the
present day (1879). In this place I can only make a few brief remarks. I think that
John Stuart Mill is substantially correct in considering our science to be a case of
what he calls2 the Physical or Concrete Deductive Method; he considers that we may
start from some obvious psychological law, as for instance, that a greater gain is
preferred to a smaller one, and we may then reason downwards, and predict the
phenomena which will be produced in society by such a law. The causes in action in
any community are, indeed, so complicated that we shall seldom be able to discover
the undisturbed effects of any one law, but, so far as we can analyse the statistical
phenomena observed, we obtain a verification of our reasoning. This view of the
matter is almost identical with that adopted by the late Professor Cairnes in his
lectures on " The Character and Logical Method of Political Economy."1
The principal objection to be urged against this treatment of the subject, is that Mill
has described the Concrete Deductive Method as if it were one of many inductive
methods. In my Elementary Lessons in Logic (p. 258), I proposed to call the method
the Complete Method, as implying that it combines observation, deduction, and
induction in the most complete and perfect way. But I subsequently arrived at the
conclusion that this so-called Deductive Method is no special method at all, but
simply induction itself in its essential form. As I have fully explained,2 Induction is
an inverse operation, the inverse of Deduction, and can only be performed by the use
of deduction. Possessing certain facts of observation, we frame an hypothesis as to the
laws governing those facts; we reason from the hypothesis deductively to the results
to be expected; and we then examine these results in connection with the facts in
question; coincidence confirms the whole reasoning; conflict obliges us either to seek
for disturbing causes, or else to abandon our hypothesis. In this procedure there is
nothing peculiar; when properly understood it is found to be the method of all the
inductive sciences.
The science of Economics, however, is in some degree peculiar, owing to the fact,
pointed out by J. S. Mill and Cairnes, that its ultimate laws are known to us
immediately by intuition, or, at any rate, they are furnished to us ready made by other
mental or physical sciences. That every person will choose the greater apparent good;
that human wants are more or less quickly satiated; that prolonged labour becomes
more and more painful, are a few of the simple inductions on which we can proceed
to reason deductively with great confidence. From these axioms we can deduce the
laws of supply and demand, the laws of that difficult conception, value, and all the
intricate results of commerce, so far as data are available. The final agreement of our
inferences with à posteriori observations ratifies our method. But unfortunately this
verification is often the least satisfactory part of the process, because, as J. S. Mill has
fully explained, the circumstances of a nation are infinitely complicated, and we
seldom get two or more instances which are comparable. To fulfil the conditions of
inductive inquiry, we ought to be able to observe the effects of a cause coming singly
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into action, while all other causes remain unaltered. Entirely to prove the good effects
of Free Trade in England, for example, we ought to have the nation unaltered in every
circumstance except the abolition of burdens and restrictions on trade.1 But it is
obvious that while Free Trade was being introduced into England, many other causes
of prosperity were also coming into action—the progress of invention, the
construction of railways, the profuse consumption of coal, the extension of the
colonies, etc. etc. Although, then, the beneficent results of Free Trade are great and
unquestionable, they could hardly be proved to exist à posteriori; they are to be
believed because deductive reasoning from premises of almost certain truth leads us
confidently to expect such results, and there is nothing in experience which in the
least conflicts with our expectations. In spite of occasional revulsions, due to
periodical fluctuations depending on physical causes, the immense prosperity of the
country since the adoption of Free Trade confirms our anticipations as far as, under
complex circumstances, facts are capable of doing so. It will thus be seen that
Political Economy tends to be more deductive than many of the physical sciences, in
which closely approximate verification is often possible; but, even so far as the
science is inductive, it involves the use of deductive reasoning, as already explained.
Within the last year or two, much discussion has been raised concerning the
Philosophical Method of Political Economy, by Mr. T. E. Cliffe Leslie's interesting
Essay on that subject,1 as also by the recent address of Dr. Ingram at the Dublin
Meeting of the British Association.1 I quite concur with these able and eminent
economists so far as to allow that historical investigation is of great importance in
Social Science. But, instead of converting our present science of economics into an
historical science, utterly destroying it in the process, I would perfect and develop
what we already possess, and at the same time erect a new branch of social science on
an historical foundation. This new branch of science, on which many learned men,
such as Richard Jones, De Laveleye, Lavergne, Cliffe Leslie, Sir Henry Maine,
Thorold Rogers, have already laboured, is doubtless a portion of what Herbert
Spencer calls Sociology, the Science of the Evolution of Social Relations. Political
Economy is in a chaotic state at present, because there is need of subdividing a too
extensive sphere of knowledge. Quesnay, Sir James Steuart, Baudeau, Le Trosne, and
Condillac first differentiated Economics sufficiently to lead it to be regarded as a
distinct science; it has since been loaded with great accretions due to the progress of
investigation. It is only by subdivision, by recognising a branch of Economic
Sociology, together possibly with two or three other branches of statistical, jural, or
social science, that we can rescue our science from its confused state. I have already
endeavoured to show the need of this step in a lecture delivered at the University
College, in October 1876,2 and I shall perhaps have a future opportunity of enlarging
more upon the subject.
To return, however, to the topic of the present work, the theory here given may be
described as the mechanics of utility and self-interest. Oversights may have been
committed in tracing out its details, but in its main features this theory must be the
true one. Its method is as sure and demonstrative as that of kinematics or statics, nay,
almost as self-evident as are the elements of Euclid, when the real meaning of the
formulæ is fully seized.
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I do not hesitate to say, too, that Economics might be gradually erected into an exact
science, if only commercial statistics were far more complete and accurate than they
are at present, so that the formulae could be endowed with exact meaning by the aid
of numerical data. These data would consist chiefly in accurate accounts of the
quantities of goods possessed and consumed by the community, and the prices at
which they are exchanged. There is no reason whatever why we should not have those
statistics, except the cost and trouble of collecting them, and the unwillingness of
persons to afford information. The quantities themselves to be measured and
registered are most concrete and precise. In a few cases we already have information
approximating to completeness, as when a commodity like tea, sugar, coffee, or
tobacco is wholly imported. But when articles are untaxed, and partly produced within
the country, we have yet the vaguest notions of the quantities consumed. Some slight
success is now, at last, attending the efforts to gather agricultural statistics; and the
great need felt by men engaged in the cotton and other trades to obtain accurate
accounts of stocks, imports, and consumption, will probably lead to the publication of
far more complete information than we have hitherto enjoyed.
The deductive science of Economics must be verified and rendered useful by the
purely empirical science of Statistics. Theory must be invested with the reality and
life of fact. But the difficulties of this union are immensely great, and I appreciate
them quite as much as does Cairnes in his admirable lectures "On the Character and
Logical Method of Political Economy." I make hardly any attempt to employ statistics
in this work, and thus I do not pretend to any numerical precision. But, before we
attempt any investigation of facts, we must have correct theoretical notions; and of
what are here presented, I would say, in the words of Hume, in his Essay on
Commerce, "If false, let them be rejected: but no one has a right to entertain a
prejudice against them merely because they are out of the common road."
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Relation Of Economics To Ethics.
I wish to say a few words, in this place, upon the relation of Economics to Moral
Science. The theory which follows is entirely based on a calculus of pleasure and
pain; and the object of Economics is to maximise happiness by purchasing pleasure,
as it were, at the lowest cost of pain. The language employed may be open to
misapprehension, and it may seem as if pleasures and pains of a gross kind were
treated as the all-sufficient motives to guide the mind of man. I have no hesitation in
accepting the Utilitarian theory of morals which does uphold the effect upon the
happiness of mankind as the criterion of what is right and wrong. 'But I have never
felt that there is anything in that theory to prevent our putting the widest and highest
interpretation upon the terms used.
Jeremy Bentham put forward the Utilitarian theory in the most uncompromising
manner. According to him, whatever is of interest or importance to us must be the
cause of pleasure or of pain; and when the terms are used with a sufficiently wide
meaning, pleasure and pain include all the forces which drive us to action. They are
explicitly or implicitly the matter of all our calculations, and form the ultimate
quantities to be treated in all the moral sciences. The words of Bentham on this
subject may require some explanation and qualification, but they are too grand and
too full of truth to be omitted. "Nature," he says,1 "has placed mankind under the
governance of two sovereign masters—pain and pleasure. It is for them alone to point
out what we ought to do, as well as to determine what we shall do. On the one hand
the standard of right and wrong, on the other the chain of causes and effects, are
fastened to their throne. They govern us in all we do, in all we say, in all we think:
every effort we can make to throw off our subjection will serve but to demonstrate
and confirm it. In words a man may pretend to abjure their empire; but, in reality, he
will remain subject to it all the while. The principle of utility recognises this
subjection, and assumes it for the foundation of that system, the object of which is to
rear the fabric of felicity by the hands of reason and of law. Systems which attempt to
question it deal in sounds instead of sense, in caprice instead of reason, in darkness
instead of light."
In connection with this passage we may take that of Paley, who says, with his usual
clear brevity,2 "I hold that pleasures differ in nothing but in continuance and
intensity."
The acceptance or non-acceptance of the basis of the Utilitarian doctrine depends, in
my mind, on the exact interpretation of the language used. As it seems to me, the
feelings of which a man is capable are of various grades. He is always subject to mere
physical pleasure or pain, necessarily arising from his bodily wants and
susceptibilities. He is capable also of mental and moral feelings of several degrees of
elevation. A higher motive may rightly overbalance all considerations belonging even
to the next lower range of feelings; but so long as the higher motive does not
intervene, it is surely both desirable and right that the lower motives should be
balanced against each other. Starting with the lowest stage—it is a man's duty, as it is
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his natural inclination, to earn sufficient food and whatever else may best satisfy his
proper and moderate desires. If the claims of a family or of friends fall upon him, it
may become desirable that he should deny his own desires and even his physical
needs their full customary gratification. But the claims of a family are only a step to a
higher grade of duties.
The safety of a nation, the welfare of great populations, may happen to depend upon
his exertions, if he be a soldier or a statesman: claims of a very strong kind may now
be overbalanced by claims of a still stronger kind. Nor should I venture to say that, at
any point, we have reached the highest rank—the supreme motives which should
guide the mind. The statesman may discover a conflict between motives; a measure
may promise, as it would seem, the greatest good to great numbers, and yet there may
be motives of uprightness and honour that may hinder his promoting the measure.
How such difficult questions may be rightly determined it is not my purpose to
inquire here.
The utilitarian theory holds, that all forces influencing the mind of man are pleasures
and pains; and Paley went so far as to say that all pleasures and pains are of one kind
only. Mr. Bain has carried out this view to its complete extent, saying,1 "No amount
of complication is ever able to disguise the general fact, that our voluntary activity is
moved by only two great classes of stimulants; either a pleasure or a pain, present or
remote, must lurk in every situation that drives us into action." The question certainly
appears to turn upon the language used. Call any motive which attracts us to a certain
course of conduct, pleasure; and call any motive which deters us from that conduct,
pain; and it becomes impossible to deny that all actions are governed by pleasure and
pain. But it then becomes indispensable to admit that a single higher pleasure will
sometimes neutralise a vast extent and continuance of lower pains. It seems hardly
possible to admit Paley's statement, except with an interpretation that would probably
reverse his intended meaning. Motives and feelings are certainly of the same kind to
the extent that we are able to weigh them against each other; but they are,
nevertheless, almost incomparable in power and authority.
My present purpose is accomplished in pointing out this hierarchy of feeling, and
assigning a proper place to the pleasures and pains with which the Economist deals. It
is the lowest rank of feelings which we here treat. The calculus of utility aims at
supplying the ordinary wants of man at the least cost of labour. Each labourer, in the
absence of other motives, is supposed to devote his energy to the accumulation of
wealth. A higher calculus of moral right and wrong would be needed to show how he
may best employ that wealth for the good of others as well as himself. But when that
higher calculus gives no prohibition, we need the lower calculus to gain us the utmost
good in matters of moral indifference. There is no rule of morals to forbid our making
two blades of grass grow instead of one, if, by the wise expenditure of labour, we can
do so. And we may certainly say, with Francis Bacon, "while philosophers are
disputing whether virtue or pleasure be the proper aim of life, do you provide yourself
with the instruments of either."
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CHAPTER II
THEORY OF PLEASURE AND PAIN
Pleasure And Pain As Quantities.
PROCEEDING to consider how pleasure and pain can be estimated as magnitudes,
we must undoubtedly accept what Bentham has laid down upon this subject. "To a
person," he says,1 "considered by himself, the value of a pleasure or pain, considered
by itself, will be greater or less according to the four following circumstances:—
(1) Its intensity.
(2) Its duration.
(3) Its certainty or uncertainty.
(4) Its propinquity or remoteness.
These are the circumstances which are to be considered in estimating a pleasure or a
pain considered each of them by itself."
Bentham 1 goes on to consider three other circumstances which relate to the ultimate
and complete result of any act or feeling; these are—
(5)Fecundity, or the chance a feeling has of being followed by feelings of the
same kind: that is, pleasures, if it be a pleasure; pains, if it be a pain.
(6)Purity, or the chance it has of not being followed by feelings of an
opposite kind. And
(7)Extent, or the number of persons to whom it extends, and who are affected
by it.
These three last circumstances are of high importance as regards the theory of morals;
but they will not enter into the more simple and restricted problem which we attempt
to solve in Economics.
A feeling, whether of pleasure or of pain, must be regarded as having two dimensions,
or modes of varying in regard to quantity. Every feeling must last some time, and it
may last a longer or shorter time; while it lasts, it may be more or less acute and
intense. If in two cases the duration of feeling is the same, that case will produce the
greater quantity which is the more intense; or we may say that, with the same
duration, the quantity will be proportional to the intensity. On the other hand, if the
intensity of a feeling were to remain constant, the quantity of feeling would increase
with its duration. Two days of the same degree of happiness are to be twice as much
desired as one day; two days of suffering are to be twice as much feared. If the
intensity ever continued fixed, the whole quantity would be found by multiplying the
number of units of intensity into the number of units of duration. Pleasure and pain,
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then, are quantities possessing two dimensions, just as superficies possesses the two
dimensions of length and breadth.
In almost every case, however, the intensity of feeling will change from moment to
moment. Incessant variation characterises our states of mind, and
this is the source of the main difficulties of the subject. Nevertheless, if these
variations can be traced out at all, or any approach to method and law can be detected,
it will be possible to form a conception of the resulting quantity of feeling. We may
imagine that the intensity changes at the end of every minute, but remains constant in
the intervals. The quantity during each minute may be represented, as in Fig. I., by a
rectangle whose base is supposed to correspond to the duration of a minute, and
whose height is proportional to the intensity of the feeling during the minute in
question. Along the line ox we measure time, and along parallels to the perpendicular
line oy we measure intensity. Each of the rectangles between pm and qn represents the
feeling of one minute. The aggregate quantity of feeling generated during the time mn
will then be represented by the aggregate area of the rectangles between pm and qn. In
this case the intensity of the feeling is supposed to be gradually declining.
But it is an artificial assumption that the intensity would vary by sudden steps and at
regular intervals. The error thus introduced will not be great if the intervals of time are
very short, and will be less the shorter the intervals are made. To avoid all error, we
must imagine the intervals of time to be infinitely short; that is, we must treat the
intensity as varying continuously. Thus the proper representation of the variation of
feeling is found in a curve of more or less complex character.
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In Fig. II. The height of each point of the curve pq, above the horizontal line ox,
indicates the intensity of feeling in a moment of time; and the whole quantity of
feeling generated in the time mn is measured by the area bounded by the lines
pm,qn,mn, and pq. The feeling belonging to any other time, ma, will be measured by
the space mabp cut off by the perpendicular line ab.
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Pain The Negative Of Pleasure.
It will be readily conceded that pain is the opposite of pleasure; so that to decrease
pain is to increase pleasure; to add pain is to decrease pleasure. Thus we may treat
pleasure and pain as positive and negative quantities are treated in algebra. The
algebraic sum of a series of pleasures and pains will be obtained by adding the
pleasures together and the pains together, and then striking the balance by subtracting
the smaller amount from the greater. Our object will always be to maximise the
resulting sum in the direction of pleasure, which we may fairly call the positive
direction. This object we shall accomplish by accepting everything, and undertaking
every action of which the resulting pleasure exceeds the pain which is undergone; we
must avoid every object or action which leaves a balance in the other direction.
The most important parts of the theory will turn upon the exact equality, without
regard to sign, of the pleasure derived from the possession of an object, and the pain
encountered in its acquisition. I am glad, therefore, to quote the following passage
from Mr. Bain's treatise on The Emotions and the Will,1 in which he exactly expresses
the opposition of pleasure and pain:—"When pain is followed by pleasure, there is a
tendency in the one, more or less, to neutralise the other. When the pleasure exactly
assuages the pain, we say that the two are equivalent, or equal in amount, although of
opposite nature, like hot and cold, positive and negative; and when two different kinds
of pleasure have the power of satiating the same amount of pain, there is fair ground
for pronouncing them of equal emotional power. Just as acids are pronounced
equivalent when in amount sufficient to neutralise the same portion of alkali, and as
heat is estimated by the quantity of snow melted by it, so pleasures are fairly
compared as to their total efficacy on the mind, by the amount of pain that they are
capable of submerging. In this sense there may be an effective estimate of degree."
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Anticipated Feeling.
Bentham has stated2 that one of the main elements in estimating the force of a
pleasure or pain is its propinquity or remoteness. It is certain that a very large part of
what we experience in life depends not on the actual circumstances of the moment so
much as on the anticipation of future events. As Mr. Bain says,1 "The foretaste of
pleasure is pleasure begun: every actual delight casts before it a corresponding ideal."
Every one must have felt that the enjoyment actually experienced at any moment is
but limited in amount, and usually fails to answer to the anticipations which have
been formed. "Man never is but always to be blest" is a correct description of our
ordinary state of mind; and there is little doubt that, in minds of much intelligence and
foresight, the greatest force of feeling and motive arises from the anticipation of a
long-continued future.
Now, between the actual amount of feeling anticipated and that which is felt there
must be some natural relation, very variable no doubt according to circumstances, the
intellectual standing of the race, or the character of the individual; and yet subject to
some general laws of variation. The intensity of present anticipated feeling must, to
use a mathematical expression, be some function of the future actual feeling and of the
intervening time, and it must increase as we approach the moment of realisation. The
change, again, must be less rapid the farther we are from the moment, and more rapid
as we come nearer to it. An event which is to happen a year hence affects us on the
average about as much one day as another; but an event of importance, which is to
take place three days hence, will probably affect us on each of the intervening days
more acutely than the last.
This power of anticipation must have a large influence in Economics; for upon it is
based all accumulation of stocks of commodity to be consumed at a future time. That
class or race of men who have the most foresight will work most for the future. The
untutored savage, like the child, is wholly occupied with the pleasures and the
troubles of the moment; the morrow is dimly felt; the limit of his horizon is but a few
days off. The wants of a future year, or of a lifetime, are wholly unforeseen. But, in a
state of civilisation, a vague though powerful feeling of the future is the main
incentive to industry and saving. The cares of the moment are but ripples on the tide
of achievement and hope. We may safely call that man happy who, however lowly his
position and limited his possessions, can always hope for more than he has, and can
feel that every moment of exertion tends to realise his aspirations. He, on the contrary,
who seizes the enjoyment of the passing moment without regard to coming times,
must discover sooner or later that his stock of pleasure is on the wane, and that even
hope begins to fail.
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Uncertainty Of Future Events.
In admitting the force of anticipated feeling, we are compelled to take account of the
uncertainty of all future events. We ought never to estimate the value of that which
may or may not happen as if it would certainly happen. When it is as likely as not that
I shall receive £100, the chance is worth but £50, because if, for a great many times in
succession, I purchase the chance at this rate, I shall almost certainly neither lose nor
gain. The test of correct estimation of probabilities is that the calculations agree with
fact on the average. If we apply this rule to all future interests, we must reduce our
estimate of any feeling in the ratio of the numbers expressing the probability of its
occurrence. If the probability is only one in ten that I shall have a certain day of
pleasure, I ought to anticipate the pleasure with one-tenth of the force which would
belong to it if certain. In selecting a course of action which depends on uncertain
events, as, in fact, does everything in life, I should multiply the quantity of feeling
attaching to every future event by the fraction denoting its probability. A great
casualty, which is very unlikely to happen, may not be so important as a slight
casualty which is nearly sure to happen. Almost unconsciously we make calculations
of this kind more or less accurately in all the ordinary affairs of life; and in systems of
life, fire, marine, or other insurance, we carry out the calculations to great perfection.
In all industry directed to future purposes, we must take similar account of our want
of knowledge of what is to be.
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CHAPTER III
THEORY OF UTILITY
Definition Of Terms.
PLEASURE and pain are undoubtedly the ultimate objects of the Calculus of
Economics. To satisfy our wants to the utmost with the least effort—to procure the
greatest amount of what is desirable at the expense of the least that is undesirable—in
other words, to maximise pleasure, is the problem of Economics. But it is convenient
to transfer our attention as soon as possible to the physical objects or actions which
are the source to us of pleasures and pains. A very large part of the labour of any
community is spent upon the production of the ordinary necessaries and conveniences
of life, such as food, clothing, buildings, utensils, furniture, ornaments, etc.; and the
aggregate of these things, therefore, is the immediate object of our attention.
It is desirable to introduce at once, and to define, some terms which facilitate the
expression of the Principles of Economics. By a commodity we shall understand any
object, substance, action, or service, which can afford pleasure or ward off pain. The
name was originally abstract, and denoted the quality of anything by which it was
capable of serving man. Having acquired, by a common process of confusion, a
concrete signification, it will be well to retain the word entirely for that signification,
and employ the term utility to denote the abstract quality whereby an object serves our
purposes, and becomes entitled to rank as a commodity. Whatever can produce
pleasure or prevent pain may possess utility. J.-B. Say has correctly and briefly
defined utility as "la faculté qu'ont les choses de pouvoir servir à l'homme, de quelque
manière que ce soit." The food which prevents the pangs of hunger, the clothes which
fend off the cold of winter, possess incontestable utility; but we must beware of
restricting the meaning of the word by any moral considerations. Anything which an
individual is found to desire and to labour for must be assumed to possess for him
utility. In the science of Economics we treat men not as they ought to be, but as they
are. Bentham, in establishing the foundations of Moral Science in his great
Introduction to the Principles of Morals and Legislation (page 3), thus
comprehensively defines the term in question: "By utility is meant that property in
any object, whereby it tends to produce benefit, advantage, pleasure, good, or
happiness (all this, in the present case, comes to the same thing), or (what comes
again to the same thing) to prevent the happening of mischief, pain, evil, or
unhappiness to the party whose interest is considered."
This perfectly expresses the meaning of the word in Economics, provided that the will
or inclination of the person immediately concerned is taken as the sole criterion, for
the time, of what is or is not useful.
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The Laws Of Human Want.
Economics must be founded upon a full and accurate investigation of the conditions
of utility; and, to understand this element, we must necessarily examine the wants and
desires of man. We, first of all, need a theory of the consumption of wealth. J. S. Mill,
indeed, has given an opinion inconsistent with this. "Political economy," he says,1
"has nothing to do with the consumption of wealth, further than as the consideration
of it is inseparable from that of production, or from that of distribution. We know not
of any laws of the consumption of wealth, as the subject of a distinct science; they can
be no other than the laws of human enjoyment."
But it is surely obvious that Economics does rest upon the laws of human enjoyment;
and that, if those laws are developed by no other science, they must be developed by
economists. We labour to produce with the sole object of consuming, and the kinds
and amounts of goods produced must be determined with regard to what we want to
consume. Every manufacturer knows and feels how closely he must anticipate the
tastes and needs of his customers: his whole success depends upon it; and, in like
manner, the theory of Economics must begin with a correct theory of consumption.
Many economists have had a clear perception of this truth. Lord Lauderdale distinctly
states,1 that "the great and important step towards ascertaining the causes of the
direction which industry takes in nations... seems to be the discovery of what dictates
the proportion of demand for the various articles which are produced." Senior, in his
admirable treatise, has also recognised this truth, and pointed out what he calls the
Law of Variety in human requirements. The necessaries of life are so few and simple,
that a man is soon satisfied in regard to these, and desires to extend his range of
enjoyment. His first object is to vary his food; but there soon arises the desire of
variety and elegance in dress; and to this succeeds the desire to build, to ornament,
and to furnish—tastes which, where they exist, are absolutely insatiable, and seem to
increase with every improvement in civilisation.2
Many French economists also have observed that human wants are the ultimate
subject-matter of Economics; Bastiat, for instance, in his Harmoniesof Political
Economy, says,1 "Wants, Efforts, Satisfaction—this is the circle of Political
Economy."
In still later years, Courcelle-Seneuil actually commenced his treatise with a definition
of want—"Le besoin économique est un désir qui a pour but la possession et la
jouissance d'un objet matériel."2 And I conceive that he has given the best possible
statement of the problem of Economics when he expresses its object as "à satisfaire
nos besoins avec la moindre somme de travail possible."3
Professor Hearn also begins his excellent treatise, entitled Plutology, or the Theory of
Efforts to supply Human Wants, with a chapter in which he considers the nature of the
wants impelling man to exertion.
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The writer, however, who seems to me to have reached the deepest comprehension of
the foundations of Economics is T. E. Banfield. His course of Lectures delivered in
the University of Cambridge in 1844, and published under the title of The
Organisation of Labour, is highly interesting, though not always correct. In the
following passage4 he profoundly points out that the scientific basis of Economics is
in a theory of consumption: I need make no excuse for quoting this passage at full
length.
"The lower wants man experiences in common with brutes. The cravings of hunger
and thirst, the effects of heat and cold, of drought and damp, he feels with more
acuteness than the rest of the animal world. His sufferings are doubtless sharpened by
the consciousness that he has no right to be subject to such inflictions. Experience,
however, shows that privations of various kinds affect men differently in degree
according to the circumstances in which they are placed. For some men the privation
of certain enjoyments is intolerable, whose loss is not even felt by others. Some,
again, sacrifice all that others hold dear for the gratification of longings and
aspirations that are incomprehensible to their neighbours. Upon this complex
foundation of low wants and high aspirations the Political Economist has to build the
theory of production and consumption.
"An examination of the nature and intensity of man's wants shows that this connection
between them gives to Political Economy its scientific basis. The first proposition of
the theory of consumption is, that the satisfaction of every lower want in the scale
creates a desire of a higher character. If the higher desire existed previous to the
satisfaction of the primary want, it becomes more intense when the latter is removed.
The removal of a primary want commonly awakens the sense of more than one
secondary privation: thus a full supply of ordinary food not only excites to delicacy in
eating, but awakens attention to clothing. The highest grade in the scale of wants, that
of pleasure derived from the beauties of nature and art, is usually confined to men
who are exempted from all the lower privations. Thus the demand for, and the
consumption of, objects of refined enjoyment has its lever in the facility with which
the primary wants are satisfied. This, therefore, is the key to the true theory of value.
Without relative values in the objects to the acquirement of which we direct our
power, there would be no foundation for Political Economy as a science."
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Utility Is Not An Intrinsic Quality.
My principal work now lies in tracing out the exact nature and conditions of utility. It
seems strange indeed that economists have not bestowed more minute attention on a
subject which doubtless furnishes the true key to the problem of Economics.
In the first place, utility, though a quality of things, is no inherent quality. It is better
described as a circumstance of things arising out of their relation to man's
requirements. As Senior most accurately says, "Utility denotes no intrinsic quality in
the things which we call useful; it merely expresses their relations to the pains and
pleasures of mankind." We can never, therefore, say absolutely that some objects have
utility and others have not. The ore lying in the mine, the diamond escaping the eye of
the searcher, the wheat lying unreaped, the fruit ungathered for want of consumers,
have no utility at all. The most wholesome and necessary kinds of food are useless
unless there are hands to collect and mouths to eat them sooner or later. Nor, when we
consider the matter closely, can we say that all portions of the same commodity
possess equal utility. Water, for instance, may be roughly described as the most useful
of all substances. A quart of water per day has the high utility of saving a person from
dying in a most distressing manner. Several gallons a day may possess much utility
for such purposes as cooking and washing; but after an adequate supply is secured for
these uses, any additional quantity is a matter of comparative indifference. All that we
can say, then, is, that water, up to a certain quantity, is indispensable; that further
quantities will have various degrees of utility; but that beyond a certain quantity the
utility sinks gradually to zero; it may even become negative, that is to say, further
supplies of the same substance may become inconvenient and hurtful.
Exactly the same considerations apply more or less clearly to every other article. A
pound of bread per day supplied to a person saves him from starvation, and has the
highest conceivable utility. A second pound per day has also no slight utility: it keeps
him in a state of comparative plenty, though it be not altogether indispensable. A third
pound would begin to be superfluous. It is clear, then, that utility is not proportional
to commodity: the very same articles vary in utility according as we already possess
more or less of the same article. The like may be said of other things. One suit of
clothes per annum is necessary, a second convenient, a third desirable, a fourth not
unacceptable; but we, sooner or later, reach a point at which further supplies are not
desired with any perceptible force, unless it be for subsequent use.
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Law Of The Variation Of Utility.
Let us now investigate this subject a little more closely. Utility must be considered as
measured by, or even as actually identical with, the addition made to a person's
happiness. It is a convenient name for the aggregate of the favourable balance of
feeling produced—the sum of the pleasure created and the pain prevented. We must
now carefully discriminate between the total utility arising from any commodity and
the utility attaching to any particular portion of it. Thus the total utility of the food we
eat consists in maintaining life, and may be considered as infinitely great; but if we
were to subtract a tenth part from what we eat daily, our loss would be but slight. We
should certainly not lose a tenth part of the whole utility of food to us. It might be
doubtful whether we should suffer any harm at all.
Let us imagine the whole quantity of food which a person consumes on an average
during twenty-four hours to be divided into ten equal parts. If his food be reduced by
the last part, he will suffer but little; if a second tenth part be deficient, he will feel the
want distinctly; the subtraction of the third tenth part will be decidedly injurious; with
every subsequent subtraction of a tenth part his sufferings will be more and more
serious, until at length he will be upon the verge of starvation. Now, if we call each of
the tenth parts an increment, the meaning of these facts is, that each increment of food
is less necessary, or possesses less utility, than the previous one. To explain this
variation of utility we may make use of space-representations, which I have found
convenient in illustrating the laws of Economics in my College lectures during fifteen
years past.
Let the line ox be used as a measure of the quantity of food, and let it be divided into
ten equal parts to correspond to the ten portions of food mentioned above. Upon these
equal lines are constructed rectangles, and the area of each rectangle may be assumed
to represent the utility of the increment of food corresponding to its base. Thus the
utility of the last increment is small, being proportional to the small rectangle on x. As
we approach towards o, each increment bears a larger rectangle, that standing upon III
being the largest complete rectangle. The utility of the next increment, II, is
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undefined, as also that of I, since these portions of food would be indispensable to
life, and their utility, therefore, infinitely great.
We can now form a clear notion of the utility of the whole food, or of any part of it,
for we have only to add together the proper rectangles. The utility of the first half of
the food will be the sum of the rectangles standing on the line oa; that of the second
half will be represented by the sum of the smaller rectangles between a and b. The
total utility of the food will be the whole sum of the rectangles, and will be infinitely
great.
The comparative utility of the several portions is, however, the most important point.
Utility may be treated1 as a quantity of two dimensions, one dimension consisting in
the quantity of the commodity, and another in the intensity of the effect produced
upon the consumer. Now, the quantity of the commodity is measured on the
horizontal line ox, and the intensity of utility will be measured by the length of the
upright lines, or ordinates. The intensity of utility of the third increment is measured
either by q, or and its utility is the product of the units in pp multiplied by those
in pq.
But the division of the food into ten equal parts is an arbitrary supposition. If we had
taken twenty or a hundred or more equal parts, the same general principle would hold
true, namely, that each small portion would be less useful and necessary than the last.
The law may be considered to hold true theoretically, however small the increments
are made; and in this way we shall at last reach a figure which is undistinguishable
from a continuous curve. The notion of infinitely small quantities of food may seem
absurd as regards the consumption of one individual; but, when we consider the
consumption of a nation as a whole, the consumption may well be conceived to
increase or diminish by quantities which are, practically speaking, infinitely small
compared with the whole consumption. The laws which we are about to trace out are
to be conceived as theoretically true of the individual; they can only be practically
verified as regards the aggregate transactions, productions, and consumptions of a
large body of people. But the laws of the aggregate depend of course upon the laws
applying to individual cases.
The law of the variation of the degree of utility of food may thus be represented by a
continuous curve pbq (Fig. IV.), and the perpendicular height of each point of the
curve above the line ox, represents the degree of utility of the commodity when a
certain amount has been consumed.
Thus, when the quantity oa has been consumed, the degree of utility corresponds to
the length of the line ab; for if we take a very little more food, aá, its utility will be
the product of aá and ab very nearly, and more nearly the less is the magnitude of aá.
The degree of utility is thus properly measured by the height of a very narrow
rectangle corresponding
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to a very small quantity of food, which theoretically ought to be infinitely small.
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Total Utility And Degree Of Utility.
We are now in a position to appreciate perfectly the difference between the total
utility of any commodity and the degree of utility of the commodity at any point.
These are, in fact, quantities of altogether different kinds, the first being represented
by an area, and the second by a line. We must consider how we may express these
notions in appropriate mathematical language.
Let x signify, as is usual in mathematical books, the quantity which varies
independently,—in this case the quantity of commodity. Let u denote the whole utility
proceeding from the consumption of x. Then u will be, as mathematicians say, a
function of x; that is, it will vary in some continuous and regular, but probably
unknown, manner, when x is made to vary. Our great object at present, however, is to
express the degree of utility.
Mathematicians employ the sign D prefixed to a sign of quantity, such as x, to signify
that a quantity of the same nature as x, but small in proportion to x, is taken into
consideration. Thus Dx means a small portion of x, and x + Dx is therefore a quantity
a little greater than x. Now, when x is a quantity of commodity, the utility of x + Dx
will be more than that of x as a general rule. Let the whole utility of x + Dx be denoted
by u + Du; then it is obvious that the increment of utility Du belongs to the increment
of commodity Dx; and if, for the sake of argument, we suppose the degree of utility
uniform over the whole of Dx, which is nearly true owing to its smallness, we shall
find the corresponding degree of utility by dividing Du by Dx.
We find these considerations fully illustrated by Fig. IV., in which oa represents x,
and ab is the degree of utility at the point a. Now, if we increase x by the small
quantity aá, or Dx, the utility is increased by the small rectangle abb'a', or Du; and,
since a rectangle is the product of its sides, we find that the length of the line ab, the
degree of utility, is represented by the fraction .
As already explained, however, the utility of a commodity may be considered to vary
with perfect continuity, so that we commit a small error in assuming it to be uniform
over the whole increment Dx. To avoid this we must imagine Dx to be reduced to an
infinitely small size, Du decreasing with it. The smaller the quantities are the more
nearly we shall have a correct expression for ab, the degree of utility at the point a.
Thus the limit of this fraction or, as it is commonly expressed, , is the degree
of utility corresponding to the quantity of commodity x.The degree of utility is, in
mathematical language, the differential coefficient of u considered as a function of x,
and will itself be another function of x.
We shall seldom need to consider the degree of utility except as regards the last
increment which has been consumed, or, which comes to the same thing, the next
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increment which is about to be consumed. I shall therefore commonly use the
expression final degree of utility, as meaning the degree of utility of the last addition,
or the next possible addition of a very small, or infinitely small, quantity to the
existing stock. In ordinary circumstances, too, the final degree of utility will not be
great compared with what it might be. Only in famine or other extreme circumstances
do we approach the higher degrees of utility. Accordingly, we can often treat the
lower portions of the curves of variation (pbq, Fig. IV.) which concern ordinary
commercial transactions, while we leave out of sight the portions beyond p or q. It is
also evident that we may know the degree of utility at any point while ignorant of the
total utility, that is, the area of the whole curve. To be able to estimate the total
enjoyment of a person would be an interesting thing, but it would not be really so
important as to be able to estimate the additions and subtractions to his enjoyment,
which circumstances occasion. In the same way a very wealthy person may be quite
unable to form any accurate statement of his aggregate wealth; but he may
nevertheless have exact accounts of income and expenditure, that is, of additions and
subtractions.
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Variation Of The Final Degree Of Utility.
The final degree of utility is that function upon which the Theory of Economics will
be found to turn. Economists, generally speaking, have failed to discriminate between
this function and the total utility, and from this confusion has arisen much perplexity.
Many commodities which are most useful to us are esteemed and desired but little.
We cannot live without water, and yet in ordinary circumstances we set no value on it.
Why is this? Simply because we usually have so much of it that its final degree of
utility is reduced nearly to zero. We enjoy, every day, the almost infinite utility of
water, but then we do not need to consume more than we have. Let the supply run
short by drought, and we begin to feel the higher degrees of utility, of which we think
but little at other times.
The variation of the function expressing the final degree of utility is the all-important
point in economic problems. We may state as a general law, that the degree of utility
varies with the quantity of commodity, and ultimately decreases as that quantity
increases. No commodity can be named which we continue to desire with the same
force, whatever be the quantity already in use or possession. All our appetites are
capable of satisfaction or satiety sooner or later, in fact, both these words mean,
etymologically, that we have had enough, so that more is of no use to us. It does not
follow, indeed, that the degree of utility will always sink to zero. This may be the case
with some things, especially the simple animal requirements, such as food, water, air,
etc. But the more refined and intellectual our needs become, the less are they capable
of satiety. To the desire for articles of taste, science, or curiosity, when once excited,
there is hardly a limit.
This great principle of the ultimate decrease of the final degree of utility of any
commodity is implied in the writings of many economists, though seldom distinctly
stated. It is the real law which lies at the basis of Senior's so-called "Law of Variety."
Indeed, Senior incidentally states the law itself. He says: "It is obvious that our desires
do not aim so much at quantity as at diversity. Not only are there limits to the pleasure
which commodities of any given class can afford, but the pleasure diminishes in a
rapidly increasing ratio long before those limits are reached. Two articles of the same
kind will seldom afford twice the pleasure of one, and still less will ten give five times
the pleasure of two. In proportion, therefore, as any article is abundant, the number of
those who are provided with it, and do not wish, or wish but little, to increase their
provision, is likely to be great; and, so far as they are concerned, the additional supply
loses all, or nearly all, its utility. And, in proportion to its scarcity, the number of
those who are in want of it, and the degree in which they want it, are likely to be
increased; and its utility, or, in other words, the pleasure which the possession of a
given quantity of it will afford, increases proportionally."1
Banfield's "Law of the Subordination of Wants" also rests upon the same basis. It
cannot be said, with accuracy, that the satisfaction of a lower want creates a higher
want; it merely permits the higher want to manifest itself. We distribute our labour
and possessions in such a way as to satisfy the more pressing wants first. If food runs
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short, the all-absorbing question is, how to obtain more, because, at the moment, more
pleasure or pain depends upon food than upon any other commodity. But, when food
is moderately abundant, its final degree of utility falls very low, and wants of a more
complex and less satiable nature become comparatively prominent.
The writer, however, who appears to me to have most clearly appreciated the nature
and importance of the law of utility, is Richard Jennings, who, in 1855, published a
small book called the Natural Elements of Political Economy.1 This work treats of the
physical groundwork of Economics, showing its dependence on physiological laws. It
displays great insight into the real basis of Economics; yet I am not aware that
economists have bestowed the slightest attention on Jennings's views.2 I give,
therefore, a full extract from his remarks on the nature of utility. It will be seen that
the law, as I state it, is no novelty, and that careful deduction from principles in our
possession is alone needed to give us a correct Theory of Economics.
"To turn from the relative effect of commodities, in producing sensations, to those
which are absolute, or dependent only on the quantity of each commodity, it is but too
well known to every condition of men, that the degree of each sensation which is
produced, is by no means commensurate with the quantity of the commodity applied
to the senses.... These effects require to be closely observed, because they are the
foundation of the changes of money price, which valuable objects command in times
of varied scarcity and abundance; we shall therefore here direct our attention to them
for the purpose of ascertaining the nature of the law according to which the sensations
that attend on consumption vary in degree with changes in the quantity of the
commodity consumed.
"We may gaze upon an object until we can no longer discern it, listen until we can no
longer hear, smell until the sense of odour is exhausted, taste until the object becomes
nauseous, and touch until it becomes painful; we may consume food until we are fully
satisfied, and use stimulants until more would cause pain. On the other hand, the same
object offered to the special senses for a moderate duration of time, and the same food
or stimulants consumed when we are exhausted or weary, may convey much
gratification. If the whole quantity of the commodity consumed during the interval of
these two states of sensation, the state of satiety and the state of inanition, be
conceived to be divided into a number of equal parts, each marked with its proper
degrees of sensation, the question to be determined will be, what relation does the
difference in the degrees of the sensation bear to the difference in the quantities of the
commodity?
"First, with respect to all commodities, our feelings show that the degrees of
satisfaction do not proceed pari passu with the quantities consumed; they do not
advance equally with each instalment of the commodity offered to the senses, and
then suddenly stop; but diminish gradually, until they ultimately disappear, and
further instalments can produce no further satisfaction. In this progressive scale the
increments of sensation resulting from equal increments of the commodity are
obviously less and less at each step,—each degree of sensation is less than the
preceding degree. Placing ourselves at that middle point of sensation, the juste milieu,
the aurea mediocritas, the of sages, which is the most usual
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status of the mass of mankind, and which, therefore, is the best position that can be
chosen for measuring deviations from the usual amount, we may say that the law
which expresses the relation of degrees of sensation to quantities of commodities is of
this character: if the average or temperate quantity of commodities be increased, the
satisfaction derived is increased in a less degree, and ultimately ceases to be increased
at all; if the average or temperate quantity be diminished, the loss of more and more
satisfaction will continually ensue, and the detriment thence arising will ultimately
become exceedingly great."1
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Disutility And Discommodity.
A few words will suffice to suggest that as utility corresponds to the production of
pleasure, or, at least, a favourable alteration in the balance of pleasure and pain, so
negative utility will consist in the production of pain, or the unfavourable alteration of
the balance. In reality we must be almost as often concerned with the one as with the
other; nevertheless, economists have not employed any distinct technical terms to
express that production of pain, which accompanies so many actions of life. They
have fixed their attention on the more agreeable aspect of the matter. It will be
allowable, however, to appropriate the good English word discommodity, to signify
any substance or action which is the opposite of commodity, that is to say, anything
which we desire to get rid of, like ashes or sewage. Discommodity is, indeed, properly
an abstract form signifying inconvenience, or disadvantage; but, as the noun
commodities has been used in the English language for four hundred years at least as a
concrete term,1 so we may now convert discommodity into a concrete term, and
speak of discommodities as substances or things which possess the quality of causing
inconvenience or harm. For the abstract notion, the opposite or negative of utility, we
may invent the term disutility, which will mean something different from inutility, or
the absence of utility. It is obvious that utility passes through inutility before changing
into disutility, these notions being related as +, 0 and -.
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Distribution Of Commodity In Different Uses.
The principles of utility may be illustrated by considering the mode in which we
distribute a commodity when it is capable of several uses. There are articles which
may be employed for many distinct purposes: thus, barley may be used either to make
beer, spirits, bread, or to feed cattle; sugar may be used to eat, or for producing
alcohol; timber may be used in construction, or as fuel; iron and other metals may be
applied to many different purposes. Imagine, then, a community in the possession of a
certain stock of barley; what principles will regulate their mode of consuming it? Or,
as we have not yet reached the subject of exchange, imagine an isolated family, or
even an individual, possessing an adequate stock, and using some in one way and
some in another. The theory of utility gives, theoretically speaking, a complete
solution of the question.
Let s be the whole stock of some commodity, and let it be capable of two distinct
uses. Then we may represent the two quantities appropriated to these uses by x
1
and
y
1
, it being a condition that x
1
+ y
1
= s. The person may be conceived as successively
expending small quantities of the commodity; now it is the inevitable tendency of
human nature to choose that course which appears to offer the greatest advantage at
the moment. Hence, when the person remains satisfied with the distribution he has
made, it follows that no alteration would yield him more pleasure; which amounts to
saying that an increment of commodity would yield exactly as much utility in one use
as in another. Let Du
1
, Du
2
, be the increments of utility, which might arise
respectively from consuming an increment of commodity in the two different ways.
When the distribution is completed, we ought to have D;
or at the limit we have the equation
which is true when x, y are respectively equal to x
1
, y
1
. We must, in other words, have
the final degrees of utility in the two uses equal.
The same reasoning which applies to uses of the same commodity will evidently
apply to any two uses, and hence to all uses simultaneously, so that we obtain a series
of equations less numerous by a unit than the number of ways of using the
commodity. The general result is that commodity, if consumed by a perfectly wise
being, must be consumed with a maximum production of utility.
We should often find these equations to fail. Even when x is equal to of the
stock, its degree of utility might still exceed the utility attaching to the remaining
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part in either of the other uses. This would mean that it was preferable to give
the whole commodity to the first use. Such a case might perhaps be said to be not the
exception but the rule; for, whenever a commodity is capable of only one use, the
circumstance is theoretically represented by saying, that the final degree of utility in
this employment always exceeds that in any other employment.
Under peculiar circumstances great changes may take place in the consumption of a
commodity. In a time of scarcity the utility of barley as food might rise so high as to
exceed altogether its utility, even as regards the smallest quantity, in producing
alcoholic liquors; its consumption in the latter way would then cease. In a besieged
town the employment of articles becomes revolutionised. Things of great utility in
other respects are ruthlessly applied to strange purposes. In Paris a vast stock of
horses were eaten, not so much because they were useless in other ways, as because
they were needed more strongly as food. A certain stock of horses had, indeed, to be
retained as a necessary aid to locomotion, so that the equation of the degrees of utility
never wholly failed.
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Theory Of Dimensions Of Economic Quantities.
In the recent progress of physical science, it has been found requisite to use notation
for the purpose of displaying clearly the natures and relations of the various kinds of
quantities concerned. Each different sort of quantity is, of course, expressed in terms
of its own appropriate unit—length in terms of yards, or metres; surface, or area, in
terms of square yards or square metres; time in terms of seconds, days, or years; and
so forth. But the more complicated quantities are evidently related to the simpler ones.
Surface is measured by the square yard—that is to say, the unit of length is involved
twice over, and if by L we denote one dimension of length, then the dimensions of
surface are LL, or L2. The dimensions of cubic capacity are in like manner LLL, or L3.
In these cases the dimensions all enter positively, because the number of units in the
cubical body, for instance, is found by multiplying the numbers of units in its length,
breadth, and depth. In other cases a dimension enters negatively. Thus denoting time
by T, it is easy to see that the dimensions of velocity will be L divided by T, or LT -1,
because the number of units in the velocity of a body is found by dividing the units of
length passed over by the units of time occupied in passing. In expressing the
dimensions of thermal and electric quantities, fractional exponents often become
necessary, and the subject assumes the form of a theory of considerable complexity.
The reader to whom this branch of science is new will find a section briefly
describing it in my Principles of Science, 3d ed., p. 325, or he may refer to the works
there mentioned.1
Now, if such a theory of dimensions is requisite in dealing with the precise ideas of
physical magnitudes, it seems to be still more desirable as regards the quantities with
which we are concerned in Economics. One of the first and most difficult steps in a
science is to conceive clearly the nature of the magnitudes about which we are
arguing. Heat was long the subject of discussion and experiment before physicists
formed any definite idea how its quantity could be measured and connected with other
physical quantities. Yet, until that was done, it could not be considered the subject of
an exact science. For one or two centuries economists have been wrangling about
wealth, demand and supply, value, production, capital, interest, and the like; but
hardly any one could say exactly what were the natures of the quantities in question.
Believing that it is in forming these primary ideas that we require to exercise the
greatest care, I have thought it well worth the trouble and space to enter fully into a
discussion of the dimensions of economic quantities.
Beginning with the easiest and simplest ideas, the dimensions of commodity regarded
merely as a physical quantity will be the dimensions of mass. It is true that
commodities are measured in various ways,—thread by length, carpet by length, corn
and liquids by cubic measure, eggs by number, metals and most other goods by
weight. But it is obvious that, though the carpet be sold by length, the breadth and the
weight of the cloth are equally taken into account in fixing the terms of sale. There
will generally be a tacit reference to weight, and through weight to mass of materials
in all measurement of commodity. Even if this be not always the case, we may, for the
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sake of simplifying our symbols in the first treatment of the subject, assume that it is
so. We need hardly recede to any ultimate analysis of the physical conditions of the
commodity, but may take it to be measured by mass, symbolised by M, the sign
usually employed in physical science to denote this dimension.
A little consideration will show, however, that we have really little to do with absolute
quantities of commodity. One hundred sacks of corn regarded merely by themselves
can have no important meaning for the economist. Whether the quantity is large or
small, enough or too much, depends in the first place upon the number of consumers
for whom it is intended, and, in the second place, upon the time for which it is to last
them. We may perhaps throw out of view the number of consumers in this theory, by
supposing that we are always dealing with the single average individual, the unit of
which population is made up. Still, we cannot similarly get rid of the element of time.
Quantity of supply must necessarily be estimated by the number of units of
commodity divided by the number of units in the time over which it is to be
expended. Thus it will involve M positively and T negatively, and its dimensions will
be represented by MT -1. Thus in reality supply should be taken to mean not supply
absolutely, but rate of supply.
Consumption of commodity must have the same dimensions. For goods must be
consumed in time; any action or effect endures a greater or less time, and commodity
which will be abundant for a less time may be scanty for a greater time. To say that a
town consumes fifty million gallons of water is unmeaning per se. Before we can
form any judgment about the statement, we must know whether it is consumed in a
day, or a week, or a month.
Following out this course of thought we shall arrive at the conclusion that time enters
into all economic questions. We live in time, and think and act in time; we are in fact
altogether the creatures of time. Accordingly it is rate of supply, rate of production,
rate of consumption, per unit of time that we shall be really treating; but it does not
follow that T -1 enters into all the dimensions with which we deal.
As was fully explained in Chapter II., the ultimate quantities which we treat in
Economics are Pleasures and Pains, and our most difficult task will be to express their
dimensions correctly. In the first place, pleasure and pain must be regarded as
measured upon the same scale, and as having, therefore, the same dimensions, being
quantities of the same kind, which can be added and subtracted; they differ only in
sign or direction. Now, the only dimension belonging properly to feeling seems to be
intensity, and this intensity must be independent both of time and of the quantity of
commodity enjoyed. The intensity of feeling must mean, then, the instantaneous state
produced by an elementary or infinitesimal quantity of commodity consumed.
Intensity of feeling, however, is only another name for degree of utility, which
represents the favourable effect produced upon the human frame by the consumption
of commodity, that is by an elementary or infinitesimal quantity of commodity.
Putting U to indicate this dimension, we must remember that U will not represent
even the full dimensions of the instantaneous state of pleasure or pain, much less the
continued state which extends over a certain duration of time. The instantaneous state
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depends upon the sufficiency or insufficiency of supply of commodity. To enjoy a
highly pleasurable condition, a person must want a good deal of commodity, and must
be well supplied with it. Now, this supply is, as already explained, rate of supply, so
that we must multiply U by MT -1 in order to arrive at the real instantaneous state of
feeling. The kind of quantity thus symbolised by MUT -1 must be interpreted as
meaning so much commodity producing a certain amount of pleasurable effect per
unit of time. But this quantity will not be quantity of utility itself. It will only be that
quantity which, when multiplied by time, will produce quantity of utility. Pleasure, as
was stated at the outset, has the dimensions of intensity and duration. It is then this
intensity which is symbolised by MUT -1, and we must multiply this last symbol by T
in order to obtain the dimensions of utility or quantity of pleasure produced. But in
making this multiplication, MUT -1 T reduces to MU, which must therefore be taken
to denote the dimensions of quantity of utility.
We here meet with an explanation of the fact, so long perplexing to me, that the
element of time does not appear throughout the diagrams and problems of this theory
relating to utility and exchange. All goes on in time, and time is a necessary element
of the question; yet it does not explicitly appear. Recurring to our diagrams, that for
instance on p. 46, it is obvious that the dimension U, or degree of utility, is measured
upon the perpendicular axis oy. The horizontal axis must, therefore, be that upon
which rate of supply of commodity or MT -1 is measured, strictly speaking. If now we
introduce the duration of the utility, we should apparently need a third axis,
perpendicular to the plane of the page, upon which to denote it. But were we to
introduce this third dimension, we should obtain a solid figure, representing a quantity
truly of three dimensions. This would be erroneous, because the third dimension T
enters negatively into the quantity represented by the horizontal axis. Thus time
eliminates itself, and we arrive at a quantity of two dimensions correctly represented
by a curvilinear area, one dimension of which corresponds to each of the factors in
MU.
This result is at first sight paradoxical; but the difficulty is exactly analogous to that
which occurs in the question of interest, and which led so profound a mathematician
as Dean Peacock into a blunder, as will be shown in the Chapter upon Capital. Interest
of money is proportional to the length of time for which the principal is lent, and also
to the amount of money lent and the rate of interest. But this rate of interest involves
time negatively, so that time is ultimately eliminated, and interest emerges with the
same dimensions as the principal sum. In the case of utility we begin with a certain
absolute stock of commodity, M. In expending it we must spread it over more or less
time, so that it is really rate of supply which is to be considered; but it is this rate
MT -1, not simply M, which influences the final degree of utility, U, at which it is
consumed. If the same commodity be made to last a longer time, the degree of utility
will be higher, because the necessity of the consumer will be less satisfied. Thus the
absolute amount of utility produced will, as a general rule, be greater as the time of
expenditure is greater: but this will also be the case with the quantity symbolised by
MU, because the quantity U will under those circumstances be greater, while M
remains constant.
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To clear up the matter still further if possible, I will recapitulate the results we have
arrived at.
M means absolute amount of commodity.
MT -1 means amount of commodity applied, so much per unit of time.
U means the resulting pleasurable effect of any increment of that supply, an
infinitesimal quantity supplied per unit of time.
MUT -1 means therefore so much pleasurable effect produced per unit of commodity
per unit of time.
MUT -1 T, or MU, means therefore so much absolute pleasurable effect produced by
commodity in an unspecified duration of time.
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Actual, Prospective, And Potential Utility.
The difficulties of Economics are mainly the difficulties of conceiving clearly and
fully the conditions of utility. Even at the risk of being tiresome, I will therefore point
out more minutely how various are the senses in which a thing may be said to have
utility.
It is quite usual, and perhaps correct, to call iron or water or timber a useful substance;
but we may mean by these words at least three distinct facts. We may mean that a
particular piece of iron is at the present moment actually useful to some person; or
that, although not actually useful, it is expected to be useful at a future time; or we
may only mean that it would be useful if it were in the possession of some person
needing it. The iron rails of a railway, the iron which composes the Britannia Bridge,
or an ocean steamer, is actually useful; the iron lying in a merchant's store is not
useful at present, though it is expected soon to be so; but there is a vast quantity of
iron existing in the bowels of the earth, which has all the physical properties of iron,
and might be useful if extracted, though it never will be. These are instances of actual,
prospective, and potential utility.
It will be apparent that potential utility does not really enter into the science of
Economics, and when I speak of utility simply, I do not mean to include potential
utility. It is a question of physical science whether a substance possesses qualities
which might make it suitable to our needs if it were within our reach. Only when there
arises some degree of probability, however slight, that a particular object will be
needed, does it acquire prospective utility, capable of rendering it a desirable
possession. As Condillac correctly remarks:1 "On diroit que les choses ne
commencent à exister pour eux, qu'au moment o ils ont un intérêt à savoir qu'elles
existent." But a very large part in industry, and the science of industry, belongs to
prospective utility. We can at any one moment use only a very small fraction of what
we possess. By far the greater part of what we hold might be allowed to perish at any
moment, without harm, if we could have it re-created with equal ease at a future
moment, when need of it arises.
We might also distinguish, as is customary with French economists, between direct
and indirect utility. Direct utility attaches to a thing like food, which we can actually
apply to satisfy our wants. But things which have no direct utility may be the means
of procuring us such by exchange, and they may therefore be said to have indirect
utility.1 To the latter form of utility I have elsewhere applied the name
acquiredutility.1 This distinction is not the same as that which is made in the Theory
of Capital between mediate and immediate utility, the former being that of any
implement, machine, or other means of procuring commodities possessing immediate
and direct utility—that is, the power of satisfying want.2
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Distribution Of A Commodity In Time.
We have seen that, when a commodity is capable of being used for different purposes,
definite principles regulate its application to those purposes. A similar question arises
when a stock of commodity is in hand, and must be expended over a certain interval
of time more or less definite. The science of Economics must point out the mode of
consuming it to the greatest advantage—that is, with a maximum result of utility. If
we reckon all future pleasures and pains as if they were present, the solution will be
the same as in the case of different uses. If a commodity has to be distributed over n
days' use, and v
1
, v
2
, etc., be the final degrees of utility on each day's consumption,
then we ought clearly to have
v
1
= v
2
= v
3
=...=v
n
.
It may, however, be uncertain during how many days we may require the stock to last.
The commodity might be of a perishable nature, so that if we were to keep some of it
for ten days, it might become unserviceable, and its utility be sacrificed. Assuming
that we can estimate more or less exactly the probability of its remaining good, let p
1
,
p
2
, p
3
... p
10
, be these probabilities. Then, on the principle (p. 36) that a future pleasure
or pain must be reduced in proportion to its want of certainty, we have the equations
v
1
p
1
= r
2
p
2
=... = v
10
p
10
.
The general result is, that as the probability is less, the commodity assigned to each
day is less, so that v, its final degree of utility, will be greater.
So far we have taken no account of the varying influence of an event according to its
propinquity or remoteness. The distribution of commodity described is that which
should be made and would be made by a being of perfect good sense and foresight.
To secure a maximum of benefit in life, all future events, all future pleasures or pains,
should act upon us with the same force as if they were present, allowance being made
for their uncertainty. The factor expressing the effect of remoteness should, in short,
always be unity, so that time should have no influence. But no human mind is
constituted in this perfect way: a future feeling is always less influential than a present
one. To take this fact into account, let q
1
, q
2
, q
3
, etc., be the undetermined fractions
which express the ratios of the present pleasures or pains to those future ones from
whose anticipation they arise. Having a stock of commodity in hand, our tendency
will be to distribute it so that the following equations will hold true—
v
1
p
1
q
1
= v
2
p
2
q
2
= v
3
p
3
q
3
=... = v
n
p
n
q
n.
It will be an obvious consequence of these equations that less commodity will be
assigned to future days in some proportion to the intervening time.
An illustrative problem, involving questions of prospective utility and probability, is
found in the case of a vessel at sea, which is insufficiently victualled for the probable
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length of the voyage to the nearest port. The actual length of the voyage depends on
the winds, and must be uncertain; but we may suppose that it will almost certainly last
ten days or more, but not more than thirty days. It is apparent that if the food were
divided into thirty equal parts, partial famine and suffering would be certainly
endured for the first ten days, to ward off later evils which may not be encountered.
To consume one-tenth part of the food on each of the first ten days would be still
worse, as almost certainly entailing starvation on the following days. To determine the
most beneficial distribution of the food, we should require to know the probability of
each day between the tenth and thirtieth days forming part of the voyage, and also the
law of variation of the degree of utility of food. The whole stock ought then to be
divided into thirty portions, allotted to each of the thirty days, and of such magnitudes
that the final degrees of utility multiplied by the probabilities may be equal. Thus, let
v
1
, v
2
, v
3
, etc., be the final degrees of utility of the first, second, third, and other days
supplied, and p
1
, p
2
, p
3
, etc., the probabilities that the days in question will form part
of the voyage; then we ought to have
p
1
v
1
= p
2
v
2
= p
3
v
3
=... = p
29
v
29
= p
30
v
30
.
If these equations did not hold true, it would be beneficial to transfer a small portion
from one lot to some other lot. As the voyage is supposed certainly to last the first ten
days, we have
p
1
= p
2
=... = p
10
= 1:
hence we must have
v
1
= v
2
=... = v
10
:
that is to say, the allotments to the first ten days should be equal. They should
afterwards decrease according to some regular law; for, as the probability decreases,
the final degree of utility should increase in inverse proportion.
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CHAPTER IV
THEORY OF EXCHANGE
Importance Of Exchange In Economics.
EXCHANGE is so important a process in the maximising of utility and the saving of
labour, that some economists have regarded their science as treating of this operation
alone. Utility arises from commodities being brought in suitable quantities and at the
proper times into the possession of persons needing them; and it is by exchange, more
than any other means, that this is effected. Trade is not indeed the only method of
economising: a single individual may gain in utility by a proper consumption of the
stock in his possession. The best employment of labour and capital by a single person
is also a question disconnected from that of exchange, and which must yet be treated
in the science. But, with these exceptions, I am perfectly willing to agree with the
high importance attributed to exchange.
It is impossible to have a correct idea of the science of Economics without a perfect
comprehension of the Theory of Exchange; and I find it both possible and desirable to
consider this subject before introducing any notions concerning labour or the
production of commodities. In these words of J. S. Mill I thoroughly concur: "Almost
every speculation respecting the economical interests of a society thus constituted,
implies some theory of Value: the smallest error on that subject infects with
corresponding error all our other conclusions; and anything vague or misty in our
conception of it creates confusion and uncertainty in everything else." But when he
proceeds to say, "Happily, there is nothing in the laws of Value which remains for the
present or any future writer to clear up; the theory of the subject is complete"1 —he
utters that which it would be rash to say of any of the sciences.
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Ambiguity Of The Term Value.
I must, in the first place, point out the thoroughly ambiguous and unscientific
character of the term value. Adam Smith noticed the extreme difference of meaning
between value in use and value in exchange; and it is usual for writers on Economics
to caution their readers against the confusion of thought to which they are liable. But I
do not believe that either writers or readers can avoid the confusion so long as they
use the word. In spite of the most acute feeling of the danger, I often detect myself
using the word improperly; nor do I think that the best authors escape the danger.
Let us turn to Mill's definition of Exchange Value,1 and we see at once the misleading
power of the term. He tells us—"Value is a relative term. The value of a thing means
the quantity of some other thing, or of things in general, which it exchanges for."
Now, if there is any fact certain about exchange value, it is, that it means not an object
at all, but a circumstance of an object. Value implies, in fact, a relation; but if so, it
cannot possibly be some other thing. A student of Economics has no hope of ever
being clear and correct in his ideas of the science if he thinks of value as at all a thing
or an object, or even as anything which lies in a thing or object. Persons are thus led
to speak of such a nonentity as intrinsic value. There are, doubtless, qualities inherent
in such a substance as gold or iron which influence its value; but the word Value, so
far as it can be correctly used, merely expresses the circumstance of its exchanging in
a certain ratio for some other substance.
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Value Expresses Ratio Of Exchange.
If a ton of pig-iron exchanges in a market for an ounce of standard gold, neither the
iron is value nor the gold; nor is there value in the iron nor in the gold. The notion of
value is concerned only in the fact or circumstance of one exchanging for the other.
Thus it is scientifically incorrect to say that the value of the ton of iron is the ounce of
gold: we thus convert value into a concrete thing; and it is, of course, equally
incorrect to say that the value of the ounce of gold is the ton of iron. The more correct
and safe expression is, that the value of the ton of iron is equal to the value of the
ounce of gold, or that their values are as one to one.
Value in exchange expresses nothing but a ratio, and the term should not be used in
any other sense. To speak simply of the value of an ounce of gold is as absurd as to
speak of the ratio of the number seventeen. What is the ratio of the number seventeen?
The question admits no answer, for there must be another number named in order to
make a ratio; and the ratio will differ according to the number suggested. What is the
value of iron compared with that of gold?—is an intelligible question. The answer
consists in stating the ratio of the quantities exchanged.
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Popular Use Of The Term Value.
In the popular use of the word value no less than three distinct though connected
meanings seem to be confused together. These may be described as
(1)Value in use;
(2)Esteem, or urgency of desire;
(3)Ratio of exchange.
Adam Smith, in the familiar passage already referred to, distinguished between the
first and the third meanings. He said,1 "The word value, it is to be observed, has two
different meanings, and sometimes expresses the power of purchasing other goods
which the possession of that object conveys. The one may be called 'value in use;' the
other 'value in exchange.' The things which have the greatest value in use have
frequently little or no value in exchange; and, on the contrary, those which have the
greatest value in exchange have frequently little or no value in use. Nothing is more
useful than water: but it will purchase scarce anything; scarce anything can be had in
exchange for it. A diamond, on the contrary, has scarce any value in use; but a very
great quantity of other goods may frequently be had in exchange for it."
It is sufficiently plain that, when Smith speaks of water as being highly useful and yet
devoid of purchasing power, he means water in abundance, that is to say, water so
abundantly supplied that it has exerted its full useful effect, or its total utility. Water,
when it becomes very scarce, as in a dry desert, acquires exceedingly great purchasing
power. Thus Smith evidently means by value in use, the total utility of a substance of
which the degree of utility has sunk very low, because the want of such substance has
been well nigh satisfied. By purchasing power he clearly means the ratio of exchange
for other commodities. But here he fails to point out that the quantity of goods
received in exchange depends just as much upon the nature of the goods received, as
on the nature of those given for them. In exchange for a diamond we can get a great
quantity of iron, or corn, or paving stones, or other commodity of which there is
abundance; but we can get very few rubies, sapphires, or other precious stones. Silver
is of high purchasing power compared with zinc, or lead, or iron, but of small
purchasing power compared with gold, platinum, or iridium. Yet we might well say in
any case that diamond and silver are things of high value. Thus I am led to think that
the word value is often used in reality to mean intensity of desire or esteem for a
thing. A silver ornament is a beautiful object apart from all ideas of traffic; it may
thus be valued or esteemed simply because it suits the taste and fancy of its owner,
and is the only one possessed. Even Robinson Crusoe must have looked upon each of
his possessions with varying esteem and desire for more, although he was incapable
of exchanging with any other person. Now, in this sense value seems to be identical
with the final degree of utility of a commodity, as defined in a previous page (p. 49);
it is measured by the intensity of the pleasure or benefit which would be obtained
from a new increment of the same commodity. No doubt there is a close connection
between value in this meaning, and value as ratio of exchange. Nothing can have a
high purchasing power unless it be highly esteemed in itself; but it may be highly
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esteemed apart from all comparison with other things; and, though highly esteemed, it
may have a low purchasing power. because those things against which it is measured
are still more esteemed.
Thus I come to the conclusion that, in the use of the word value, three distinct
meanings are habitually confused together, and require to be thus distinguished—
(1) Value in use = total utility;
(2) Esteem = final degree of utility;
(3) Purchasing power = ratio of exchange.
It is not to be expected that we could profitably discuss such matters as economical
doctrines, while the fundamental ideas of the subject are thus jumbled up together in
one ambiguous word. The only thorough remedy consists in substituting for the
dangerous name value that one of three stated meanings which is intended in each
case. In this work, therefore, I shall discontinue the use of the word value altogether,
and when, as will be most often the case in the remainder of the book, I need to refer
to the third meaning, often called by economists exchange or exchangeable value, I
shall substitute the wholly unequivocal expression Ratio of exchange, specifying at
the same time what are the two articles exchanged. When we speak of the ratio of
exchange of pig-iron and gold, there can be no possible doubt that we intend to refer
to the ratio of the number of units of the one commodity to the number of units of the
other commodity for which it exchanges, the units being arbitrary concrete
magnitudes, but the ratio an abstract number.
When I proposed, in the first edition of this book, to use Ratio of Exchange instead of
the word value, the expression had been so little, if at all, employed by English
economists, that it amounted to an innovation. J. S. Mill, indeed, in his chapters on
Value, speaks once and again of things exchanging for each other "in the ratio of their
cost of production;" but he always omits to say distinctly that exchange value is itself
a matter of ratio. As to Ricardo, Malthus, Adam Smith, and other great English
economists, although they usually discourse at some length upon the meanings of the
word value, I am not aware that they ever explicitly apply the name ratio to exchange
or exchangeable value. Yet ratio is unquestionably the correct scientific term, and the
only term which is strictly and entirely correct.
It is interesting, therefore, to find that, although overlooked by English economists,
the expression had been used by two or more of the truly scientific French
economists, namely, Le Trosne and Condillac. Le Trosne carefully defines value in
the following terms:1 "La valeur consiste dans le rapport d'échange qui se trouve entre
telle chose et telle autre, entre telle mesure d'une production et telle mesure des
autres." Condillac apparently adopts the words of Le Trosne, saying1 of value:
"Qu'elle consiste dans le rapport d'échange entre telle chose et telle autre." Such
economical works as those of Baudeau, Le Trosne, and Condillac were almost wholly
unknown to English readers until attention was drawn to them by Mr. H. D. Mácleod
and Professor Adamson; but I shall endeavour for the future to make proper use of
them.
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Dimension Of Value.
There is no difficulty in seeing that, when we use the word Value in the sense of ratio
of exchange, its dimension will be simply zero. Value will be expressed, like angular
magnitude and other ratios in general, by abstract number. Angular magnitude is
measured by the ratio of a line to a line, the ratio of the are subtended by the angle to
the radius of the circle. So value in this sense is a ratio of the quantity of one
commodity to the quantity of some other commodity exchanged for it. If we compare
the commodities simply as physical quantities, we have the dimensions M divided by
M, or MM-1, or M0. Exactly the same result would be obtained if, instead of taking
the mere physical quantities, we were to compare their utilities, for we should then
have MU divided by MU or M0U0, which, as it really means unity, is identical in
meaning with M0.
When we use the word value in the sense of esteem, or urgency of desire, the feeling
with which Oliver Twist must have regarded a few more mouthfuls when he "asked
for more," the meaning of the word, as already explained, is identical with degree of
utility, of which the dimension is U. Lastly, the value in use of Adam Smith, or the
total utility, is the integral of U d M, and has the dimensions MU. We may thus
tabulate our results concerning the ambiguous uses of the word value—
Popular Expression of Meaning. Scientific Expression. Dimensions.
(1) Value in use Total Utility MU.
(2) Esteem, or Urgency of Desire for moreFinal Degree of UtilityU.
(3) Purchasing Power Ratio of Exchange M0.
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Definition Of Market.
Before proceeding to the Theory of Exchange, it will be desirable to place beyond
doubt the meanings of two other terms which I shall frequently employ.
By a Market I shall mean much what commercial men use it to express. Originally a
market was a public place in a town where provisions and other objects were exposed
for sale; but the word has been generalised, so as to mean any body of persons who
are in intimate business relations and carry on extensive transactions in any
commodity. A great city may contain as many markets as there are important
branches of trade, and these markets may or may not be localised. The central point of
a market is the public exchange,—mart or auction rooms, where the traders agree to
meet and transact business. In London, the Stock Market, the Corn Market, the Coal
Market, the Sugar Market, and many others, are distinctly localised; in Manchester,
the Cotton Market, the Cotton Waste Market, and others. But this distinction of
locality is not necessary. The traders may be spread over a whole town, or region of
country, and yet make a market, if they are, by means of fairs, meetings, published
price lists, the post office, or otherwise, in close communication with each other.
Thus, the common expression Money Market denotes no locality: it is applied to the
aggregate of those bankers, capitalists, and other traders who lend or borrow money,
and who constantly exchange information concerning the course of business.1
In Economics we may usefully adopt this term with a clear and well-defined meaning.
By a market I shall mean two or more persons dealing in two or more commodities,
whose stocks of those commodities and intentions of exchanging are known to all. It
is also essential that the ratio of exchange between any two persons should be known
to all the others. It is only so far as this community of knowledge extends that the
market extends. Any persons who are not acquainted at the moment with the
prevailing ratio of exchange, or whose stocks are not available for want of
communication, must not be considered part of the market. Secret or unknown stocks
of a commodity must also be considered beyond reach of a market so long as they
remain secret and unknown. Every individual must be considered as exchanging from
a pure regard to his own requirements or private interests, and there must be perfectly
free competition, so that any one will exchange with any one else for the slightest
apparent advantage. There must be no conspiracies for absorbing and holding supplies
to produce unnatural ratios of exchange. Were a conspiracy of farmers to withhold all
corn from market, the consumers might be driven, by starvation, to pay prices bearing
no proper relation to the existing supplies, and the ordinary conditions of the market
would be thus overthrown.
The theoretical conception of a perfect market is more or less completely carried out
in practice. It is the work of brokers in any extensive market to organise exchange, so
that every purchase shall be made with the most thorough acquaintance with the
conditions of the trade. Each broker strives to gain the best knowledge of the
conditions of supply and demand, and the earliest intimation of any change. He is in
communication with as many other traders as possible, in order to have the widest
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range of information, and the greatest chance of making suitable exchanges. It is only
thus that a definite market price can be ascertained at every moment, and varied
according to the frequent news capable of affecting buyers and sellers. By the
mediation of a body of brokers a complete consensus is established, and the stock of
every seller or the demand of every buyer brought into the market. It is of the very
essence of trade to have wide and constant information. A market, then, is
theoretically perfect only when all traders have perfect knowledge of the conditions of
supply and demand, and the consequent ratio of exchange; and in such a market, as
we shall now see, there can only be one ratio of exchange of one uniform commodity
at any moment.
So essential is a knowledge of the real state of supply and demand to the smooth
procedure of trade and the real good of the community, that I conceive it would be
quite legitimate to compel the publication of any requisite statistics. Secrecy can only
conduce to the profit of speculators who gain from great fluctuations of prices.
Speculation is advantageous to the public only so far as it tends to equalise prices; and
it is, therefore, against the public good to allow speculators to foster artificially the
inequalities of prices by which they profit. The welfare of millions, both of consumers
and producers, depends upon an accurate knowledge of the stocks of cotton and corn;
and it would, therefore, be no unwarrantable interference with the liberty of the
subject to require any information as to the stocks in hand. In Billingsgate fish market
there was long ago a regulation to the effect that salesmen shall fix up in a
conspicuous place every morning a statement of the kind and amount of their stock.1
The same principle has long been recognised in the Acts of Parliament concerning the
collection of statistics of the quantities and prices of corn sold in English market
towns. More recently similar legislation has taken place as regards the cotton trade, in
the Cotton Statistics Act of 1868. Publicity, whenever it can thus be enforced on
markets by public authority, tends almost always to the advantage of everybody
except perhaps a few speculators and financiers.
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Definition Of Trading Body.
I find it necessary to adopt some expression for any number of people whose
aggregate influence in a market, either in the way of supply or demand, we have to
consider. By a trading body I mean, in the most general manner, any body either of
buyers or sellers. The trading body may be a single individual in one case; it may be
the whole inhabitants of a continent in another; it may be the individuals of a trade
diffused through a country in a third. England and North America will be trading
bodies if we are considering the corn we receive from America in exchange for iron
and other goods. The continent of Europe is a trading body as purchasing coal from
England. The farmers of England are a trading body when they sell corn to the
millers, and the millers both when they buy corn from the farmers and sell flour to the
bakers.
We must use the expression with this wide meaning, because the principles of
exchange are the same in nature, however wide or narrow may be the market
considered. Every trading body is either an individual or an aggregate of individuals,
and the law, in the case of the aggregate, must depend upon the fulfilment of law in
the individuals. We cannot usually observe any precise and continuous variation in
the wants and deeds of an individual, because the action of extraneous motives, or
what would seem to be caprice, overwhelms minute tendencies. As I have already
remarked (p. 15), a single individual does not vary his consumption of sugar, butter,
or eggs from week to week by infinitesimal amounts, according to each small change
in the price. He probably continues his ordinary consumption until accident directs his
attention to a rise in price, and he then, perhaps, discontinues the use of the articles
altogether for a time. But the aggregate, or what is the same, the average
consumption, of a large community will be found to vary continuously or nearly so.
The most minute tendencies make themselves apparent in a wide average. Thus, our
laws of Economics will be theoretically true in the case of individuals, and practically
true in the case of large aggregates; but the general principles will be the same,
whatever the extent of the trading body considered. We shall be justified, then, in
using the expression with the utmost generality.
It should be remarked, however, that the economical laws representing the conduct of
large aggregates of individuals will never represent exactly the conduct of any one
individual. If we could imagine that there were a thousand individuals all exactly alike
in regard to their demand for commodities, and their capabilities of supplying them,
then the average laws of supply and demand deduced from the conduct of such
individuals would agree with the conduct of any one individual. But a community is
composed of persons differing widely in their powers, wants, habits, and possessions.
In such circumstances the average laws applying to them will come under what I have
elsewhere1 called the "Fictitious Mean," that is to say, they are numerical results
which do not pretend to represent the character of any existing thing. But average
laws would not on this account be less useful, if we could obtain them; for the
movements of trade and industry depend upon averages and aggregates, not upon the
whims of individuals.
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The Law Of Indifference.
When a commodity is perfectly uniform or homogeneous in quality, any portion may
be indifferently used in place of an equal portion: hence, in the same market, and at
the same moment, all portions must be exchanged at the same ratio. There can be no
reason why a person should treat exactly similar things differently, and the slightest
excess in what is demanded for one over the other will cause him to take the latter
instead of the former. In nicely-balanced exchanges it is a very minute scruple which
turns the scale and governs the choice. A minute difference of quality in a commodity
may thus give rise to preference, and cause the ratio of exchange to differ. But where
no difference exists at all, or where no difference is known to exist, there can be no
ground for preference whatever. If, in selling a quantity of perfectly equal and
uniform barrels of flour, a merchant arbitrarily fixed different prices on them, a
purchaser would of course select the cheaper ones; and where there was absolutely no
difference in the thing purchased, even an excess of a penny in the price of a thing
worth a thousand pounds would be a valid ground of choice. Hence follows what is
undoubtedly true, with proper explanations, that in the same open market, at any one
moment, there cannot be two prices for the same kind of article. Such differences as
may practically occur arise from extraneous circumstances, such as the defective
credit of the purchasers, their imperfect knowledge of the market, and so on.
The principle above expressed is a general law of the utmost importance in
Economics, and I propose to call it The Law of Indifference, meaning that, when two
objects or commodities are subject to no important difference as regards the purpose
in view, they will either of them be taken instead of the other with perfect indifference
by a purchaser. Every such act of indifferent choice gives rise to an equation of
degrees of utility, so that in this principle of indifference we have one of the central
pivots of the theory.
Though the price of the same commodity must be uniform at any one moment, it may
vary from moment to moment, and must be conceived as in a state of continual
change. Theoretically speaking, it would not usually be possible to buy two portions
of the same commodity successively at the same ratio of exchange, because, no sooner
would the first portion have been bought than the conditions of utility would be
altered. When exchanges are made on a large scale, this result will be verified in
practice.1 If a wealthy person invested £100,000 in the funds in the morning, it is
hardly likely that the operation could be repeated in the afternoon at the same price. In
any market, if a person goes on buying largely, he will ultimately raise the price
against himself. Thus it is apparent that extensive purchases would best be made
gradually, so as to secure the advantage of a lower price upon the earlier portions. In
theory this effect of exchange upon the ratio of exchange must be conceived to exist
in some degree, however small may be the purchases made. Strictly speaking, the
ratio of exchange at any moment is that of dy to dx, of an infinitely small quantity of
one commodity to the infinitely small quantity of another which is given for it. The
ratio of exchange is really a differential coefficient. The quantity of any article
purchased is a function of the price at which it is purchased, and the ratio of exchange
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expresses the rate at which the quantity of the article increases compared with what is
given for it.
We must carefully distinguish, at the same time, between the Statics and Dynamics of
this subject. The real condition of industry is one of perpetual motion and change.
Commodities are being continually manufactured and exchanged and consumed. If
we wished to have a complete solution of the problem in all its natural complexity, we
should have to treat it as a problem of motion—a problem of dynamics. But it would
surely be absurd to attempt the more difficult question when the more easy one is yet
so imperfectly within our power. It is only as a purely statical problem that I can
venture to treat the action of exchange. Holders of commodities will be regarded not
as continuously passing on these commodities in streams of trade, but as possessing
certain fixed amounts which they exchange until they come to equilibrium.
It is much more easy to determine the point at which a pendulum will come to rest
than to calculate the velocity at which it will move when displaced from that point of
rest. Just so, it is a far more easy task to lay down the conditions under which trade is
completed and interchange ceases, than to attempt to ascertain at what rate trade will
go on when equilibrium is not attained.
The difference will present itself in this form: dynamically we could not treat the ratio
of exchange otherwise than as the ratio of dy and dx, infinitesimal quantities of
commodity. Our equations would then be regarded as differential equations, which
would have to be integrated. But in the statical view of the question we can substitute
the ratio of the finite quantities y and x. Thus, from the self-evident principle, stated
on pp. 91, 92, that there cannot, in the same market, at the same moment, be two
different prices for the same uniform commodity, it follows that the last increments in
an act of exchange must be exchanged in the same ratio as the whole quantities
exchanged. Suppose that two commodities are bartered in the ratio of x for y; then
every mth part of x is given for the mth part of y, and it does not matter for which of
the mth parts. No part of the commodity can be treated differently to any other part.
We may carry this division to an indefinite extent by imagining m to be constantly
increased, so that, at the limit, even an infinitely small part of x must be exchanged for
an infinitely small part of y, in the same ratio as the whole quantities. This result we
may express by stating that the increments concerned in the process of exchange must
obey the equation
The use which we shall make of this equation will be seen in the next section.
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The Theory Of Exchange.
The keystone of the whole Theory of Exchange, and of the principal problems of
Economics, lies in this proposition—The ratio of exchange of any two commodities
will be the reciprocal of the ratio of the final degrees of utility of the quantities of
commodity available for consumption after the exchange is completed. When the
reader has reflected a little upon the meaning of this proposition, he will see, I think,
that it is necessarily true, if the principles of human nature have been correctly
represented in previous pages.
Imagine that there is one trading body possessing only corn, and another possessing
only beef. It is certain that, under these circumstances, a portion of the corn may be
given in exchange for a portion of the beef with a considerable increase of utility.
How are we to determine at what point the exchange will cease to be beneficial? This
question must involve both the ratio of exchange and the degrees of utility. Suppose,
for a moment, that the ratio of exchange is approximately that of ten pounds of corn
for one pound of beef: then if, to the trading body which possesses corn, ten pounds of
corn are less useful than one of beef, that body will desire to carry the exchange
further. Should the other body possessing beef find one pound less useful than ten
pounds of corn, this body will also be desirous to continue the exchange. Exchange
will thus go on until each party has obtained all the benefit that is possible, and loss of
utility would result if more were exchanged. Both parties, then, rest in satisfaction and
equilibrium, and the degrees of utility have come to their level, as it were.
This point of equilibrium will be known by the criterion, that an infinitely small
amount of commodity exchanged in addition, at the same rate, will bring neither gain
nor loss of utility. In other words, if increments of commodities be exchanged at the
established ratio, their utilities will be equal for both parties. Thus, if ten pounds of
corn were of exactly the same utility as one pound of beef, there would be neither
harm nor good in further exchange at this ratio.
It is hardly possible to represent this theory completely by means of a diagram, but the
accompanying figure may, perhaps, render it clearer. Suppose the line pqr to be a
small portion of the curve of utility of one commodity, while the broken line p'q is
the like curve of another commodity which has been reversed and superposed on the
other. Owing to this reversal, the quantities of the first commodity are measured along
the base line from a towards b, whereas those of the second must be measured in the
opposite direction. Let units of both commodities be represented by equal lengths:
then the little line áa indicates an increase of the first commodity, and a decrease of
the second. Assume the ratio of exchange to be that of unit for unit, or
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1 to 1: then, by receiving the commodity áa the person will gain the utility ad, and
lose the utility ác; or he will make a net gain of the utility corresponding to the
mixtilinear figure cd. He will, therefore, wish to extend the exchange. If he were to go
up to the point , and were still proceeding, he would, by the next small exchange,
receive the utility be, and part with b'f; or he would have a net loss of ef. He would,
therefore, have gone too far; and it is pretty obvious that the point of intersection, q,
defines the place where he would stop with the greatest advantage. It is there that a
net gain is converted into a net loss, or rather where, for an infinitely small quantity,
there is neither gain nor loss. To represent an infinitely small quantity, or even an
exceedingly small quantity, on a diagram is, of course, impossible; but on either side
of the line mq I have represented the utilities of a small quantity of commodity more
or less, and it is apparent that the net gain or loss upon the exchange of these
quantities would be trifling.
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Symbolic Statement Of The Theory.
To represent this process of reasoning in symbols, let Dx denote a small increment of
corn, and Dy a small increment of beef exchanged for it. Now our Law of Indifference
comes into play. As both the corn and the beef are homogeneous commodities, no
parts can be exchanged at a different ratio from other parts in the same market: hence,
if x be the whole quantity of corn given for y, the whole quantity of beef received, Dy
must have the same ratio to Dx as y to x: we have then,
In a state of equilibrium, the utilities of these increments must be equal in the case of
each party, in order that neither more nor less exchange would be desirable. Now the
increment of beef, Dy, is times as great as the increment of corn, Dx, so that, in
order that their utilities shall be equal, the degree of utility of beef must be times
as great as the degree of utility of corn. Thus we arrive at the principle that the
degrees of utility of commodities exchanged will be in the inverse proportion of the
magnitudes of the increments exchanged.
Let us now suppose that the first body, A, originally possessed the quantity a of corn,
and that the second body, B, possessed the quantity b of beef. As the exchange
consists in giving x of corn for y of beef, the state of things after exchange will be as
follows:—
A holds a - x of corn, and y of beef. B holds x of corn, and b - y of beef.
Let f
1
(a - x) denote the final degree of utility of corn to A, and f
2
x the corresponding
function for B. Also let y
1
y denote A's final degree of utility for beef, and y
2
(b - y)
B's similar function. Then, as explained on p. 96, A will not be satisfied unless the
following equation holds true:—
Hence, substituting for the second member by the equation given on p. 95, we have
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What holds true of A will also hold true of B, mutatis mutandis. He must also derive
exactly equal utility from the final increments, otherwise it will be for his interest to
exchange either more or less, and he will disturb the conditions of exchange.
Accordingly the following equation must hold true:—
y
2
(b - y). dy = f
2
x.dx:
or, substituting as before,
We arrive, then, at the conclusion, that whenever two commodities are exchanged for
each other, and more or less can be given or received in infinitely small quantities, the
quantities exchanged satisfy two equations, which may be thus stated in a concise
form—
The two equations are sufficient to determine the results of exchange; for there are
only two unknown quantities concerned, namely, x and y, the quantities given and
received.
A vague notion has existed in the minds of economical writers, that the conditions of
exchange may be expressed in the form of an equation. Thus, J. S. Mill has said:1
"The idea of a ratio, as between demand and supply, is out of place, and has no
concern in the matter: the proper mathematical analogy is that of an equation.
Demand and supply, the quantity demanded and the quantity supplied, will be made
equal." Mill here speaks of an equation as only a proper mathematical analogy. But if
Economics is to be a real science at all, it must not deal merely with analogies; it must
reason by real equations, like all the other sciences which have reached at all a
systematic character. Mill's equation, indeed, is not explicitly the same as any at
which we have arrived above. His equation states that the quantity of a commodity
given by A is equal to the quantity received by B. This seems at first sight to be a
mere truism, for this equality must necessarily exist if any exchange takes place at all.
The theory of value, as expounded by Mill, fails to reach the root of the matter, and
show how the amount of demand or supply is caused to vary. And Mill does not
perceive that, as there must be two parties and two quantities to every exchange, there
must be two equations.
Nevertheless, our theory is perfectly consistent with the laws of supply and demand;
and if we had the functions of utility determined, it would be possible to throw them
into a form clearly expressing the equivalence of supply and demand. We may regard
x as the quantity demanded on one side and supplied on the other; similarly, y is the
quantity supplied on the one side and demanded on the other. Now, when we hold the
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two equations to be simultaneously true, we assume that the x and y of one equation
equal those of the other. The laws of supply and demand are thus a result of what
seems to me the true theory of value or exchange.
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Analogy To The Theory Of The Lever.
I have heard objections made to the general character of the equations employed in
this book. It is remarked that the equations in question continually involve
infinitesimal quantities, and yet they are not treated as differential equations usually
are, that is integrated. There is, indeed, no reason why the process of integration
should not be applied when it is required, and I will here show that the equations
employed do not differ in general character from those which are really treated in
many branches of physical science. Whenever, in fact, we deal with continuously
varying quantities, the ultimate equations must lie between infinitesimals. The process
of integration, if I understand the matter aright, only ascertains other equations, the
truth of which follows from the fundamental differential equation.
The mode in which mechanies is usually treated in elementary work tends to disguise
the real foundation of the science which is to be found in the so-called theory of
virtual velocities. Let us take the description of the lever of the first order as it is given
in some of the best modern elementary works, as, for instance, in Mr. Magnus's
Lessons in Elementary Mechanics, p. 128. We here read as follows:—
"Let AB be a lever turning freely about C, the fulcrum, and let P be the force applied
at A, and W the force exerted, or resistance overcome, or weight raised at B. Suppose
the lever turned through the angle ACA', then the work done by P equals P × are AA',
and work done by W equals W × arc BB', if P and W act perpendicularly to the arm.
Therefore, by the law of energy,
P × AA' = W × BB', and since
we have P × AC = W × BC,
or, P × its arm = W × its arm."
Now, in such a statement as this, we seem to be dealing with plain finite quantities,
and there is no apparent difficulty in the matter. In reality the difficulty is only
disguised by assuming that P and W act perpendicularly to the arm through finite arcs.
This condition is, indeed, carried out with approximate exactness in the problem of
the wheel and axle,1 which may be regarded as combining together an infinite series
of straight levers, coming successively into operation. In this machine, therefore, the
weights, roughly speaking, always act perpendicularly to arms of invariable length.
But, in the generality of cases of the lever, the theory is only true for infinitely small
displacements, and no sooner has the lever begun to move through any finite arc AA',
than it ceases to be exactly true that the work done by P equals P × arc AA'.
Nevertheless, the theory is quite correct as applied to the lever considered statically,
that is, as in a state of rest and equilibrium, because the finite arcs of displacement,
when it really is displaced, are exactly proportional to the infinitely small arcs, known
as virtual velocities, through which it would be displaced, if instead of being at rest, it
suffered an infinitely small displacement.
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It is curious, moreover, that, when we take the theory of the lever treated according to
the principle of virtual velocities, we get equations exactly similar in form to those of
the theory of value as established above. The general principle of virtual velocities is
to the effect that, if any number of forces be in equilibrium at one or more points of a
rigid body, and if this body receive an infinitely small displacement, the algebraic
sum of the products of each force into its displacement is equal to zero. In the case of
a lever of the first order, this amounts to saying that one force multiplied into its
displacement will be neutralised by the other force multiplied into its negative
displacement. But inasmuch as the displacements are exactly proportional to the
lengths of the arms of the lever, we obtain as a derivative equation, that the forces
multiplied each by its own arm are equal to each other. No doubt in the quotation
given above, P × AC = W × BC is an equation between finite quantities; but the real
equation derived immediately from the principle of virtual velocities, is P × AA' = W
× BB', in which P and W are finite, but AA' and BB' are in strictness infinitely small
displacements. Let us write this equation in the form
then as we also have
we can substitute; hence
I dwell upon this matter at some length because we here have exactly the forms of the
equations of exchange. As we have seen, the original equation is of the general form
where fx and yy represent finite expressions for the degrees of utility of the
commodities Y and X, as regards some individual, and dy and dx are infinitesimal
quantities of those commodities exchanged. But these infinitesimals may in this case
at least be eliminated, because, in virtue of the Law of Indifference, they are exactly
proportional to the whole finite quantities exchanged. Hence for we substitute
. We may write the equations one below the other, so as to make the analogy
visible—thus
To put this analogy of the theories of exchange and of the lever in the clearest
possible light, I give below a diagram, in which the several economic qualities are
represented by the parts of the diagram to which they correspond or are proportional.
Now in statical problems no such process as integration is applicable. The equation
lies actually between imaginary infinitesimal quantities, and there is no effect to be
summed up. Yet there is no statical problem which is not subject to the principle of
virtual velocities, and Poisson, in his Traité de Mécanique,
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Impediments To Exchange.
We have hitherto treated the theory of exchange as if the action of exchange could be
carried on without trouble or cost. In reality, the cost of conveyance is almost always
of importance, and it is sometimes the principal element in the question. To the cost
of mere transport must be added a variety of charges of brokers, agents, packers,
dock, harbour, light dues, etc., together with any customs duties imposed either on the
importation or exportation of commodities. All these charges, whether necessary or
arbitrary, are so many impediments to commerce, and tend to reduce its advantages.
The effect of any one such charge, or of the aggregate of the costs of exchange, can be
represented in our formulæ in a very simple manner.
In whatever mode the charges are payable, they may be conceived as paid by the
surrender on importation of a certain fraction of the commodity received; for the
amount of the charges will usually be proportional to the quantity of goods, and, if
expressed in money, can be considered as turned into commodity.
Thus, if A gives x in exchange, this is not the quantity received by B; a part of x is
previously subtracted, so that B receives say mx, which is less than x, and the terms of
exchange must be adjusted on his part so as to agree with this condition. Hence the
second equation will be
Again, A, though giving x, will not receive the whole of y; but say ny, so that his
equation similarly will be
The result is, that there is not one ratio of exchange, but two ratios; and the more these
differ, the less advantage will there be in exchange. It is obvious that A has either to
remain satisfied with less of the second commodity than before, or has to give more of
his own in purchasing it. By an obvious transfer of the factors m and n we may state
the equations of impeded exchange in the concise form—
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Illustrations Of The Theory Of Exchange.
As stated above, the Theory of Exchange may seem to be of a somewhat abstract and
perplexing character; but it is not difficult to find practical illustrations which will
show how it is verified in the actual working of a great market. The ordinary laws of
supply and demand, when properly stated, are the practical manifestation of the
theory. Considerable discussion has taken place concerning these laws, in
consequence of Mr. W. T. Thornton's writings upon the subject in the Fortnightly
Review, and in his work on the Claims of Labour. Mill, although he had previously
declared the Theory of Value to be complete and perfect (see p. 76), was led by Mr.
Thornton's arguments to allow that modification was required.
For my own part, I think that most of Mr. Thornton's arguments are beside the
question. He suggests that there are no regular laws of supply and demand, because he
adduces certain cases in which no regular variation can take place. Those cases might
be indefinitely multiplied, and yet the laws in question would not be touched. Of
course, laws which assume a continuity of variation are inapplicable where
continuous variation is impossible. Economists can never be free from difficulties
unless they will distinguish between a theory and the application of a theory.
Because, in retail trade, in English or Dutch auction, or other particular modes of
traffic, we cannot at once observe the operation of the laws of supply and demand, it
is not in the least to be supposed that those laws are false. In fact, Mr. Thornton seems
to allow that, if prospective demand and supply are taken into account, they become
substantially true. But, in the actual working of any market, the influence of future
events should never be neglected, neither by a merchant nor an economist.
Though Mr. Thornton's objections are mostly beside the question, his remarks have
served to show that the action of the laws of supply and demand was inadequately
explained by previous economists. What constitutes the demand and the supply was
not carefully enough investigated. As Mr. Thornton points out, there may be a number
of persons willing to buy; but if their highest offer is ever so little short of the lowest
price which the seller is willing to take, their influence is nil. If in an auction there are
ten people willing to buy a horse at £20, but not higher, their demand instantly ceases
when any one person offers £21. I am inclined not only to accept such a view, but to
carry it further. Any change in the price of an article will be determined not with
regard to the large numbers who might or might not buy it at other prices, but by the
few who will or will not buy it according as a change is made close to the existing
price.
The theory consists in carrying out this view to the point of asserting that it is only
comparatively insignificant quantities of supply and demand which are at any moment
operative on the ratio of exchange. This is practically verified by what takes place in
any very large market—say that of the Consolidated Three Per Cent Annuities. As the
whole amount of the English funds is nearly eight hundred millions sterling, the
quantity bought or sold by any ordinary purchaser is inconsiderably small in
comparison. Even £1000 worth of stock may be taken as an infinitesimally small
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increment, because it does not appreciably affect the total existing supply. Now the
theory consists in asserting that the market price of the funds is affected from hour to
hour not by the enormous amounts which might be bought or sold at extreme prices,
but by the comparatively insignificant amounts which are being sold or bought at the
existing prices. A change of price is always occasioned by the overbalancing of the
inclinations of those who will or will not sell just about the point at which prices
stand. When Consols are at 93½, and business is in a tranquil state, it matters not how
many buyers there are at 93, or sellers at 94. They are really off the market. Those
only are operative who may be made to buy or sell by a rise or fall of an eighth. The
question is, whether the price shall remain at 93½, or rise to , or fall to .
This is determined by the sale or purchase of comparatively very small amounts. It is
the purchasers who find a little stock more profitable to them than the corresponding
sum of money who make the price rise by . When the price of the funds is very
steady and the market quiescent, it means that the stocks are distributed among
holders in such a way that the exchange of more or less at the prevailing price is a
matter of indifference.
In practice, no market ever long fulfils the theoretical conditions of equilibrium,
because, from the various accidents of life and business, there are sure to be people
every day compelled to sell, or having sudden inducements to buy. There is nearly
always, again, the influence of prospective supply or demand, depending upon the
political intelligence of the moment. Speculation complicates the action of the laws of
supply and demand in a high degree, but does not in the least degree arrest their action
or alter their nature. We shall never have a Science of Economics unless we learn to
discern the operation of law even among the most perplexing complications and
apparent interruptions.
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Problems In The Theory Of Exchange.
We have hitherto considered only one simple case of the Theory of Exchange. In all
other cases where the commodities are capable of indefinite subdivision, the
principles will be exactly the same, but the particular conditions may be subject to
variation.
We may, firstly, express the conditions of a great market where vast quantities of
some stock are available, so that any one small trader will not appreciably affect the
ratio of exchange. This ratio is, then, approximately a fixed number, and each trader
exchanges at that ratio just so much as suits him. These circumstances may be
represented by supposing A to be a trading body possessing two very large stocks of
commodities, a and b. Let C be a person who possesses a comparatively small
quantity c of the second commodity, and gives a portion of it, y, which is very small
compared with b, in exchange for a portion x of a, which is very small compared with
a. Then, after exchange, we shall find A in possession of the quantities a - x and b + y,
and C in possession of x and c - y. The equations will become
Since a - x and b + y, by supposition, do not appreciably differ from a and b, we may
substitute the latter quantities, and we have, for the first equation, approximately,
The ratio of exchange being an approximately fixed ratio determined by the
conditions of the trading body A, there is, in reality, only one undetermined quantity,
x, the quantity of commodity which C finds it advantageous to purchase by expending
part of c. This will now be determined by the equation
This equation will represent the condition in regard to any one distinct commodity of
a very small country trading with a much larger one. It might represent, to some
extent, the circumstances of trade between the Channel Islands and the great markets
of England, though, of course, it is never absolutely verified, because the smallest
purchasers do affect the market in some degree. The equation still more accurately
represents the position of an individual consumer with regard to the aggregate trade of
a large community, since he must buy at the current prices, which he cannot in an
appreciable degree affect.
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A still simpler formula, however, is needed to represent the conditions of a large part
of our purchases. In many cases we want so little of a commodity, that an individual
need not give more than a very small fraction of his possessions to obtain it. We may
suppose, then, that y in the last problem is a very small part of c, so that y
2
(c - y) does
not differ appreciably from y
2
c. Taking m as before to be the existing ratio of
exchange, we have only one equation—
This means that C will buy of the commodity until its degree of utility falls below that
of the commodity he gives. A person's expenditure on salt is in this country an
inconsiderable item of expense; what he thus spends does not make him appreciably
poorer; yet, if the established price or ratio is one penny for each pound of salt, he
buys in any time, say one year, so many pounds of salt that an additional pound would
not have so much utility to him as a penny. In the above equation m. y
2
c represents
the utility to him of a penny, which being an inconsiderable fraction of his
possessions, is approximately invariable in utility, and he buys salt until f
2
x, which is
approximately the utility of the next pound, is equal to, or it may be somewhat less
than that of the penny. But this case must not be confused with that of purchases
which appreciably affect the possessions of the purchaser. Thus, if a poor family
purchase much butchers'-meat, they will probably have to go without something else.
The more they buy, the lower the final degree of utility of the meat, and the higher the
final degree of utility of something else; and thus these purchases will be the more
narrowly limited.
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Complex Cases Of The Theory.
We have hitherto considered the Theory of Exchange as applying only to two trading
bodies possessing and dealing in two commodities. Exactly the same principles hold
true, however numerous and complicated may be the conditions. The main point to be
remembered in tracing out the results of the theory is, that the same pair of
commodities in the same market can have only one ratio of exchange, which must
therefore prevail between each body and each other, the costs of conveyance being
considered as nil. The equations become rapidly more numerous as additional bodies
or commodities are considered; but we may exhibit them as they apply to the case of
three trading bodies and three commodities.
Thus, suppose that
A possesses the stock a of cotton, and gives x
1
of it to B, x
2
to C.
B possesses the stock b of silk, and gives y
1
to A, y
2
to C.
C possesses the stock c of wool, and gives z
1
to A, z
2
to B.
We have here altogether six unknown quantities—x
1
, x
2
, y
1
, y
2
, z
1
, z
2
; but we have
also sufficient means of determining them. They are exchanged as follows—
A gives x
1
for y
1
, and x
2
for z
1
.
B gives 'y
1
for x
1
, and y
2
for z
2
.
C gives z
1
for x
2
, and z
2
for y
2
.
These may be treated as independent exchanges; each body must be satisfied in regard
to each of its exchanges, and we must therefore take into account the functions of
utility or the final degrees of utility of each commodity in respect of each body. Let us
express these functions as follows—
f
1
, y
1
, c
1
are the respective functions of utility for A.
f
2
, y
2
, c
2
are the respective functions of utility for B.
f
3
, y
3
, c
3
are the respective functions of utility for C.
Now A, after the exchange, will hold a - x
1
- x
2
of cotton and y
1
of silk; and B will
hold x
1
of cotton and b - y
1
- y
2
of silk: their ratio of exchange, y
1
for x
1
, will
therefore be governed by the following pair of equations:—
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The exchange of A with C will be similarly determined by the ratio of the degrees of
utility of wool and cotton on each side subsequent to the exchange; hence we have
There will also be interchange between B and C which will be independently
regulated on similar principles, so that we have another pair of equations to complete
the conditions, namely—
We might proceed in the same way to lay down the conditions of exchange between
more numerous bodies, but the principles would be exactly the same. For every
quantity of commodity which is given in exchange something must be received; and if
portions of the same kind of commodity be received from several distinct parties, then
we may conceive the quantity which is given for that commodity to be broken up into
as many distinct portions. The exchanges in the most complicated case may thus
always be decomposed into simple exchanges, and every exchange will give rise to
two equations sufficient to determine the quantities involved. The same can also be
done when there are two or more commodities in the possession of each trading body.
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Competition In Exchange.
One case of the Theory of Exchange is of considerable importance, and arises when
two parties compete together in supplying a third party with a certain commodity.
Thus, suppose that A, with the quantity of one commodity denoted by a, purchases
another kind of commodity both from B and from C, who respectively possess b and c
of it. All the quantities concerned are as follows—
A gives x
1
of a to B and x
2
to C,
B gives y
1
of b to A,
C gives y
2
of c to A.
As each commodity may be supposed to be perfectly homogeneous, the ratio of
exchange must be the same in one case as in the other, so that we have one equation
thus furnished—
Now, provided that A gets the right commodity in the proper quantity, he does not
care whence it comes, so that we need not, in his equation, distinguish the source or
destination of the quantities; he simply gives x
1
+ x
2
, and receives in exchange y
1
+
y
2
. Observing, then, that by (1)
we have the usual equation of exchange—
But B and C must both be separately satisfied with their shares in the transaction.
Thus
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There are altogether four unknown quantities—x
1
, x
2
, y
1
, y
2
; and we have four
equations by which to determine them. Various suppositions might be made as to the
comparative magnitudes of the quantities b and c, or the character of the functions
concerned; and conclusions could then be drawn as to the effect upon the trade. The
general result would be, that the smaller holder must more or less conform to the
prices of the larger holder.
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Failure Of The Equations Of Exchange.
Cases constantly occur in which equations of the kind set forth in the preceding pages
fail to hold true, or lead to impossible results. Such failure may indicate that no
exchange at all takes place, but it may also have a different meaning.
In the first case, it may happen that the commodity possessed by A has a high degree
of utility to A, and a low degree to B, and that vice versâ B's commodity has a high
degree of utility to B and less to A. This difference of utility might exist to such an
extent, that though B were to receive very little of A's commodity, yet the final degree
of utility to him would be less than that of his own commodity, of which he enjoys
much more. In such a case no benefit can arise from exchange, and no exchange will
consequently take place. This failure of exchange will be indicated by a failure of the
equations.
It may also happen that the whole quantities of commodity possessed are exchanged,
and yet the equations fail. A may have so low a desire for consuming his own
commodity, that the very last increment of it has less degree of utility to him than a
small addition to the commodity received in exchange. The same state of things might
happen to exist with B as regards his commodity: under these circumstances the
whole possessions of one might be exchanged for the whole of the other, and the ratio
of exchange would of course be defined by the ratio of these quantities. Yet each
party might desire the last increment of the commodity received more than he desires
the last increment of that given, so that the equations would fail to be true. This case
will hardly occur practically in international trade, since two nations usually trade in
many commodities, a fact which would alter the conditions.
Again, the equations of exchange will fail to be possible when the commodity or
useful article possessed on one or both sides is indivisible. We have always assumed
hitherto that more or less of a commodity may be had, down to infinitely small
quantities. This is approximately true of all ordinary trade, especially international
trade between great industrial nations. Any one sack of corn or any one bar of iron is
practically infinitesimal compared with the quantities exchanged by America and
England; and even one cargo or parcel of corn or iron is a small fraction of the whole.
But, in exceptional cases, even international trade might involve indivisible articles.
We might conceive the British Government giving the Koh-i-noor diamond to the
Khedive of Egypt in exchange for Pompey's Pillar, in which case it would certainly
not answer the purpose to break up one article or the other.1 When an island or
portion of territory is transferred from one possessor to another, it is often necessary
to take the whole, or none. America, in purchasing Alaska from Russia, would hardly
have consented to purchase less than the whole. In every sale of a house, factory, or
other building, it is usually impracticable to make any division without greatly
lessening the utility of the whole. In all such cases our equations must fail to exist,
because we cannot contemplate the existence of an increment or a decrement to an
indivisible article.
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Suppose, for example, that A and B each possess a book: they cannot break up the
books, and must therefore exchange them entire, if at all. Under what conditions will
they do so? Plainly on the condition that each makes a gain of utility by so doing.
Here we deal not with the final degree of utility depending on an infinitesimal
quantity, but on the whole utility of the complete article. Now let us assign the
symbols as follows:—
u
1
= theutility ofA's book to A,
u
2
= theutility ofA's book to B,
v
1
= the utility ofB's book to A,
v
2
= the utility ofB's book to B.
Then the conditions of exchange are simply
v
1
> u
1
,
u
2
> v
2
.
We might indeed theoretically contemplate the case where the utilities were exactly
equal on one side; thus
v
1
> u
1
,
u
2
= v
2
;
B would then be wholly indifferent to the exchange, and I do not see any means of
deciding whether he would or would not consent to it. But we need hardly consider
the case, as it could seldom practically occur. Were the utilities exactly equal on both
sides in respect to both objects, there would obviously be no motive to exchange.
Again, the slightest loss of utility on either side would be a complete bar to the
transaction, because we are not supposing, at present, that any other commodities are
in possession so as to allow of separate inducements, or that any other motives than
such as arise out of simple desire of one's own convenience enter into the question.
A much more difficult problem arises when we suppose an indivisible article
exchanged for a divisible commodity. When Russia sold Alaska this was a practically
indivisible thing; but it was bought with money of which more or less might be given
to indefinitely small quantities. A bargain of this kind is exceedingly common; indeed
it occurs in the case of every house, mansion, estate, factory, ship, or other complete
whole, which is sold for money. Our former equations of exchange certainly fail, for
they involve increments of commodity on both sides. The theory seems to give a very
unsatisfactory answer, for the problem proves to be, within certain limits,
indeterminate.
Let X be the indivisible article; u
1
its utility to its possessor A, and u
2
its utility to B.
Let y be the quantity of commodity given for it, a commodity which is supposed to be
divisible ad infinitum; let v
1
be the total utility of y to A, and v
2
its total utility to B.
Then it is quite evident that, in order to give rise to exchange, v
1
must be greater than
u
1
, and u
2
must be greater than v
2
; that is, there must, as before, be a gain of utility on
each side. The quantity y must not be so great then as to deprive B of gain, nor so
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small as to deprive A of gain. The following is an extract from Mr. Thornton's work
which exactly expresses the problem:—
"There are two opposite extremes—one above which the price of a commodity cannot
rise, the other below which it cannot fall. The upper of these limits is marked by the
utility, real or supposed, of the commodity to the customer; the lower, of its utility to
the dealer. No one will give for a commodity a quantity of money or money's worth,
which, in his opinion, would be of more use to him than the commodity itself. No one
will take for a commodity a quantity of money or of anything else which he thinks
would be of less use to himself than the commodity. The price eventually given and
taken may be either at one of the opposite extremes, or may be anywhere intermediate
between them."1
Three distinct cases might occur, which can best be illustrated by a concrete example.
Suppose we can read the thoughts of the parties in the sale of a house. If A says £1200
is the least price which will satisfy him, and B holds that £800 is the highest price
which it will be profitable for him to give, no exchange can possibly take place. If A
should find £1000 to be his lowest limit, while B happens to name the same sum for
his highest limit, the transaction can be closed, and the price will be exactly defined.
But supposing, finally, that A is really willing to sell at £900, and B is prepared to buy
at £1100, in what manner can we theoretically determine the price? I see no mode of
solving the question. Any price between £900 and £1100 will leave a profit on each
side, and both parties will lose if they do not come to terms. I conceive that such a
transaction must be settled upon other than strictly economical grounds. The result of
the bargain will greatly depend upon the comparative amount of knowledge of each
other's positions and needs which either bargainer may possess or manage to obtain in
the course of the transaction. Thus the power of reading another man's thoughts is of
high importance in business, and the art of bargaining mainly consists in the buyer
ascertaining the lowest price at which the seller is willing to part with his object,
without disclosing if possible the highest price which he, the seller, is willing to give.
The disposition and force of character of the parties, their comparative persistency,
their adroitness and experience in business, or it may be feelings of justice or of
kindliness, will also influence the decision. These are motives more or less extraneous
to a theory of Economics, and yet they appear necessary considerations in this
problem. It may be that indeterminate bargains of this kind are best arranged by an
arbitrator or third party.
The equations of exchange may fail again when commodities are divisible, but not to
infinitely small quantities. There is always, in retail trade, a convenient unit below
which we do not descend in purchases. Paper may be bought in quires, or even in
packets, which it may not be desirable to break up. Wine cannot be bought from the
wine merchant in less than a bottle at a time. In all such cases exchange cannot,
theoretically speaking, be perfectly adjusted, because it will be infinitely improbable
that an integral number of units will precisely verify the equations of exchange. In a
large proportion of cases, indeed, the unit may be so small compared with the whole
quantities exchanged as practically to be infinitely small. But suppose that a person be
buying ink which is only to be had, under the circumstances, in one shilling bottles. If
one bottle be not quite enough, how will he decide whether to take a second or not?
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Clearly by estimating the aggregate utility of the bottle of ink compared with the
shilling. If there be an excess, he will certainly purchase it, and proceed to consider
whether a third be desirable or not.
This case might be illustrated by Fig. VI., in which the spaces o q
1
, p
1
q
2
, p
2
q
3
, etc.,
represent the total utilities of successive bottles of ink; while the equal spaces o r
1
,
p
1
r
2
, etc., represent the total utilities of successive shillings, which we may assume to
be practically invariable. There is no doubt that three bottles will be
purchased, but the fourth will not be purchased unless the mixtilinear figure p
3
q
3
q
4
p
4
exceed in area the rectangle p
3
r
3
r
4
p
4
.
Cases of this kind are similar to those treated in pp. 120-124, where the things
exchanged are indivisible, except that the question of exchange or no exchange occurs
over and over again with respect to each successive unit, and is decided in respect to
each by the excess of the total utility of the unit to be received over the total utility of
that to be given. There is indeed perfect harmony between the cases where equations
can and where they cannot be established; for we have only to imagine the indivisible
units of commodity to be indefinitely lessened in size to enable us to pass gradually
down to the case where equality of the increments of utility is ultimately established.
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Negative And Zero Value.
Only a few economists, notably Mr. H. D. Macleod in several of his publications,
have noticed the fact that there may be such a thing as negative value. Yet there
cannot be the least doubt that people often labour, or pay money to other labourers, in
order to get rid of things, and they would not do this unless such things were hurtful,
that is, had the opposite quality to utility—disutility. Water, when it gets into a mine,
is a costly thing to get out again, and many people have been ruined by wet mines.
Quarries and mines usually produce great quantities of valueless rock or earth,
variously called duff, spoil, waste, rubbish, and no inconsiderable part of the cost of
working arises from the need of raising and carrying this profitless mass of matter and
then finding land on which to deposit it. Every furnace yields cinders, dross, or slag,
which can seldom be sold for any money, and every household is at the expense of
getting rid, in one way or another, of sewage, ashes, swill, and other rejectanea.
Reflection soon shows, in short, that no inconsiderable part of the values with which
we deal in practical economics must be negative values.
It will hardly be needful to show at full length that this negative value may be
regarded as varying continuously in the same way as positive value. If after a long
drought rain begins to fall heavily, it is at first hailed as a great benefit; the rain-water
may be so valuable as to produce a crop, when otherwise successful agriculture would
have been impossible. Rain may thus avert famine; but after the rain has fallen for a
certain length of time, the farmer begins to think he has had enough of it; more rain
will retard his operations, or injure the growing plants. As the rain continues to fall he
fears further injury; water begins to flood his land, and there is even danger of the soil
and crops being all washed away together. But the rain unfortunately pours down
more and more heavily, until at length perhaps the crops, soil, house, stock,—nay, the
farmer himself, are all swept bodily away. That same water, then, which in moderate
quantity would have been of the greatest possible benefit, has only to be supplied in
greater and greater quantities to become injurious, until it ends with occasioning the
ruin, and even the death, of the individual. Those acquainted with the floods and
droughts of Australia know that this is no fancy sketch.1
In many other cases it might be shown similarly that matter, we can hardly call it
commodity, acquires a higher and higher degree of disutility the greater the quantity
which has to be disposed of. Such is the case with the sewage of great towns, the foul
or poisoned water from mines, dye-works, etc. Any obstacle, however, may be
regarded as so much discommodity, whether it be a mountain which has to be bored
through to make a railway, or a hollow which has to be filled up with an expensive
embankment. If a building site requires a certain expenditure in levelling and draining
before it can be made use of, the cost of this work is, of course, subtracted from the
value which the land would otherwise possess. As every advantage in property gives
rise to value, so every disadvantage must be set against that value.
We now come to the question how negative value is to be represented in our
equations. Let us suppose a person possessing a of some commodity to find it
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insufficient: then it has positive degree of utility for him, that is to say f(a) is positive.
Suppose x to be added to a and gradually increased: f(a + x) will gradually decrease.
Let us assume that for a certain value of x it becomes zero; then, if the further increase
of x turns utility into disutility, f(a + x) will become a negative quantity. How will this
negative sign affect the validity of the equations which we have been employing in
preceding pages, and in which each member has appeared to be both formally and
intrinsically positive? It is plain that we cannot equate a positive to a negative
quantity; but it will be found that if, at the same time that we introduce negative
utility, we also assign to each increment of commodity the positive or negative sign,
according as it is added to or subtracted from the exchanger's possessions, that is to
say, received or given in exchange, no such difficulty arises.
Suppose A and B respectively to hold a and b, and to exchange dx and dy of the
commodities X and Y. Then it will be apparent from the general character of the
argument on pp. 98-100, that the fundamental equation there adopted will be included
in the more general form—
In this equation either factor of either term may be intrinsically negative, while the
alternative signs before x and y allow for every possible case of giving and receiving
in exchange.
Four possible cases will arise. In the first case, both commodities have utility for each
person, that is to say, f and y are both positive functions; but A gives some of X in
return for some of Y. This means that dx is negative, and dy positive, while the
quantities in possession after exchange are a - x, and b+y. Thus the equation becomes
We should have merely to transpose the negative term to the other side of the
equation, and to assume b = 0, to obtain the equation on p. 99.
As the second case, suppose that Y possesses disutility for A, so that the function y
becomes for him negative; in order to get rid of y, he must also pay x with it, and both
these quantities as well as dy and dx receive the negative sign. Then the equation takes
the shape
The third case is the counterpart of the last, and represents B's position, who receives
both x and y, on the ground that one of these quantities is discommodity to him. But
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putting the matter as the case of A, we may assume f to be positive, y negative, and
giving the positive sign to all of x,y,dx, and dy, we obtain the equation—
It is possible to conceive yet a fourth case in which people should be exchanging two
discommodities; that is to say, getting rid of one hurtful substance by accepting in
place of it what is felt to be less hurtful, though still possessing disutility. In this case
we have both f and y negative, as well as one of the quantities exchanged; taking x
and dx as positive, and y and dy as negative, the equation assumes the form
It might be difficult to discover any distinct cases of this last kind of exchange.
Generally speaking, when a person receives assistance in getting rid of some
inconvenient possession, he pays in money or other commodity for the service of him
who helps to remove the burden. It must naturally be a very rare case that the remover
has some burden which it would suit the other party to receive in exchange. Yet the
contingency may, and no doubt does, sometimes occur. Two adjacent landowners, for
instance. might reasonably agree that, if A allows B to throw the spoil of his mine on
A's land, then A shall be allowed to drain his mine into B's mine. It might happen that
B was comparatively more embarrassed by the great quantity of his spoil than by
water, and that A had room for the spoil, but could not get rid of the water in other
ways without great difficulty. An exchange of inconveniences would then be plainly
beneficial.
Looking at the equations obtained in the four cases as stated above, it is apparent that
the general equation of exchange consists in equating to zero the sum of one positive
and one negative term, so that the signs, both of the utility functions and of the
increments, may be disregarded. Thus the fundamental equation may be written in the
general form
We may express the result of this theory in general terms by saying that the algebraic
sum of the utility or disutility received or parted with, as regards the last increments
concerned in an act of traffic, will always be zero. It also follows that, without regard
to sign, the increments are in magnitude inversely as their degrees of utility or
disutility. The reader will not fail to notice the remarkable analogy between this
theory and that of the equilibrium of two forces regarded according to the principle of
virtual velocities. A rigid lever will remain in equilibrium under the action of two
forces, provided that the algebraic sum of the forces, each multiplied by its infinitely
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small displacement, be zero. Substitute for force degree of utility, positive or negative,
and for infinitely small displacements infinitely small quantities of commodity
exchanged, and the principles are identical.
It still remains to consider the imaginary case in which substances possess or are
supposed to possess neither utility nor disutility, and are yet exchanged in finite
quantities. Substituting the ratio of y and x for that of dy and dx, the general equation
will give the value
both the functions of utility being zero. This means that the quantities exchanged will
be indeterminate so far as the theory of utility goes. If one substance possesses utility,
and the other does not, the ratio of exchange becomes either , infinity or
zero, indicating that there can be no comparison in our theory between things which
do and those which do not possess utility. Practically speaking, such cases do not
occur except in an approximate manner. Such things as cinders, shavings, night soil,
etc., have either low degrees of utility or disutility. If the dustman takes them away for
nothing, they must have utility for him sufficient to pay the cost of removal. When the
dust is riddled, one part is usually found to have utility just sufficient to balance the
disutility of the remainder, giving us an instance of the second or third form of the
equation of exchange according as we regard the matter from the householder's or the
dustman's point of view.
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Equivalence Of Commodities.
Much confusion is thrown into the statistical investigation of questions of supply and
demand by the circumstance that one commodity can often replace another, and serve
the same purposes more or less perfectly. The same, or nearly the same, substance is
often obtained from two or three sources. The constituents of wheat, barley, oats, and
rye are closely similar, if not identical. Vegetable structures are composed mainly of
the same chemical compound in nearly all cases. Animal meat, again, is of nearly the
same composition from whatever animal derived. There are endless differences of
flavour and quality, but these are often insufficient to prevent one kind from serving
in place of another.
Whenever different commodities are thus applicable to the same purposes, their
conditions of demand and exchange are not independent. Their mutual ratio of
exchange cannot vary much, for it will be closely defined by the ratio of their utilities.
Beef and mutton, for instance, differ so slightly, that people eat them almost
indifferently. But the whole-sale price of mutton, on an average, exceeds that of beef
in the ratio of 9 to 8, and we must therefore conclude that people generally esteem
mutton more than beef in this proportion, otherwise they would not buy the dearer
meat. It follows that the final degrees of utility of these meats are in this ratio, or that
if fx be the degree of utility of mutton, and yy that of beef, we have
8. fx = 9. yy.
This equation would doubtless not hold true in extreme circumstances; if mutton
became comparatively scarce, there would probably be some persons willing to pay a
higher price, merely because it would then be considered a delicacy. But this is
certain, that, so long as the equation of utilities holds true, the ratio of exchange
between mutton and beef will not diverge from that of 8 to 9. If the supply of beef
falls off to a small extent, people will not pay a higher price for it, but will eat more
mutton; and if the supply of mutton falls off, they will eat more beef. The conditions
of supply will have no effect upon the ratio of exchange; we must, in fact, treat beef
and mutton as one commodity of two different strengths, just as gold at eighteen and
gold at twenty carats are hardly considered as two but rather as one commodity, of
which twenty parts of one are equivalent to eighteen of the other.
It is upon this principle that we must explain, in harmony with Cairnes' views, the
extraordinary permanence of the ratio of exchange of gold and silver, which from the
commencement of the eighteenth century up to recent years never diverged much
from 15 to 1. That this fixedness of ratio did not depend entirely upon the amount or
cost of production is proved by the very slight effect of the Australian and Californian
gold discoveries, which never raised the gold price of silver more than about 4 2/3 per
cent, and failed to have a permanent effect of more than 1½ per cent. This
permanence of relative values may have been partially due to the fact, that gold and
silver can be employed for exactly the same purposes, but that the superior brilliancy
of gold occasions it to be preferred, unless it be about 15 or 15½ times as costly as
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silver. Much more probably, however, the explanation of the fact is to be found in the
fixed ratio of 15½ to 1, according to which these metals are exchanged in the currency
of France and some other continental countries. The French Currency Law of the Year
XI. established an artificial equation—
Utility of gold = 15½ × Utility of silver;
and it is probably not without some reason that Wolowski and other recent French
economists attributed to this law of replacement an important effect in preventing
disturbance in the relations of gold and silver.
Since the first edition of this work was published, the views of Wolowski have
received striking verification in the unprecedented fall in the value of silver which has
occurred in the last three or four years. The ratio of equivalent weights of silver and
gold, which had never before risen much above 16 to 1, commenced to rise in 1874,
and was at one time (July 1876) as high as 22·5 to 1 in the London market. Though it
has since fallen, the ratio continues to be subject to frequent considerable oscillations.
The great production of silver in Nevada may contribute somewhat to this
extraordinary result, but the principal cause must be the suspension of the French Law
of the Double Standard, and the demonetisation of silver in Germany, Scandinavia,
and elsewhere. As I have treated the subject of the value of silver and the Double
Standard elsewhere,1 I need not pursue it here.
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Acquired Utility Of Commodities.
The Theory of Exchange, as explained above, rests entirely on the consideration of
quantities of utility, and no reference to labour or cost of production has been made.
The value of a divisible commodity, if I may for a moment use the dangerous term, is
measured, not, indeed, by its total utility, but by its final degree of utility, that is by
the intensity of the need we have for more of it. But the power of exchanging one
commodity for another greatly extends the range of utility. We are no longer limited
to considering the degree of utility of a commodity as regards the wants of its
immediate possessor; for it may have a higher usefulness to some other person, and
can be transferred to that person in exchange for some commodity of a higher degree
of utility to the purchaser. The general result of exchange is, that all commodities
sink, as it were, to the same level of utility in respect of the last portions consumed.
In the Theory of Exchange we find that the possessor of any divisible commodity will
exchange such a portion of it, that the next increment would have exactly equal utility
with the increment of other produce which he would receive for it. This will hold
good however various may be the kinds of commodity he requires. Suppose that a
person possesses one single kind of commodity, which we may consider to be money,
or income, and that p,q,r,s,t, etc., are quantities of other commodities which he
purchases with portions of his income. Let x be the uncertain quantity of money
which he will desire not to exchange; what relation will exist between these quantities
x,p,q,r, etc.? This relation will partly depend upon the ratio of exchange, partly on the
final degree of utility of these commodities. Let us assume, for a moment, that all the
ratios of exchange are equalities, or that a unit of one is always to be purchased with a
unit of another. Then, plainly, we must have the degrees of utility equal, otherwise
there would be advantage in acquiring more of that possessing the higher degree of
utility. Let the sign f denote the function of utility, which will be different in each
case; then we have simply the equations—
f
1
x = f
2
p = f
3
q = f
4
r = f
5
s = etc.
But, as a matter of fact, the ratio of exchange is seldom or never that of unit for unit;
and when the quantities exchanged are unequal, the degrees of utility will not be
equal. If for one pound of silk I can have three of cotton, then the degree of utility of
cotton must be a third that of silk, otherwise I should gain by exchange. Thus the
general result of the facility of exchange prevailing in a civilised country is, that a
person procures such quantities of commodities that the final degrees of utility of any
pair of commodities are inversely as the ratios of exchange of the commodities.
Let x
1
, x
2
, x
3
, x
4
, etc., be the portions of his income given for p,q,r,s, etc.,
respectively, then we must have
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and so on. The theory thus represents the fact, that a person distributes his income in
such a way as to equalise the utility of the final increments of all commodities
consumed. As water runs into hollows until it fills them up to the same level, so
wealth runs into all the branches of expenditure. This distribution will vary greatly
with different individuals, but it is self-evident that the want which an individual feels
most acutely at the moment will be that upon which he will expend the next increment
of his income. It obviously follows that in expending a person's income to the greatest
advantage, the algebraic sum of the quantities of commodity received or parted with,
each multiplied by its final degree of utility, will be zero.
We can now conceive, in an accurate manner, the utility of money, or of that supply
of commodity which forms a person's income. Its final degree of utility is measured
by that of any of the other commodities which he consumes. What, for instance, is the
utility of one penny to a poor family earning fifty pounds a year? As a penny is an
inconsiderable portion of their income, it may represent one of the infinitely small
increments, and its utility is equal to the utility of the quantity of bread, tea, sugar, or
other articles which they could purchase with it, this utility depending upon the extent
to which they were already provided with those articles. To a family possessing one
thousand pounds a year, the utility of a penny may be measured in an exactly similar
manner; but it will be much less, because their want of any given commodity will be
satiated or satisfied to a much greater extent, so that the urgency of need for a
pennyworth more of any article is much reduced.
The general result of exchange is thus to produce a certain equality of utility between
different commodities, as regards the same individual; but between different
individuals no such equality will tend to be produced. In Economics we regard only
commercial transactions, and no equalisation of wealth from charitable motives is
considered. The degree of utility of wealth to a very rich man will be governed by its
degree of utility in that branch of expenditure in which he continues to feel the most
need of further possessions. His primary wants will long since have been fully
satisfied; he could find food, if requisite, for a thousand persons, and so, of course, he
will have supplied himself with as much as he in the least desires. But so far as is
consistent with the inequality of wealth in every community, all commodities are
distributed by exchange so as to produce the maximum of benefit. Every person
whose wish for a certain thing exceeds his wish for other things, acquires what he
wants provided he can make a sufficient sacrifice in other respects. No one is ever
required to give what he more desires for what he less desires, so that perfect freedom
of exchange must be to the advantage of all.
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The Gain By Exchange.
It is a most important result of this theory that the ratio of exchange gives no
indication of the real benefit derived from the action of exchange. So many trades are
occupied in buying and selling, and make their profits by buying low and selling high,
that there arises a fallacious tendency to believe that the whole benefit of trade
depends upon the differences of prices. It is implied that to pay a high price is worse
than doing without the article, and the whole financial system of a great nation may be
distorted in the effort to carry out a false theory.
This is the result to which some of J. S. Mill's remarks, in his Theory of International
Trade, would lead. That theory is always ingenious, and as it seems to me, nearly
always true; but he draws from it the following conclusion:1 —"The countries which
carry on their foreign trade on the most advantageous terms are those whose
commodities are most in demand by foreign countries, and which have themselves the
least demand for foreign commodities. From which, among other consequences, it
follows that the richest countries, cœteris paribus, gain the least by a given amount of
foreign commerce: since, having a greater demand for commodities generally, they
are likely to have a greater demand for foreign commodities, and thus modify the
terms of interchange to their own disadvantage. Their aggregate gains by foreign
trade, doubtless, are generally greater than those of poorer countries, since they carry
on a greater amount of such trade, and gain the benefit of cheapness on a larger
consumption: but their gain is less on each individual article consumed."
In the absence of any explanation to the contrary, this passage must be taken to mean
that the advantage of foreign trade depends upon the terms of exchange, and that
international trade is less advantageous to a rich than to a poor country. But such a
conclusion involves confusion between two distinct things—the price of a commodity
and its total utility. A country is not merely like a great mercantile firm buying and
selling goods, and making a profit out of the difference of price; it buys goods in
order to consume them. But, in estimating the benefit which a consumer derives from
a commodity, it is the total utility which must be taken as the measure, not the final
degree of utility on which the terms of exchange depend.
To illustrate this truth we may employ the curves in Fig. VII. to represent the
functions of utility of two commodities. Let the wool of Australia be represented by
the line ob, and its total utility to Australia by the area of the curvilinear figure obrp.
Let the utility of a second commodity, say cotton goods, to Australia be similarly
represented in the lower curve, so that the quantity of commodity measured by o'b'
gives a total utility represented by the figure o'p'r'b'. Then, if Australia gives half its
wool, ab, for the quantity of cotton goods represented by o'a', it loses the utility aqrb,
but gains that represented by the larger area o'p'q'a'. There is accordingly a
considerable net gain of utility, which is the real object of exchange. Even had
Australia sold its wool at a lower price, obtaining cotton goods
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only to the amount of o'c, the utility of this amount, op'sc, would have exceeded that
of the wool given for it.
So far is Mill's statement from being fundamentally correct, that I believe the truth
lies in the opposite direction. As a general rule, the greatness of the price which a
country is willing and able to pay for the productions of other countries, measures, or
at least manifests, the greatness of the benefit which it derives from such imports. He
who pays a high price must either have a very great need of that which he buys, or
very little need of that which he pays for it; on either supposition there is gain by
exchange. In questions of this sort there is but one rule which can be safely laid down,
namely, that no one will buy a thing unless he expects advantage from the purchase;
and perfect freedom of exchange, therefore, tends to the maximising of utility.
One advantage of the Theory of Economics, carefully studied, will be to make us very
careful in our conclusions when the matter is not of the simplest possible nature. The
fact that we can most imperfectly estimate the total utility of any one commodity
should prevent us, for instance, from attempting to measure the benefit of any trade.
Accordingly, when Mill proceeds from his theory of international trade to that of
taxation, and arrives at the conclusion that one nation may, by means of taxes on
commodities imported, "appropriate to itself, at the expense of foreigners, a larger
share than would otherwise belong to it of the increase in the general productiveness
of the labour and capital of the world,"1 I venture to question the truth of his results. I
conceive that his arguments involve a confusion between the ratio of exchange and
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the total utility of a commodity, and a far more accurate knowledge of economical
laws than any one yet possesses would be required to estimate the true effect of a tax.
Customs duties may be requisite as a means of raising revenue, but the time is past
when any economist should give the slightest countenance to their employment for
manipulating trade, or for interfering with the natural tendency of exchange to
increase utility.
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Numerical Determination Of The Laws Of Utility.
The future progress of Economics as a strict science must greatly depend upon our
acquiring more accurate notions of the variable quantities concerned in the theory. We
cannot really tell the effect of any change in trade or manufacture until we can with
some approach to truth express the laws of the variation of utility numerically. To do
this we need accurate statistics of the quantities of commodities purchased by the
whole population at various prices. The price of a commodity is the only test we have
of the utility of the commodity to the purchaser; and if we could tell exactly how
much people reduce their consumption of each important article when the price rises,
we could determine, at least approximately, the variation of the final degree of
utility—the all-important element in Economics.
In such calculations we may at first make use of the simpler equation given on p. 113.
For the first approximation we may assume that the general utility of a person's
income is not affected by the changes of price of the commodity; so that, if in the
equation
f x = m. y c
we may have many different corresponding values for x and m, we may treat yc, the
utility of money, as a constant, and determine the general character of the function fx,
the final degree of utility. This function would doubtless be a purely empirical one—a
mere aggregate of terms devised so that their sum shall vary in accordance with
statistical facts. The subject is too complex to allow of our expecting any simple
precise law like that of gravity. Nor, when we have got the laws, shall we be able to
give any exact explanation of them. They will be of the same character as the
empirical formulæ used in many of the physical sciences—mere aggregates of
mathematical symbols intended to replace a tabular statement.1 Nevertheless, their
determination will render Economics a science as exact as many of the physical
sciences; as exact, for instance, as Meteorology is likely to be for a very long time to
come.
The method of determining the function of utility explained above will hardly apply,
however, to the main elements of expenditure. The price of bread, for instance, cannot
be properly brought under the equation in question, because, when the price of bread
rises much, the resources of poor persons are strained, money becomes scarcer with
them, and yc, the utility of money, rises. The natural result is, the lessening of
expenditure in other directions; that is to say, all the wants of a poor person are
supplied to a less degree of satisfaction when food is dear than when it is cheap.
When in the long course of scientific progress a sufficient supply of suitable statistics
has been at length obtained, it will become a mathematical problem of no great
difficulty how to disentangle the functions expressing the degrees of utility of various
commodities. One of the first steps, no doubt, will be to ascertain what proportion of
the expenditure of poor people goes to provide food, at various prices of that food.
But great difficulty is thrown in the way of all such inquiries by the vast differences in
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the condition of persons; and still greater difficulties are created by the complicated
ways in which one commodity replaces or serves instead of another.
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Opinions As To The Variation Of Price.
There is no difficulty in finding in works of Economists remarks upon the relation
between a change in the supply of a commodity and the consequent rise of price. The
general principles of the variation of utility have been familiar to many writers.
As a general rule the variation of price is much more marked in the case of
necessaries of life than in the case of luxuries. This result would follow from the fact
observed by Adam Smith, that "The desire for food is limited in every man by the
narrow capacity of the human stomach; but the desire of the conveniences and
ornaments of building, dress, equipage, and household furniture, seems to have no
limit or certain boundary." As I assert that value depends upon desire for more, it
follows that any excessive supply of food will lower its price very much more than in
the case of articles of luxury. Reciprocally, a deficiency of food will raise its price
much more than would happen in the case of less necessary articles. This conclusion
is in harmony with facts; for Chalmers says:1 "The necessaries of life are far more
powerfully affected in the price of them by a variation in their quantity than are the
luxuries of life. Let the crop of grain be deficient by one-third in its usual amount, or
rather, let the supply of grain in the market, whether from the home produce or by
importation, be curtailed to the same extent, and this will create a much greater
addition than of one-third to the price of it. It is not an unlikely prediction that its cost
would be more than doubled by the shortcoming of one-third or one-fourth in the
supply."
He goes on to explain, at considerable length, that the same would not happen with
such an article as rum. A deficiency in the supply of rum from the West Indies would
occasion a rise of price, but not to any great extent, because there would be a
substitution of other kinds of spirits, or else a reduction in the amount consumed. Men
can live without luxuries, but not without necessaries. "A failure in the general supply
of esculents to the extent of one-half would more than quadruple the price of the first
necessaries of life, and would fall with very aggravated pressure on the lower orders.
A failure to the same extent in all the vineyards of the world would most assuredly not
raise the price of wine to anything near this proportion. Rather than pay four times the
wonted price for Burgundy, there would be a general descent to claret, or from that to
port, or from that to the home-made wines of our own country, or from that to its
spirituous, or from that to its fermented liquors."1 He points to sugar especially as an
article which would be extensively thrown out of consumption by any great rise in
price,1 because it is a luxury, and at the same time forms a considerable element in
expenditure. But he thinks that, if an article occasions a total expenditure of very
small amount, variations of price will not much affect its consumption.
Speaking of nutmeg, he says: "There is not sixpence a year consumed of it for each
family in Great Britain; and perhaps not one family that spends more than a guinea on
this article alone. Let the price then be doubled or trebled; this will have no
perceptible effect on the demand; and the price will far rather be paid than that the
wonted indulgence should in any degree be foregone.... The same holds true of cloves,
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and cinnamon, and Cayenne pepper, and all the precious spiceries of the East; and it is
thus that while, in the general, the price of necessaries differs so widely from that of
luxuries, in regard to the extent of oscillation, there is a remarkable approximation in
this matter between the very commonest of these necessaries and the very rarest of
these luxuries."1
In these interesting observations Chalmers correctly distinguishes between the effect
of desire for the commodity in question and that for other çommodities. The cost of
nutmeg does not appreciably affect the general expenditure on other things, and the
equation on p. 113 therefore applies. But if sugar becomes scarce, to consume as
before would necessitate a reduction of consumption in other directions; and as the
degree of utility of more necessary articles rises much more rapidly than that of sugar,
it is the latter article which is thrown out of use by preference. This is a far more
complex case, which includes also the case of corn and all large articles of
consumption.
Chalmers' remarks on the price of sugar are strongly supported by facts concerning
the course of the sugar markets in 1855-6. In the year 1855, as is stated in Tooke's
History of Prices,1 attention was suddenly drawn to a considerable reduction which
had taken place in the stocks of sugar. The price rapidly advanced, but before it had
reached the highest point the demand became almost wholly suspended. Not only did
retail dealers avoid replenishing their stocks, but there was an immediate and
sometimes entire cessation of consumption among extensive classes. There were
instances among the retail grocers of their not selling a single pound of sugar until
prices receded to what the public was satisfied was a reasonable rate.
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Variation Of The Price Of Corn.
As to Chalmers' ingenious remarks upon the consumption of nutmeg, he seems to be
at least partially correct. To a certain extent he brings into view the principle
explained above, that when only a small quantity of income is required to purchase a
certain kind of commodity in sufficient abundance, the degree of utility of income
will not be appreciably affected by the price paid, that is to say (p. 113) yc remains
approximately constant. It follows that is constant, or in other words the final
degree of utility of the small commodity purchased must be directly proportional to
the price. If then the price rise much, either the consumer must relinquish the use of
that commodity almost entirely, or else he must feel such need of it, that a small
decrease of consumption is irksome to him; that is to say, looking to our curves of
utility, either we must recede to a part of the curve very close to the axis of y, or else
the curve must be one which rises rapidly as we move towards the origin. Now
Chalmers assumes that with nutmeg the latter is the case. People accustomed to use it
in his time were so fond of it that they would pay a much higher price rather than
decrease their consumption considerably. This means that it possessed a high degree
of utility to them, which could only be overbalanced by some serious increase in the
value of yc, which would ultimately mean the need of the necessaries of life.
It is very curious that in this subject, which reaches to the very foundations of
Political Economy, we owe more to early than later writers. Before our science could
be said to exist at all, writers on Political Arithmetic had got about as far as we have
got at present. In a pamphlet of 1737,1 it is remarked that "People who understand
trade will readily agree with me, that the tenth part of a commodity in a market, more
than there is a brisk demand for, is apt to lower the market, perhaps, twenty or thirty
per cent, and that a deficiency of a tenth part will cause as exorbitant an advance." Sir
J. Dalrymple,1 again, says: "Merchants observe, that if the commodity in market is
diminished one-third beneath its mean quantity, it will be nearly doubled in value; and
that if it is augmented one-third above its mean quantity, it will sink near one-half in
its value; or that, by further diminishing or augmenting the quantity, these
disproportions between the quantity and prices vastly increase." These remarks bear
little signs of accuracy, indeed, for the writers have spoken of commodities in general
as if they all varied in price in a similar degree. It is probable that they were thinking
of corn or other kinds of the more necessary food. In the Spectator we find a
conjecture,1 that the production of one-tenth part more of grain than is usually
consumed would diminish the value of the grain one-half. I know nothing more
strange and discreditable to statists and economists than that in so important a point as
the relations of price and supply of the main article of food, we owe our most accurate
estimates to writers who lived from one to two centuries ago.
There is a celebrated estimate of the variation of the price of corn which I have found
quoted in innumerable works on Economics. It is commonly attributed to Gregory
King, whose name should be held in honour as one of the fathers of statistical science
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in England. Born at Lichfield in 1648, King devoted himself much to mathematical
studies, and was often occupied in surveying. His principal public appointments were
those of Lancaster Herald and Secretary to the Commissioners of Public Accounts;
but he is known to fame by the remarkable statistical tables concerning the population
and trade of England, which he completed in the year 1696. His treatise was entitled
Natural and Political Observations and Conclusions upon the State and Condition of
England, 1696. It was never printed in the author's lifetime, but the contents were
communicated in a most liberal manner to Dr. Davenant, who, making suitable
acknowledgments as to the source of his information, founded thereupon his Essay
upon the Probable Methods of making a People gainers in the Balance of Trade.1
Our knowledge of Gregory King's conclusions was derived from this and other essays
of Davenant, until George Chalmers printed the whole treatise at the end of the third
edition of his well-known Estimate of the Comparative Strength of Great Britain.
The estimate of which I am about to speak is given by Davenant in the following
words:1 "We take it, that a defect in the harvest may raise the price of corn in the
following proportions:—
So that when corn rises to treble the common rate, it may be presumed that we want
above of the common produce; and if we should want , or half the common
produce, the price would rise to near five times the common rate."
Though this estimate has always been attributed to Gregory King, I cannot find it in
his published treatise; nor does Davenant, who elsewhere makes full
acknowledgments of what he owes to King, here attribute it to his friend. It is
therefore, perhaps, due to Davenant.
We may re-state this estimate in the following manner, taking the average harvest and
the average price of corn as unity:—
Quantity of Corn1.0.9 .8 .7 .6 .5
Price 1.01.31.82.63.85.5
Many writers have commented on this estimate. Thornton1 observes that it is
probably exceedingly inaccurate, and that it is not clear whether the total stock, or
only the harvest of a single year, is to be taken as deficient. Tooke,2 however, than
whom on such a point there is no higher authority, believes that King's estimate "is
not very wide of the truth, judging from the repeated occurrence of the fact that the
price of corn in this country has risen from one hundred to two hundred per cent and
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upwards when the utmost computed deficiency of the crops has not been more than
between one-sixth and one-third of an average."
I have endeavoured to ascertain the law to which Davenant's figures conform, and the
mathematical function obtained does not greatly differ from what we might have
expected. It is probable that the price of corn should never sink to zero, as, if
abundant, it could be used for feeding horses, poultry, and cattle, or for other purposes
for which it is too costly at present. It is said that in America corn, no doubt Indian
corn, has been occasionally used as fuel. On the other hand, when the quantity is
much diminished, the price should rise rapidly, and should become infinite before the
quantity is zero, because famine would then be impending. The substitution of
potatoes and other kinds of food renders the famine point very uncertain; but I think
that a total deficiency of corn could not be made up by other food. Now a function of
the form
fulfils these conditions; for it becomes infinite when x is reduced to b, but for greater
values of x always decreases as x increases. An inspection of the numerical data
shows that n is about equal to 2, and, assuming it to be exactly 2, I find that the most
probable values of a and b are a = .824 and b = .12. The formula thus becomes
The following numbers show the degree of approximation between the first of these
formulæ and the data of Davenant:—
Harvest 1.0 .9 .8 .7 .6 .5
Price (Davenant)1.0 1.3 1.8 2.6 3.8 5.5
Price calculated 1.061.361.782.453.585.71
I cannot undertake to say how nearly Davenant's estimate agrees with experience; but,
considering the close approximation in the above numbers, we may safely substitute
the empirical formula for his numbers; and there are other reasons already stated for
supposing that this formula is not far from the truth. Roughly speaking, the price of
corn may be said to vary inversely as the square of the supply, provided that this
supply be not unusually small. I find that this is nearly the same conclusion as
Whewell drew from the same numbers. He says:1 "If the above numbers were to be
made the basis of a mathematical rule, it would be found that the price varies
inversely as the square of the supply, or rather in a higher ratio."
There is further reason for believing that the price of corn varies more rapidly than in
the inverse ratio of the quantity. Tooke estimates1 that in 1795 and 1796 the farmers
of England gained seven millions sterling in each year by a deficiency of one-eighth
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part in the wheat crop, not including the considerable profit on the rise of price of
other agricultural produce. In each of the years 1799 and 1800, again, farmers
probably gained eleven millions sterling by deficiency. If the price of wheat varied in
the simple inverse proportion of the quantity, they would neither gain nor lose, and
the fact that they gained considerably agrees with our formula as given above.
The variation of utility has not been overlooked by mathematicians, who had
observed, as long ago as the early part of last century—before, in fact, there was any
science of Political Economy at all—that the theory of probabilities could not be
applied to commerce or gaming without taking notice of the very different utility of
the same sum of money to different persons. Suppose that an even and fair bet is
made between two persons, one of whom has £10,000 a year, the other £100 a year;
let it be an equal chance whether they gain or lose £50. The rich person will, in
neither case, feel much difference; but the poor person will receive far more harm by
losing £50 than he can be benefited by gaining it. The utility of money to a poor
person varies rapidly with the amount; to a rich person less so. Daniel Bernoulli,
accordingly, distinguished in any question of probabilities between the moral
expectation and the mathematical expectation, the latter being the simple chance of
obtaining some possession, the former the chance as measured by its utility to the
person. Having no means of ascertaining numerically the variation of utility,
Bernoulli had to make assumptions of an arbitrary kind, and was then able to obtain
reasonable answers to many important questions. It is almost self-evident that the
utility of money decreases as a person's total wealth increases; if this be granted, it
follows at once that gaming is, in the long run, a sure way to lose utility; that every
person should, when possible, divide risks, that is, prefer two equal chances of £50 to
one similar chance of £100; and the advantage of insurance of all kinds is proved
from the same theory. Laplace drew a similar distinction between the fortune
physique, or the actual amount of a person's income, and the fortune morale, or its
benefit to him."1
In answer to the objections of an ingenious correspondent, it may be remarked that
when we say gaming is a sure way to lose utility, we take no account of the
utility—that is, the pleasure attaching to the pursuit of gaming itself; we regard only
the commercial loss or gain. If a person with a certain income prefers to run the risk
of losing a portion of it at play, rather than spending it in any other way, it must no
doubt be conceded that the political economist, as such, can make no conclusive
objection. If the gamester is so devoid of other tastes that to spend money over the
gaming-table is the best use he can discover for it, economically speaking, there is
nothing further to be said. The question then becomes a moral, legislative, or political
one. A source of amusement which, like gaming, betting, dram-drinking, or opium-
eating, is not in itself always pernicious, may come to be regarded as immoral, if in a
considerable proportion of cases it leads to excessive and disastrous results. But this
question evidently leads us into a class of subjects which could not be appropriately
discussed in this work treating of pure economic theory.
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The Origin Of Value.
The preceding pages contain, if I am not mistaken, an explanation of the nature of
value which will, for the most part, harmonise with previous views upon the subject.
Ricardo has stated, like most other economists, that utility is absolutely essential to
value; but that "possessing utility, commodities derive their exchangeable value from
two sources: from their scarcity, and from the quantity of labour required to obtain
them."1 Senior, again, has admirably defined wealth, or objects possessing value, as
"those things, and those things only, which are transferable, are limited in supply, and
are directly or indirectly productive of pleasure or preventive of pain." Speaking only
of things which are transferable, or capable of being passed from hand to hand, we
find that two of the clearest definitions of value recognise utility and scarcity as the
essential qualities. But the moment that we distinguish between the total utility of a
mass of commodity and the degree of utility of different portions, we may say that it
is scarcity which prevents the fall in the final degree of utility. Bread has the almost
infinite utility of maintaining life, and when it becomes a question of life or death, a
small quantity of food exceeds in value all other things. But when we enjoy our
ordinary supplies of food, a loaf of bread has little value, because the utility of an
additional loaf is small, our appetites being satiated by our customary meals.
I have pointed out the excessive ambiguity of the word Value, and the apparent
impossibility of using it safely. When intended to express the mere fact of certain
articles exchanging in a particular ratio, I have proposed to substitute the unequivocal
expression—ratio of exchange. But I am inclined to believe that a ratio is not the
meaning which most persons attach to the word Value. There is a certain sense of
esteem or desirableness, which we may have with regard to a thing apart from any
distinct consciousness of the ratio in which it would exchange for other things. I may
suggest that this distinct feeling of value is probably identical with the final degree of
utility. While Adam Smith's often-quoted value in use is the total utility of a
commodity to us, the value in exchange is defined by the terminal utility, the
remaining desire which we or others have for possessing more.
There remains the question of labour as an element of value. Economists have not
been wanting who put forward labour as the cause of value, asserting that all objects
derive their value from the fact that labour has been expended on them; and it is thus
implied, if not stated, that value will be proportional to labour. This is a doctrine
which cannot stand for a moment, being directly opposed to facts. Ricardo disposes of
such an opinion when he says:1 "There are some commodities, the value of which is
determined by their scarcity alone. No labour can increase the quantity of such goods,
and therefore their value cannot be lowered by an increased supply. Some rare statues
and pictures, scarce books and coins, wines of a peculiar quality, which can be made
only from grapes grown on a particular soil, of which there is a very limited quantity,
are all of this description. Their value is wholly independent of the quantity of labour
originally necessary to produce them, and varies with the varying wealth and
inclinations of those who are desirous to possess them."
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The mere fact that there are many things, such as rare ancient books, coins,
antiquities, etc., which have high values, and which are absolutely incapable of
production now, disperses the notion that value depends on labour. Even those things
which are producible in any quantity by labour seldom exchange exactly at the
corresponding values.1 The market price of corn, cotton, iron, and most other things
is, in the prevalent theories of value, allowed to fluctuate above or below its natural or
cost value. There may, again, be any discrepancy between the quantity of labour spent
upon an object and the value ultimately attaching to it. A great undertaking like the
Great Western Railway, or the Thames Tunnel, may embody a vast amount of labour,
but its value depends entirely upon the number of persons who find it useful. If no use
could be found for the Great Eastern steamship, its value would be nil, except for the
utility of some of its materials. On the other hand, a successful undertaking, which
happens to possess great utility, may have a value, for a time at least, far exceeding
what has been spent upon it, as in the case of the Atlantic cable. The fact is, that
labour once spent has no influence on the future value of any article: it is gone and
lost for ever. In commerce bygones are for ever bygones; and we are always starting
clear at each moment, judging the values of things with a view to future utility.
Industry is essentially prospective, not retrospective; and seldom does the result of
any undertaking exactly coincide with the first intentions of its promoters.
But though labour is never the cause of value, it is in a large proportion of cases the
determining circumstance, and in the following way:—Value depends solely on the
final degree of utility. How can we vary this degree of utility?—By having more or
less of the commodity to consume. And how shall we get more or less of it?—By
spending more or less labour in obtaining a supply. According to this view, then,
there are two steps between labour and value. Labour affects supply, and supply
affects the degree of utility, which governs value, or the ratio of exchange. In order
that there may be no possible mistake about this all-important series of relations. I
will re-state it in a tabular form, as follows:—
Cost of production determines supply.
Supply determines final degree of utility.
Final degree of utility determines value.
But it is easy to go too far in considering labour as the regulator of value; it is equally
to be remembered that labour is itself of unequal value. Ricardo, by a violent
assumption, founded his theory of value on quantities of labour considered as one
uniform thing. He was aware that labour differs infinitely in quality and efficiency, so
that each kind is more or less scarce, and is consequently paid at a higher or lower rate
of wages. He regarded these differences as disturbing circumstances which would
have to be allowed for; but his theory rests on the assumed equality of labour. This
theory rests on a wholly different ground. I hold labour to be essentially variable, so
that its value must be determined by the value of the produce, not the value of the
produce by that of the labour. I hold it to be impossible to compare à priori the
productive powers of a navvy, a carpenter, an iron-puddler, a schoolmaster, and a
barrister. Accordingly, it will be found that not one of my equations represents a
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comparison between one man's labour and another's. The equation, if there is one at
all, is between the same person in two or more different occupations. The subject is
one in which complicated action and reaction takes place, and which we must defer
until after we have described, in the next chapter, the Theory of Labour.
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CHAPTER V
THEORY OF LABOUR
Definition Of Labour.
ADAM SMITH said, "The real price of everything, what everything really costs to the
man who wants to acquire it, is the toil and trouble of acquiring it.... Labour was the
first price, the original purchase-money, that was paid for all things."1 If subjected to
a very searching analysis, this celebrated passage might not prove to be so entirely
true as it would at first sight seem to most readers to be. Yet it is substantially true,
and luminously expresses the fact that labour is the beginning of the processes treated
by economists, as consumption is the end and purpose. Labour is the painful exertion
which we undergo to ward off pains of greater amount, or to procure pleasures which
leave a balance in our favour. Courcelle-Seneuil2 and Hearn have stated the problem
of Economics with the utmost truth and brevity in saying, that it is to satisfy our wants
with the least possible sum of labour.
In defining labour for the purposes of the economist we have a choice between two
courses. In the first place, we may, if we like, include in it all exertion of body or
mind. A game of cricket would, in this case, be labour; but if it be undertaken solely
for the sake of the enjoyment attaching to it, the question arises whether we need take
it under our notice. All exertion not directed to a distant and distinct end must be
repaid simultaneously. There is no account of good or evil to be balanced at a future
time. We are not prevented in any way from including such cases in our Theory of
Economics; in fact, our Theory of Labour will, of necessity, apply to them. But we
need not occupy our attention by cases which demand no calculus. When we exert
ourselves for the sole amusement of the moment, there is but one rule needed,
namely, to stop when we feel inclined—when the pleasure no longer equals the pain.
It will probably be better, therefore, to take the second course and concentrate our
attention on such exertion as is not completely repaid by the immediate result. This
would give us a definition nearly the same as that of Say, who defined labour as
"Action suivée, dirigée vers un but." Labour, I should say, is any painful exertion of
mind or body undergone partly or wholly with a view to future good.1 It is true that
labour may be both agreeable at the time and conducive to future good; but it is only
agreeable in a limited amount, and most men are compelled by their wants to exert
themselves longer and more severely than they would otherwise do. When a labourer
is inclined to stop, he clearly feels something that is irksome, and our theory will only
involve the point where the exertion has become so painful as to nearly balance all
other considerations. Whatever there is that is wholesome or agreeable about labour
before it reaches this point may be taken as a net profit of good to the labourer; but it
does not enter into the problem. It is only when labour becomes effort that we take
account of it, and, as Hearn truly says,1 "such effort, as the very term seems to imply,
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is more or less troublesome." In fact, we must, as will shortly appear, measure labour
by the amount of pain which attaches to it.
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Quantitative Notions Of Labour.
Let us endeavour to form a clear notion of what we mean by amount of labour. It is
plain that duration will be one element of it; for a person labouring uniformly during
two months must be allowed to labour twice as much as during one month. But labour
may vary also in intensity. In the same time a man may walk a greater or less
distance; may saw a greater or less amount of timber; may pump a greater or less
quantity of water; in short, may exert more or less muscular and nervous force. Hence
amount of labour will be a quantity of two dimensions, the product of intensity and
time when the intensity is uniform, or the sum represented by the area of a curve
when the intensity is variable.
But intensity of labour may have more than one meaning; it may mean the quantity of
work done, or the painfulness of the effort of doing it. These two things must be
carefully distinguished, and both are of great importance for the theory. The one is the
reward, the other the penalty, of labour. Or rather, as the produce is only of interest to
us so far as it possesses utility, we may say that there are three quantities involved in
the theory of labour—the amount of painful exertion, the amount of produce, and the
amount of utility gained. The variation of utility, as depending on the quantity of
commodity possessed, has already been considered; the variation of the amount of
produce will be treated in the next chapter; we will here give attention to the variation
of the painfulness of labour.
Experience shows that as labour is prolonged the effort becomes as a general rule
more and more painful. A few hours' work per day may be considered agreeable
rather than otherwise; but so soon as the overflowing energy of the body is drained
off, it becomes irksome to remain at work. As exhaustion approaches, continued
effort becomes more and more intolerable. Jennings has so clearly stated this law of
the variation of labour, that I must quote his words.1 "Between these two points, the
point of incipient effort and the point of painful suffering, it is quite evident that the
degree of toilsome sensations endured does not vary directly as the quantity of work
performed, but increases much more rapidly, like the resistance offered by an
opposing medium to the velocity of a moving body.
"When this observation comes to be applied to the toilsome sensations endured by the
working classes, it will be found convenient to fix on a middle point, the average
amount of toilsome sensation attending the average amount of labour, and to measure
from this point the degrees of variation. If, for the sake of illustration, this average
amount be assumed to be of ten hours' duration, it would follow that, if at any period
the amount were to be supposed to be reduced to five hours, the sensations of labour
would be found, at least by the majority of mankind, to be almost merged in the
pleasures of occupation and exercise, whilst the amount of work performed would
only be diminished by one-half; if, on the contrary, the amount were to be supposed to
be increased to twenty hours, the quantity of work produced would only be doubled,
whilst the amount of toilsome suffering would become insupportable. Thus, if the
quantity produced, greater or less than the average quantity, were to be divided into
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any number of parts of equal magnitude, the amount of toilsome sensation attending
each succeeding increment would be found greater than that which would attend the
increment preceding; and the amount of toilsome sensation attending each succeeding
decrement would be found less than that which would attend the decrement
preceding."
There can be no question of the general truth of the above statement, although we may
not have the data for assigning the exact law of the variation. We may imagine the
painfulness of labour in proportion to produce to be represented by some such curve
as abcd in Fig. VIII. In this diagram the height of points above the line ox denotes
pleasure, and depth below it pain. At the moment of commencing labour it is usually
more irksome than when the mind and body are well bent to the work. Thus, at first,
the pain is measured by oa. At b there is neither pain nor pleasure. Between b and c an
excess of pleasure is represented as due to the exertion itself. But after c the energy
begins to be rapidly exhausted, and the resulting pain is shown by the downward
tendency of the line cd.
We may at the same time represent the degree of utility of the produce by some such
curve as pq, the amount of produce being measured along the line ox. Agreeably to
the theory of utility, already given, the curve shows that, the larger the wages earned,
the less is the pleasure derived from a further increment.
There will, of necessity, be some point m such that qm = dm, that is to say, such that
the pleasure gained is exactly equal to the labour endured. Now, if we pass the least
beyond this point, a balance of pain will result: there will be an ever-decreasing
motive in favour of labour, and an ever-increasing motive against it. The labourer will
evidently cease, then, at the point m. It would be inconsistent with human nature for a
man to work when the pain of work exceeds the desire of possession, including all the
motives for exertion.
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We must consider the duration of labour as measured by the number of hours' work
per day. The alternation of day and night on the earth has rendered man essentially
periodic in his habits and actions. In a natural and wholesome condition a man should
return each twenty-four hours to exactly the same state; at any rate, the cycle should
be closed within the seven days of the week. Thus the labourer must not be supposed
to be either increasing or diminishing his normal strength. But the theory might also
be made to apply to cases where special exertion is undergone for many days or
weeks in succession, in order to complete work, as in collecting the harvest. Adequate
motives may lead to and warrant overwork, but, if long continued, excessive labour
reduces the strength and becomes insupportable; and the longer it continues the worse
it is, the law being somewhat similar to that of periodic labour.
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Symbolic Statement Of The Theory.
In attempting to represent these conditions of labour with accuracy, we shall find that
there are no less than four quantities concerned; let us denote them as follows:—
t = time, or duration of labour.
l = amount of labour, as meaning the aggregate balance of pain accompanying it,
irrespective of the produce.
x = amount of commodity produced.
v = total utility of that commodity.
The amount of commodity produced will be very different in different cases. In any
one case the rate of production will be determined by dividing the whole quantity
produced by the time of production, provided that the rate of production has been
uniform; it will then be . But if the rate of production be variable, it can only be
determined at any moment by comparing a small quantity of produce with the small
portion of time occupied in its production. More strictly speaking, we must ascertain
the ratio of an infinitely small quantity of produce to the corresponding infinitely
small portion of time. Thus the rate of production is properly denoted by or at
the limit by .
Again, the degree of painfulness of labour would be if it remained invariable; but
as it is highly variable, we must again compare small increments, and or, at the
limit, correctly represents the degree of painfulness of labour. But we must also
take into account the fact that the utility of commodity is not constant. If a man works
regularly twelve hours a day, he will produce more commodity than in ten hours;
therefore the final degree of utility of his commodity, whether he consume it himself
or whether he exchange it, will not be quite so high as when he produced less. This
degree of utility is denoted, as before, by the ratio of the increment of utility to
the increment of commodity.
The amount of reward of labour can now be expressed; for it is
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that is to say, it is the product of the ratio of the commodity produced to the time,
multiplied by the ratio of the utility to the amount of produce. Thus, the last two hours
of work in the day generally gives less reward, both because less produce is then
created in proportion to the time spent, and because that produce is less necessary and
useful to one who makes enough to support himself in the other ten hours.
We can now ascertain the length of time which should be selected as the most
advantageous term of labour. A free labourer endures the irksomeness of work
because the pleasure he expects to receive, or the pain he expects to ward off, by
means of the produce, exceeds the pain of exertion. When labour itself is a worse evil
than that which it saves him from, there can be no motive for further exertion, and he
ceases. Therefore he will cease to labour just at the point when the pain becomes
equal to the corresponding pleasure gained; and we thus have t defined by the
equation
In this, as in the other questions of Economics, all depends upon the final increments,
and we have expressed in the above formula the final equivalence of labour and
utility. A man must be regarded as earning all through his hours of labour an excess of
utility; what he produces must be considered not merely the exact equivalent of the
labour he gives for it, for it would be, in that case, a matter of indifference whether he
laboured or not. As long as he gains, he labours, and when he ceases to gain, he
ceases to labour.
In some cases, as in some kinds of machine labour, the rate of production is uniform,
or nearly so, and by choice of suitable units may be made equal to unity; the result
may then be put more simply in this way. Labour may be considered as expended in
successive small quantities, Dl, each lasting, for instance, for a quarter of an hour; the
corresponding benefit derived from the labour will then be denoted by Du. Now, so
long as Du exceeds in amount of pleasure the negative quantity or pain of Dl, the
difference of sign being disregarded, there will be gain inducing to continued labour.
Were Du to fall below Dl, there would be more harm than good in labouring;
therefore, the boundary between labour and inactivity will be defined by the equality
of Du and Dl, and at the limit we have the equation
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Dimensions Of Labour.
If I have correctly laid down, in preceding chapters, the Theory of Dimensions of
Utility and Value, there ought not to be much difficulty in stating the similar theory as
regards Labour. We might in fact treat labour as simply one case of disutility or
negative utility, that is as pain, or at any rate as a generally painful balance of pleasure
and pain, endured in the action of acquiring commodity. Thus its dimensions might be
described as identical with those of utility; U would then denote intensity of labour, or
degree of labour, just as it was used to denote degree of utility. If we measure labour
with respect to the quantity of commodity produced, that is, if we make commodity
the variable, then total amount of labour will be the integral of U dM, and the
dimensions of amount of labour will be MU, identical with those of total utility.
If for any reasons of convenience we prefer to substitute a new symbol, specially
appropriated to express the dimensions of labour, and say that intensity of labour is
represented by E (Endurance), and total quantity of labour incurred in the production
of certain commodity by ME, it must be remembered that the change is one of
convenience only; U and E are essentially quantities of the same nature, and the
difference, so far as there is any, arises from the fact that quantities symbolised by E
will usually be negative as compared with those symbolised by U. Labour, however,
is often measured and bought and sold by time, instead of by piecework or commodity
produced; in this case, while E continues to express intensity of labour, ET will
express the dimensions of amount of labour.
Rate of production will obviously possess the same dimensions as rate of
consumption (p. 64), namely, MT-1, and this quantity forms a link between labour as
measured by time and by produce; for ET × MT-1 = ME. It would be possible to
invent various other economic quantities, such as acceleration of production, with the
dimensions MT-2; but, until it is apparent how such quantities enter into economic
theorems, it seems needless to consider them further.
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Balance Between Need And Labour.
In considering this Theory of Labour an interesting question presents itself. Supposing
that circumstances alter the relation of produce to labour, what effect will this have
upon the amount of labour which will be exerted? There are two effects to be
considered. When labour produces more commodity, there is more reward, and
therefore more inducement to labour. If a workman can earn ninepence an hour
instead of sixpence, may he not be induced to extend his hours of labour by this
increased result? This would doubtless be the case were it not that the very fact of
getting half as much more than he did before, lowers the utility to him of any further
addition. By the produce of the same number of hours he can satisfy his desires more
completely; and if the irksomeness of labour has reached at all a high point, he may
gain more pleasure by relaxing that labour than by consuming more products. The
question thus depends upon the direction in which the balance between the utility of
further commodity and the painfulness of prolonged labour turns.
In our ignorance of the exact form of the functions either of utility or of labour, it will
be impossible to decide this question in an à priori manner; but there are a few facts
which indicate in which direction the balance does usually turn. Statements are given
by Porter, in his Progress of the Nation,1 which show that when a sudden rise took
place in the prices of provisions in the early part of this century, workmen increased
their hours of labour, or, as it is said, worked double time, if they could obtain
adequate employment. Now, a rise in the price of food is really the same as a decrease
of the produce of labour, since less of the necessaries of life can be acquired in
exchange for the same money wages. We may conclude, then, that English labourers
enjoying little more than the necessaries of life, will work harder the less the produce;
or, which comes to the same thing, will work less hard as the produce increases.
Evidence to the like effect is found in the general tendency to reduce the hours of
labour at the present day, owing to the improved real wages now enjoyed by those
employed in mills and factories. Artisans, mill-hands, and others, seem generally to
prefer greater ease to greater wealth, thus proving that the painfulness of labour varies
so rapidly as easily to overbalance the gain of utility. The same rule seems to hold
throughout the mercantile employments. The richer a man becomes, the less does he
devote himself to business. A successful merchant is generally willing to give a
considerable share of his profits to a partner, or to a staff of managers and clerks,
rather than bear the constant labour of superintendence himself. There is also a
general tendency to reduce the hours of labour in mercantile offices, due to increased
comfort and opulence.
It is obvious, however, that there are many intricacies in a matter of this sort. It is not
always possible to graduate work to the worker's liking; in some businesses a man
who insisted on working only a few hours a day would soon have no work to do. In
the professions of law, medicine, and the like, it is the reputation of enjoying a large
practice which attracts new clients. Thus a successful barrister or physician generally
labours more severely as his success increases. This result partly depends upon the
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fact that the work is not easily capable of being performed by deputy. A successful
barrister, too, soon begins to look forward to the extrinsic rewards of a high judicial or
parliamentary position. But the case of an eminent solicitor, architect, or engineer is
one where the work is to a great extent done by employees, and done without
reference to social or political rewards, and where yet the most successful man
endures the most labour, or rather is most constantly at work. This indicates that the
irksomeness of the labour does not increase so as to over-balance the utility of the
increment of reward. In some characters and in some occupations, in short, success of
labour only excites to new exertions, the work itself being of an interesting and
stimulating nature. But the general rule is to the contrary effect, namely, that a certain
success disinclines a man to increased labour. It may be added that in the highest
kinds of labour, such as those of the philosopher, scientific discoverer, artist, etc., it is
questionable how far great success is compatible with ease; the mental powers must
be kept in perfect training by constant exertion, just as a racehorse or an oarsman
needs to be constantly exercised.
It is evident that questions of this kind depend greatly upon the character of the race.
Persons of an energetic disposition feel labour less painfully than their fellowmen,
and, if they happen to be endowed with various and acute sensibilities, their desire of
further acquisition never ceases. A man of lower race, a negro for instance, enjoys
possession less, and loathes labour more; his exertions, therefore, soon stop. A poor
savage would be content to gather the almost gratuitous fruits of nature, if they were
sufficient to give sustenance; it is only physical want which drives him to exertion.
The rich man in modern society is supplied apparently with all he can desire, and yet
he often labours unceasingly for more. Bishop Berkeley, in his Querist,1 has very
well asked, "Whether the creating of wants be not the likeliest way to produce
industry in a people? And whether, if our (Irish) peasants were accustomed to eat beef
and wear shoes, they would not be more industrious?"
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Distribution Of Labour.
We now come to consider the conditions which regulate the comparative amounts of
different commodities produced in a country. Theoretically speaking, we might regard
each person as capable of producing various commodities, and dividing his labour
according to certain rules between the different employments; it would not be
impossible, too, to mention cases where such division does take place. But the result
of commerce and the division of labour is usually to make a man find his advantage in
performing one trade only; and I give the formulæ as they would apply to an
individual, only because they are identical in general character with those which apply
to a whole nation.
Suppose that an individual is capeble of producing two kinds of commodity. His sole
object, of course, is to produce the greatest amount of utility; but this will depend
partly upon the comparative degrees of utility of the commodities, and partly on his
comparative facilities for producing them. Let x and y be the respective quantities of
the commodities already produced, and suppose that he is about to apply more labour;
on which commodity shall he spend the next increment of labour?—Plainly, on that
which will yield most utility. Now, if an increment of labour, Dl, will yield either of
the increments of commodity Dx and Dy, the ratios of produce to labour, namely,
will form one element in the problem. But to obtain the comparative utilities of these
commodities, we must multiply respectively by
For instance,
expresses the amount of utility which can be obtained by producing a little more of
the first commodity; if this be greater than the same expression for the other
commodity, it would evidently be best to make more of the first commodity until it
ceased to yield any excess of utility. When the labour is finally distributed, we must
have the increments of utility from the several employments equal, and at the limit we
have the equation—
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When this equation holds, there can be no motive for altering or regretting the
distribution of labour, and the utility produced is at its maximum.
There are in this problem two unknown quantities, namely, the two portions of labour
appropriated to the two commodities. To determine them, we require one other
equation in addition to the above. If we put
l = l
1
+ l
2
,
we have still an unknown quantity to determine, namely, l; but the principles of
labour (pp. 172-177) now give us an equation. Labour will be carried on until the
increment of utility from any of the employments just balances the increment of pain.
This amounts to saying that du, the increment of utility derived from the first
employment of labour, is equal in amount of feeling to dl
1
, the increment of labour by
which it is obtained. This gives us then the further equation—
If we pay regard to sign, indeed, we must remember that dl is, when measured in the
same scale as du, intrinsically negative, but inasmuch as it is given in exchange for
du, which is received, it will in this respect be taken negatively, and thus the above
equation holds true.1
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Relation Of The Theories Of Labour And Exchange.
It may tend to give the reader confidence in the preceding theories when he finds that
they lead directly to the well-known law, as stated in the ordinary language of
economists, that value is proportional to the cost of production. As I prefer to state the
same law, it is to the effect that the ratio of exchange of commodities will conform in
the long run to the ratio of productiveness, which is the reciprocal of the ratio of the
costs of production. The somewhat perplexing relations of these quantities will be
fully explained in the next section, but we may now proceed to prove the above result
symbolically.
To simplify our expressions, let us substitute for the rate of production the
symbol . Then express the relative quantities of two different
commodities produced by an increment of labour, and we have the following
equation, identical with that on page 184.
Let us suppose that the person to whom it applies is in a position to exchange with
other persons. The conditions of production will now, in all probability, be modified.
For x the quantity of our commodity may perhaps be increased to x + x
1
, and y
diminished to y - y
1
, by an exchange of the quantities x
1
and y
1
. If this be so, we shall,
as shown in the Theory of Exchange, have the equation
Our equation of production will now be modified, and become
But this equation has its first member identical with the first member of the equation
of exchange given above, so that we may at once deduce the all-important equation
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The reader will remember that
lf0237_figure_i042
expresses the ratio of produce to labour; thus we have proved that commodities will
exchange in any market in the ratio of the quantities produced by the same quantity of
labour. But as the increment of labour considered is always the final one, our equation
also expresses the truth, that articles will exchange in quantities inversely as the costs
of production of the most costly portions, i.e. the last portions added. This result will
prove of great importance in the theory of Rent.
Let it be observed that, in uniting the theories of exchange and production, a
complicated double adjustment takes place in the quantities of commodity involved.
Each party adjusts not only its consumption of articles in accordance with their ratio
of exchange, but it also adjusts its production of them. The ratio of exchange governs
the production as much as the production governs the ratio of exchange. For instance,
since the Corn Laws have been abolished in England, the effect has been, not to
destroy the culture of wheat, but to lessen it. The land less suitable to the growth of
wheat has been turned to grazing or other purposes more profitable comparatively
speaking. Similarly the importation of hops or eggs or any other article of food does
not even reduce the quantity raised here, but prevents the necessity for resorting to
more expensive modes of increasing the supply. It is not easy to express in words how
the ratios of exchange are finally determined. They depend upon a general balance of
producing power and of demand as measured by the final degree of utility. Every
additional supply tends to lower the degree of utility; but whether that supply will be
forthcoming from any country depends upon its comparative powers of producing
different commodities.
Any very small tract of country cannot appreciably affect the comparative supply of
commodities: it must therefore adjust its productions in accordance with the general
state of the market. The county of Bedford, for instance, would not appreciably affect
the markets for corn, cheese, or cattle, whether it devoted every acre to corn or to
grazing. Therefore the agriculture of Bedfordshire will have to be adapted to
circumstances, and each field will be employed for arable or grazing land according
as prevailing prices render one employment or the other more profitable. But any
large country will affect the markets as well as be affected. If the whole habitable
surface of Australia, instead of producing wool, could be turned to the cultivation of
wine, the wool market would rise, and the wine market fall. If the Southern States of
America abandoned cotton in favour of sugar, there would be a revolution in these
markets. It would be inevitable for Australia to return to wool and the American
States to cotton. These are illustrations of the reciprocal relation of exchange and
production.
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Relations Of Economic Quantities.
I hope that I may sometime be able, in a future and much larger work, to explain in
detail the results which can be derived from the mathematical theory expounded in the
previous pages. This essay gives them only in an implicit manner. But, before leaving
the subject of exchange, it may be well without delay to point out how the results so
far set forth connect themselves with the recognised doctrines of political economy.
For the sake of accuracy I have avoided the use of the word value; the expression cost
of production, so continually recurring in most economical treatises, is also here
conspicuous by its absence. The reader then, unless he be very careful, may be thrown
into some perplexity, when he proceeds to compare my results with those familiar to
him elsewhere. I will therefore proceed to trace out the connections between the
several quantitative expressions, which most commonly occur in discussions
concerning value, exchange, and production.
In the first place, the ratio of exchange is the actual numerical ratio of the quantities
given and received. Let X and Y be the names of the commodities: x and y the
quantities of them respectively exchanged. Then the ratio of exchange is that of y to x.
But the value of a commodity in exchange is greater as the quantity received is less,
so that the ratio of the quantities dealt with must be the reciprocal of the ratio of the
values of the substances, meaning by value the value per unit of the commodity. Thus
we may say
Value is of course very frequently estimated by price, that is, by the quantity of legal
money for which the commodity may be exchanged. Price is indeed ambiguous in the
same way as value; it means either the price of the whole quantity, or the price per
unit of the quantity. Let p
1
be the price per unit of X, and p
2
the similar price of Y.
Then it is apparent that y × p
2
will be the whole price of y, and x × p
1
will be the
whole price of x. These two must be equal to each other, so that we get
Thus we find that, when price means price per unit, the quantities exchanged are
reciprocally as the prices. When price means price of the whole quantity, the
quantities given and received are always of equal price.
Turning now to the production of commodity, it is sufficiently obvious that the cost of
production, so far as this expression can be accurately interpreted, varies as the
reciprocal of the degree of productiveness. The rate of wages remaining constant, the
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cost per unit of commodity must of course be lower as the quantity produced in return
for a certain amount of wages is greater. Thus we may lay down the equation
Now, it was shown in pp. 186, 187 that the quantities exchanged are directly
proportional to the degrees of productiveness, or
But the ratio of the values is the reciprocal of and the ratio of the costs of
production is the reciprocal of the other member of the above equation. Thus it
follows that
or, in other words, value is proportional to cost of production. As, moreover, the final
degrees of utility of commodities are inversely as the quantities exchanged, it follows
that the values per unit are directly proportional to the final degrees of utility.
As it is quite indispensable that the student of political economy should keep the
relations of these quantities before his mind with perfect clearness, I repeat the results
in several forms of statement. Thus we may group the ratios together—
We may state the matter more briefly in the following words:—The quantities of
commodity given or received in exchange are directly proportional to the degrees of
productiveness of labour applied to their production, and inversely proportional to
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the values and prices of those commodities and to their costs of production per unit,
as well as to their final degrees of utility. I will even repeat the same statements once
more in the form of a diagram—
Quantities of Commodity exchanged vary
directly as the quantities inversely as their
produced by the same labour.(1) Values.
(2) Prices.
(3) Costs of production.
(4) Final degrees of utility.
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Various Cases Of The Theory.
As we have now reached the principal question in Economics, it will be well to
consider the meaning and results of our equations in some detail.
It will, in the first place, be apparent that the absolute facility of producing
commodities will not determine the character and amount of trade. The ratio of
exchange is not determined by nor by separately, but by their
comparative magnitudes. If the producing power of a country were doubled, no direct
effect would be produced upon the terms of its commerce provided that the increase
were equal in all branches of production. This is a point of great importance, which
was correctly conceived by Ricardo, and has been fully explained by J. S. Mill.
But though there is no such direct effect, it may happen that there will be an indirect
effect through the variation in the degree of utility of different articles. When an
increased amount of every commodity can be produced, it is not likely that the
increase will be equally desired in each branch of consumption. Hence the degree of
utility will fall in some cases more than in others. An alteration of the ratios of
exchange must result, and the production of the less needed commodities will not be
extended so much as in the case of the more needed ones. We might find in such
instances new proofs that value depends not upon labour but upon the degree of
utility.
It will also be apparent that nations possessing exactly similar powers of production
cannot gain by mutual commerce, and consequently will not have any such
commerce, however free from artificial restrictions. We get this result as
follows:—Taking as before, to be the final ratios of productiveness in one
country, and in a second, then, if the conditions of production are exactly
similar, we have
But when a country does not trade at all, its labour and consumption is distributed
according to the condition
Now, from these equations, it follows necessarily that
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that is to say, the production and consumption already conform to the conditions of
production of the second country, and will not undergo any alteration when trade with
this country becomes possible.
This is the doctrine usually stated in works on Political Economy, and for which there
are good grounds. But I do not think the statement will hold true if the conditions of
consumption be very different in two countries. There might be two countries exactly
similar in regard to their powers of producing beef and corn, and if their habits of
consumption were also exactly similar, there would be no trade in these articles. But
suppose that the first country consumed proportionally more beef, and the second
more corn; then, if there were no trade, the powers of the soil would be differently
taxed, and different ratios of exchange would prevail. Freedom of trade would cause
an interchange of corn for beef. Thus I conclude that it is only where the habits of
consumption, as well as the powers of production, are alike, that trade brings no
advantage.
The general effect of foreign commerce is to disturb, to the advantage of a country,
the mode in which it distributes its labour. Excluding from view the cost of carriage,
and the other expenses of commerce, we must always have true
If, then, was originally less in proportion to than is in accordance with
these equations, some labour will be transferred from the production of y to that of x
until, by the increased magnitude of and the lessened magnitude of w equality is
brought about.
As in the theory of exchange, so in the theory of production, any of the equations may
fail, and the meaning is capable of interpretation. Thus, if the equation
cannot be established, it is impossible that the production of both commodities, y and
x, can go on. One of them will be produced at an expenditure of labour constantly out
of proportion to that at which it may be had by exchange. If we could not, for
instance, import oranges from abroad, part of the labour of the country would
probably be diverted from its present employment to raise them; but the cost of
production would be always above that of getting them indirectly by exchange, so that
free trade necessarily destroys such a wasteful branch of industry It is on this principle
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that we import the whole of our wines, teas, sugar, coffee, spices, and many other
articles from abroad.
The ratio of exchange of any two commodities will be determined by a kind of
struggle between the conditions of consumption and production; but here again failure
of the equations may take place. In the all-important equations
expresses the ease with which we may make additions to y. If we find any
means, by machinery or otherwise, of increasing y without limit, and with the same
ease as before, we must, in all probability, alter the ratio of exchange in a
corresponding degree. But if we could imagine the existence of a large population,
within reach of the supposed country, whose desire to consume the quantity y
1
never
decreased, however large was the quantity available, then we should never have
equal to and the producers of y would make large gains of the nature of rent.
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Joint Production.
In one of the most interesting chapters of his Principles of Political Economy, Book
III., chap. xvi., John Stuart Mill has treated of what he calls "Some peculiar Cases of
Value." Under this title he refers to those commodities which are not produced by
separate processes, but are the concurrent or joint results of the same operations. "It
sometimes happens," he says, "that two different commodities have what may be
termed a joint cost of production. They are both products of the same operation, or set
of operations, and the outlay is incurred for the sake of both together, not part for one
and part for the other. The same outlay would have to be incurred for either of the
two, if the other were not wanted or used at all. There are not a few instances of
commodities thus associated in their production. For example, coke and coal-gas are
both produced from the same material, and by the same operation. In a more partial
sense, mutton and wool are an example; beef, hides, and tallow; calves and dairy
produce; chickens and eggs. Cost of production can have nothing to do with deciding
the values of the associated commodities relatively to each other. It only decides their
joint value.... A principle is wanting to apportion the expenses of production between
the two." He goes on to explain that, since the cost of production principle fails us, we
must revert to a law of value anterior to cost of production, and more fundamental,
namely, the law of supply and demand.
On some other occasion I may perhaps more fully point out the fallacy involved in
Mill's idea that he is reverting to an anterior law of value, the law of supply and
demand, the fact being that in introducing the cost of production principle, he had
never quitted the laws of supply and demand at all. The cost of production is only one
circumstance which governs supply, and thus indirectly influences values.
Again, I shall point out that these cases of joint production, far from being "some
peculiar cases," form the general rule, to which it is difficult to point out any clear or
important exceptions. All the great staple commodities at any rate are produced
jointly with minor commodities. In the case of corn, for instance, there are the straw,
the chaff, the bran, and the different qualities of flour or meal, which are products of
the same operations. In the case of cotton, there are the seed, the oil, the cotton waste,
the refuse, in addition to the cotton itself. When beer is brewed the grains regularly
return a certain price. Trees felled for timber yield not only the timber, but the
loppings, the bark, the outside cuts, the chips, etc. No doubt the secondary products
are often nearly valueless, as in the case of cinders, slag from blast furnaces, etc. But
even these cases go to show all the more impressively that it is not cost of production
which rules values, but the demand and supply of the products.
The great importance of these cases of joint production renders it necessary for us to
consider how they can be brought under our theory. Let us suppose that there are two
commodities, X and Y, yielded by one same operation, which always produces them
in the same ratio, say of m of X to n of Y. It might seem at first sight as if this ratio
would correspond to the ratio of the degrees of productiveness, as shown a few pages
above, that we might say
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and thus arrive at the conclusion that things jointly produced would always exchange
in the ratio of productiveness. But this would be entirely false, because that equation
can only be established when there is freedom of producing one or the other, at each
application of a new increment of labour. It is the freedom of varying the quantities of
each that allows of the produce being accommodated to the need of it, so that the ratio
of the degrees of utility, of the degrees of productiveness, and of the quantities
exchanged are brought to equality. But in cases of joint production there is no such
freedom; the one substance cannot be made without making a certain fixed proportion
of the other, which may have little or no utility.
It will easily be seen, however, that such cases are brought under our theory by simply
aggregating together the utilities of the increments of the joint products. If dx cannot
be produced without dy, these being the products of the same increment of labour, dl,
then the ratio of produce to labour cannot be written otherwise than as
It is impossible to divide up the labour and say that so much is expended on producing
X, and so much on Y. But we must estimate separately the utilities of dx and dy, by
multiplying by their degrees of utility and and we then have the
aggregate ratio of utility to labour as
It is plain that we have no equation arising out of these conditions of production, so
that the ratio of exchange of X and Y will be governed only by the degrees of utility.
But if we compare X and Y with a third commodity Z, as regards its production, we
shall arrive at the equation
In other words, the increment of utility obtained by applying an increment of labour to
the production of Z, must equal the sum of the increments of utility which would be
obtained if the same increment of labour were applied to the joint production of X and
Y. It is evident that the above equation taken alone gives us no information as to the
ratios existing between the quantities dx,dy, and dz. Before we can obtain any ratios of
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exchange we must have the further equation between the degrees of utility of X and
Y, namely,
As a general rule, however, any two processes of production will both yield joint
products, so that the equation of productiveness will take the form of a sum of
increments of utility on both sides, which we may thus write briefly—
Such an equation becomes then a kind of equation of condition of which the influence
may be very slight regarding the ratio of exchange of any two of the commodities
concerned. And if in some cases the terms on one side of such an equation are
reduced to one or two, it is probably because the other increments of produce are
nearly or quite devoid of utility. As in the cases of cinders, chips, sawdust, spent dyes,
potato stalks, chaff, etc. etc., almost every process of industry yields refuse results, of
which the utility is zero or nearly so. To solve the subject fully, however, we should
have to admit negative utilities, as elsewhere explained, so that the increment of
utility from any increment dl of labour would really take the form
du
1
± du
2
± du
3
±...
The waste products of a chemical works, for instance, will sometimes have a low
value; at other times it will be difficult to get rid of them without fouling the rivers
and injuring the neighbouring estates; in this case they are discommodities and take
the negative sign in the equations.
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Over-production.
The theory of the distribution of labour enables us to perceive clearly the meaning of
over-production in trade. Early writers on Economics were always in fear of a
supposed glut, arising from the powers of production surpassing the needs of
consumers, so that industry would be stopped, employment fail, and all but the rich
would be starved by the superfluity of commodities. The doctrine is evidently absurd
and self-contradictory. As the acquirement of suitable commodities is the whole
purpose of industry and trade, the greater the supplies obtained the more perfectly
industry fulfils its purpose. To bring about a universal glut would be to accomplish
completely the aim of the economist, which is to maximise the products of labour. But
the supplies must be suitable—that is, they must be in proportion to the needs of the
population. Over-production is not possible in all branches of industry at once, but it
is possible in some as compared with others. If, by miscalculation, too much labour is
spent in producing one commodity, say silk goods, our equations will not hold true.
People will be more satiated with silk goods than cotton, woollen, or other goods.
They will refuse, therefore, to purchase them at ratios of exchange corresponding to
the labour expended. The producers will thus receive in exchange goods of less utility
than they might have acquired by a better distribution of their labour.
In extending industry, therefore, we must be careful to extend it proportionally to all
the requirements of the population. The more we can lower the degree of utility of all
goods by satiating the desires of the purchasers the better; but we must lower the
degrees of utility of different goods in a corresponding manner, otherwise there is an
apparent glut and a real loss of labour.
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Limits To The Intensity Of Labour.
I have mentioned (p. 170) that labour may vary either in duration or intensity, but
have yet paid little attention to the latter circumstance. We may approximately
measure the intensity of labour by the amount of physical force undergone in a certain
time, although it is the pain attending that exertion of force which is the all-important
element in Economics. Interesting laws have been or may be detected connecting the
amount of work done with the intensity of labour. Even where these laws have not
been ascertained, long experience has led men, by a sort of unconscious process of
experimentation and inductive reasoning, to select that rate of work which is most
advantageous.
Let us take such a simple kind of work as digging. A spade may be made of any size,
and if the same number of strokes be made in the hour, the requisite exertion will vary
nearly as the cube of the length of the blade. If the spade be small the fatigue will be
slight, but the work done will also be slight. A very large spade, on the other hand,
will do a great quantity of work at each stroke, but the fatigue will be so great that the
labourer cannot long continue at his work. Accordingly, a certain medium-sized spade
is adopted, which does not overtax a labourer and prevent him doing a full day's work,
but enables him to accomplish as much as possible. The size of a spade should depend
partly upon the tenacity and weight of the material, and partly upon the strength of the
labourer. It may be observed that, in excavating stiff clay, navvies use a small strong
spade; for ordinary garden purposes a larger spade is employed; for shovelling loose
sand or coals a broad capacious shovel is used; and a still larger instrument is
employed for removing corn, malt, or any loose light powder.
In most cases of muscular exertion the weight of the body or of some limb is of great
importance. If a man be employed to carry a single letter, he really moves a weight of
say a hundred and sixty pounds for the purpose of conveying a letter weighing
perhaps half an ounce. There will be no appreciable increase of labour if he carries
twenty letters, so that his efficiency will be multiplied twenty times. A hundred letters
would probably prove a slight burden, but there would still be a vast gain in the work
done. It is obvious, however, that we might go on loading a postman with letters until
the fatigue became excessive; the maximum useful result would be obtained with the
largest load which does not severely fatigue the man, and trial soon decides the
weight with considerable accuracy.
The most favourable load for a porter was investigated by Coulomb, and he found that
most work could be done by a man walking upstairs without any load, and raising his
burden by means of his own weight in descending. A man could thus raise four times
as much in a day as by carrying bags on his back with the most favourable load. This
great difference doubtless arises from the muscles being perfectly adapted to raising
the human body, whereas any additional weight throws irregular or undue stress upon
them. Charles Babbage, also, in his admirable Economy of Manufactures, has
remarked on this subject, and has pointed out that the weight of some limb of the
body is an element in all calculations of human labour.
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"The fatigue produced on the muscles of the human frame," says Babbage, "does not
altogether depend on the actual force employed in each effort, but partly on the
frequency with which it is exerted. The exertion necessary to accomplish every
operation consists of two parts: one of these is the expenditure of force which is
necessary to drive the tool or instrument; and the other is the effort required for the
motion of some limb of the animal producing the action. In driving a nail into a piece
of wood, one of these is lifting the hammer, and propelling its head against the nail;
the other is raising the arm itself, and moving it in order to use the hammer. If the
weight of the hammer is considerable, the former part will cause the greatest portion
of the exertion. If the hammer is light, the exertion of raising the arm will produce the
greatest part of the fatigue. It does therefore happen that operations requiring very
trifling force, if frequently repeated, will tire more effectually than more laborious
work. There is also a degree of rapidity beyond which the action of the muscles
cannot be pressed."1
It occurred to me, some time since, that this was a subject admitting of interesting
inquiry, and I tried to determine, by several series of experiments, the relation
between the amount of work done by certain muscles and the rate of fatigue. One
series consisted in holding weights varying from one pound to eighteen pounds in the
hand while the arm was stretched out at its full length. The trials were two hundred
and thirty-eight in number, and were made at intervals of at least one hour, so that the
fatigue of one trial should not derange the next. The average number of seconds
during which each weight could be sustained was found to be as follows:—
Weight in pounds . .18 1410 7 4 2 1
Time in seconds... 153260 87148 219321.
If the arm had been thus employed in any kind of useful work, we should have
estimated the useful effect by the product of the weight sustained and the time. The
results would be as follows, in pounds- seconds:—
Weight... 18 14 10 7 4 2 1
Useful effect...266 455603 612592 438321.
The maximum of useful effect would here appear to be about seven pounds, which is
about the weight usually chosen for dumb-bells and other gymnastic instruments.
Details of the other series of experiments are described in an article in Nature (30th
June 1870, vol. ii. p. 158).
I undertook these experiments as a mere illustration of the mode in which some of the
laws forming the physical basis of Economics might be ascertained. I was unaware
that Professor S. Haughton had already, by experiment, arrived at a theory of
muscular action, communicated to the Royal Society in 1862. I was gratified to find
that my entirely independent results proved to be in striking agreement with his
principles, as was pointed out by Professor Haughton in two articles in Nature.1
I am not aware that any exact experiments upon walking or marching have been
made, but, as Professor Haughton has remarked to me, they might easily be carried
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out in the movements of an army. It would only be necessary, on each march which is
carried up to the limits of endurance, to register the time and distance passed over.
Had we a determination of the exact relations of time, space, and fatigue, it would be
possible to solve many interesting problems. For instance, if one person has to
overtake another, what should be their comparative rates of walking? Assuming the
fatigue to increase as the square of the velocity multiplied by the time, we easily
obtain an exact solution, showing that the total fatigue will be least when one person
walks twice as quickly as he whom he wishes to overtake.
In different cases of muscular exertion we shall find different problems to solve. The
most advantageous rate of marching will greatly depend upon whether the loss of time
or the fatigue is the most important. To march at the rate of four miles an hour would
soon occasion enormous fatigue, and could only be resorted to under circumstances of
great urgency. The distance passed over would bear a much higher ratio to the fatigue
at the rate of three, or even two and a half miles an hour. But, if the speed were still
further reduced, a loss of strength would again arise, owing to that expended in
merely sustaining the body, as distinguished from that of moving it forward.
The Economics of Labour will constantly involve questions of this kind. When a work
has to be completed in a brief space of time, workmen may be incited by unusual
reward to do far more than their usual amount of work; but so high a rate would not
be profitable in other circumstances. The fatigue always rapidly increases when the
speed of work passes a certain point, so that the extra result is far more costly in
reality. In a regular and constant employment the greatest result will always be gained
by such a rate as allows a workman each day, or each week at the most, to recover all
fatigue and recommence with an undiminished store of energy.
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CHAPTER VI
THEORY OF RENT
Accepted Opinions Concerning Rent.
THE general correctness of the views put forth in preceding chapters derives great
probability from their close resemblance to the Theory of Rent, as it has been
accepted by English writers for nearly a century. It has not been usual to state this
theory in mathematical symbols, and clumsy arithmetical illustrations have been
employed instead; but it is easy to show that the fluxional calculus is the branch of
mathematics which most correctly applies to the subject.
The Theory of Rent was first discovered and clearly stated by James Anderson in a
tract published in 1777, and called An Inquiry into the Nature of the Corn Laws, with
a view to the Corn Bill proposed for Scotland. An extract from this work may be
found in MacCulloch's edition of the Wealth of Nations, p. 453, giving a most clear
explanation of the effect of the various fertility of land, and showing that it is not the
rent of land which determines the price of its produce, but the price of the produce
which determines the rent of the land. The following passage must be given in
Anderson's own words:—1
"... In every country there is a variety of soils, differing considerably from one another
in point of fertility. These we shall at present suppose arranged into different classes,
which we shall denote by the letters A, B, C, D, E, F, etc., the class A comprehending
the soils of the greatest fertility, and the other letters expressing different classes of
soils, gradually decreasing in fertility as you recede from the first. Now, as the
expense of cultivating the least fertile soil is as great or greater than that of the most
fertile field, it necessarily follows that if an equal quantity of corn, the produce of
each field, can be sold at the same price, the profit on cultivating the most fertile soil
must be much greater than that of cultivating the others; and as this continues to
decrease as the sterility increases, it must at length happen that the expense of
cultivating some of the inferior soils will equal the value of the whole produce."
The theory really rests upon the principle, which I have called the Law of
Indifference, that for the same commodity in the same market there can only be one
price or ratio of exchange. Hence, if different qualities of land yield different amounts
of produce to the same labour, there must be an excess of profit in some over others.
There will be some land which will not yield the ordinary wages of labour, and which
will, therefore, not be taken into cultivation, or if, by mistake, it is cultivated, will be
abandoned. Some land will just pay the ordinary wages; better land will yield an
excess, so that the possession of such land will become a matter of competition, and
the owner will be able to exact as rent from the cultivators the whole excess above
what is sufficient to pay the ordinary wages of labour.
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There is a secondary origin for rent in the fact, that if more or less labour and capital
be applied to the same portion of land, the produce will not increase proportionally to
the amount of labour. It is quite impossible that we could go on constantly increasing
the yield of one farm without limit, otherwise we might feed the whole country upon a
single farm. Yet there is no definite limit; for, by better and better culture, we may
always seem able to raise a little more. But the last increment of produce will come to
bear a smaller and smaller ratio to the labour required to produce it, so that it soon
becomes, in the case of all land, undesirable to apply more labour.
MacCulloch has given, in his edition of the Wealth of Nations,1 a supplementary note,
in which he explains, with the utmost clearness and scientific accuracy, the nature of
the theory. This note contains by far the best statement of the theory, as it seems to
me, and I will therefore quote his recapitulation of the principles which he establishes.
"1. That if the produce of land could always be increased in proportion to the outlay
on it, there would be no such thing as rent.
"2. That the produce of land cannot, at an average, be increased in proportion to the
outlay, but may be indefinitely increased in a less proportion.
"3. That the least productive portion of the outlay, which, speaking generally, is the
last, must yield the ordinary profits of stock. And
"4. That all which the other portions yield more than this, being above ordinary
profits, is rent."
A most satisfactory account of the theory is also given in James Mill's Elements of
Political Economy, a work which I never read without admiring its brief, clear, and
powerful style. James Mill constantly uses the expression dose of capital. "The time
comes," he says, "at which it is necessary either to have recourse to land of the second
quality, or to apply a second dose of capital less productively upon land of the first
quality." He evidently means by a dose of capital a little more capital, and though the
name is peculiar, the meaning is simply that of an increment of capital. The number
of doses or increments mentioned is only three, but this is clearly to avoid prolixity of
explanation. There is no reason why we should not consider the whole capital divided
into many more doses. The same general law which makes the second dose less
productive than the first, will make a hundredth dose, speaking generally, less
productive than the preceding ninety-ninth dose. Theoretically speaking, there is no
need or possibility of stopping at any limit. A mathematical law is in theory always
continuous, so that the doses considered are indefinitely small and indefinitely
numerous. I consider, then, that James Mill's mode of expression is exactly equivalent
to that which I have adopted in earlier parts of this book. As mathematicians have
invented a precise and fully recognised mode of expressing doses or increments, I
know not why we should exclude language from Economics which is found
convenient in all other sciences. It is mere pedantry to insist upon calling that a dose
in Economics, which in all the other sciences is called by the perfectly established and
expressive term increment.
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The following are James Mill's general conclusions as to the nature of Rent.1 "In
applying capital, either to lands of various degrees of fertility, or in successive doses
to the same land, some portions of the capital so employed are attended with a greater
produce, some with a less. That which yields the least yields all that is necessary for
reimbursing and rewarding the capitalist. The capitalist will receive no more than this
remuneration for any portion of the capital which he employs, because the
competition of others will prevent him. All that is yielded above this remuneration the
landlord will be able to appropriate. Rent, therefore, is the difference between the
return yielded to that portion of the capital which is employed upon the land with the
least effect, and that which is yielded to all the other portions employed upon it with a
greater effect."
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Symbolic Statement Of The Theory.
The accepted Theory of Rent, as given above, needs little or no alteration to adapt it to
expression in mathematical symbols. For doses or increments of capital I shall
substitute increments of labour, partly because the functions of capital remain to be
considered in the next chapter, and partly because James Mill, J. S. Mill, and
MacCulloch hold the application of capital to be synonymous with the application of
labour. This assumption is implied in James Mill's statement (p. 13); it is expressly
stated in J. S. Mill's First Fundamental Proposition concerning the Nature of
Capital;1 and MacCulloch adds a footnote2 to make it clear, that as all capital was
originally produced by labour, the application of additional capital is the application
of additional labour. "Either the one phrase or the other may be used
indiscriminately." This doctrine is in itself altogether erroneous, but it will not be
erroneous to assume as a mode of simplifying the problem that the increments of
labour applied are equally assisted by capital. It is a separate and subsequent problem
to determine how rent or interest arises when the same labour is assisted by different
quantities of capital.
I shall suppose that a certain labourer, or, what comes to exactly the same thing, a
body of labourers, expend labour on several different pieces of ground. On what
principle will they distribute their labour between the several pieces? Let us imagine
that a certain amount has been spent upon each, and that another small portion, Dl, is
going to be applied. Let there be two pieces of land, and let Dx
1
, Dx
2
, be the
increments of produce to be expected from the pieces respectively. They will
naturally apply the labour to the land which yields the greatest result. So long as there
is any advantage in one use of labour over another, the most advantageous will
certainly be adopted. Therefore, when they are perfectly satisfied with the distribution
made, the increment of produce to the same labour will be equal in each case; or we
have
To attain scientific accuracy, we must decrease the increments infinitely, and then we
obtain the equation—
Now represents the ratio of produce, or the productiveness of
labour, as regards the last increment of labour applied. We may say, then, that
whenever a labourer or body of labourers distribute their labour over pieces of land
with perfect economy, the final ratios of produce to labour will be equal.
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We may now take into account the general law, that when more and more labour is
applied to the same piece of land, the produce ultimately does not increase
proportionately to the labour. This means that the function dx/dl diminishes without
limit towards zero after x has passed a certain quantity. The whole produce of a piece
of land is x, the whole labour spent upon it is l; and x varies in some way as l varies,
never decreasing when l increases. We may say, then, that x is a function of l; let us
call it Pl. When a little more labour is expended, the increment of produce dx is dPl,
and is the final rate of production, the same as was previously denoted by .
In the Theory of Labour it was shown that no increment of labour would be expended
unless there was sufficient recompense in the produce, but that labour would be
expended up to the point at which the increment of utility exactly equals the
increment of pain incurred in acquiring it. Here we find an exact definition of the
amount of labour which will be profitably applied.
It was also shown that the last increment of labour is the most painful, so that if a
person is recompensed for the last increment of labour which he applies to land by the
rate of production , it follows that all the labour he applies might be
recompensed sufficiently at the same rate. The whole labour is l, so that if the
recompense were equal over the whole, the result would be . Consequently,
he obtains more than the necessary return to labour by the amount
or, as we may write it,
Pl-l · P'l,
in which P'l is the differential coefficient of Pl, or the final rate of production. This
expression represents the advantage he derives from the possession of land in
affording him more profit than other methods of employing his labour. It is therefore
the rent which he would ask before yielding it up to another person, or equally the
rent which he would be able and willing to pay if hiring it from another.
The same considerations apply to every piece of land cultivated. When the same
person or body of labourers cultivates several pieces, P'l will be of the same
magnitude in each case, but the quantities of labour, and possibly the functions of
labour, will be different. Thus with two pieces of land the rent may be represented as
P
1
l
1
+ P
2
l
2
- (l
1
+ l
2
) P
1
'l
1
;
or, speaking generally of any number of pieces, it is the sum of the quantities of the
form Pl, minus the sum of the quantities of the form l.P'l.
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Illustrations Of The Theory.
It is very easy to illustrate the Theory of Rent by diagrams. For, let distances along the
line ox denote quantities of labour, and let the curve apc represent the variation of the
rate of production, so that the area of the curve will be the measure of the produce.
Thus when labour has been applied to the amount om, the produce will correspond to
the area apmo. Let a small new increment of labour, mm', be applied, and
suppose the rate of production equal over the whole of the increment. Then the small
parallelogram, pp'm'm, will be the produce. This will be proportional in quantity to
pm, so that the height of any point of the curve perpendicularly above a point of the
line ox represents the rate of production at that point in the application of labour.
If we further suppose that the labourer considers his labour, mm', repaid by the
produce pm', there is no reason why any other part of his labour should not be repaid
at the same rate. Drawing, then, a horizontal line, rpq, through the point p, his whole
labour, om, will be repaid by the produce represented by the area orpm. Consequently,
the overlying area, rap, is the excess of produce which can be exacted from him as
rent, if he be not himself the owner of the land.
Imagining the same person to cultivate another piece of land, we might take the curve,
bqc, to represent its productiveness. The same rate of production will repay the
labourer in this case as in the last, so that the intersection of the same horizontal line,
rpq, with the curve, will determine the final point of labour, n. The area, rn, will be
the measure of the sufficient recompense to the whole labour, on, spent upon the land;
and the excess of produce or rent will be the area, rbq. In a similar manner, any
number of pieces of land might be considered. The figure might have been drawn so
that the curves would rise on leaving the initial line oy, indicating that a very little
labour will have a poor rate of production; and that a certain amount of labour is
requisite to develop the fertility of the soil. This may often or always be the case, as a
considerable quantity of labour is generally requisite in first bringing land into
cultivation, or merely keeping it in a fit state for use. The laws of rent depend on the
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undoubted principle, that the curves always ultimately decline towards the base line
ox, that is, the final rate of production always ultimately sinks towards zero.
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CHAPTER VII
THEORY OF CAPITAL
The Function Of Capital.
IN considering the nature and principles of Capital, we enter a distinct branch of our
subject. There is no close or necessary connection between the employment of capital
and the processes of exchange. Both by the use of capital and by exchange we are
enabled vastly to increase the sum of utility which we enjoy; but it is conceivable that
we might have the advantages of capital without those of exchange. An isolated man
like Alexander Selkirk might feel the benefit of a stock of provisions, tools, and other
means of facilitating industry, although cut off from traffic with other men.
Economics, then, is not solely the science of Exchange or Value: it is also the science
of Capitalisation.
The views which I shall endeavour to establish on this subject are in fundamental
agreement with those adopted by Ricardo; but I shall try to put the Theory of Capital
in a more simple and consistent manner than has been the case with some later
economists. We are told, with perfect truth, that capital consists of wealth employed
to facilitate production; but when economists proceed to enumerate the articles of
wealth constituting capital, they obscure the subject. "The capital of a country," says
Mac-Culloch,1 "consists of those portions of the produce of industry existing in it
which may be directly employed either to support human beings, or to facilitate
production." Professor Fawcett again says:2 "Capital is not confined to the food
which feeds the labourers, but includes machinery, buildings, and, in fact, every
product due to man's labour which can be applied to assist his industry; but capital
which is in the form of food does not perform its functions in the same way as capital
that is in the form of machinery: the one is termed circulating capital, the other fixed
capital."
The notion of capital assumes a new degree of simplicity as soon as we recognise that
what has been called a part is really the whole. Capital, as I regard it, consists merely
in the aggregate of those commodities which are required for sustaining labourers of
any kind or class engaged in work. A stock of food is the main element of capital; but
supplies of clothes, furniture, and all the other articles in common daily use are also
necessary parts of capital. The current means of sustenance constitute capital in its
free or uninvested form. The single and all-important function of capital is to enable
the labourer to await the result of any long-lasting work,—to put an interval between
the beginning and the end of an enterprise.
Not only can we, by the aid of capital, erect large works which would otherwise have
been impossible, but the production of articles which would have been very costly in
labour may be rendered far more easy. Capital enables us to make a great outlay in
providing tools, machines, or other preliminary works, which have for their sole
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object the production of some important commodity, and which will greatly facilitate
production when we enter upon it.
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Capital Is Concerned With Time.
Several economists have clearly perceived that the time elapsing between the
beginning and end of a work is the difficulty which capital assists us to surmount.
Thus James Mill has said: "If the man who subsists on animals cannot make sure of
his prey in less than a day, he cannot make sure of his prey in less than a day, he
cannot have less than a whole day's subsistence in advance. If hunting excursions are
undertaken which occupy a week or a month, subsistence for several days may be
required. It is evident, when men come to live upon those productions which their
labour raises from the soil, and which can be brought to maturity only once in the
year, that subsistence for a whole year must be laid up in advance."1
Much more recently, Professor Hearn has said, in his admirable work entitled
Plutology:1 "The first and most obvious mode in which capital directly operates as an
auxiliary of industry is to render possible the performance of work which requires for
its completion some considerable time. In the simplest agricultural operations there is
the seed-time and the harvest. A vineyard is unproductive for at least three years
before it is thoroughly fit for use. In gold mining there is often a long delay,
sometimes even of five or six years, before the gold is reached. Such mines could not
be worked by poor men unless the storekeepers gave the miners credit, or, in other
words, supplied capital for the adventure. But, in addition to this great result, capital
also implies other consequences which are hardly less momentous. One of these is the
steadiness and continuity that labour thus acquires. A man, when aided by capital, can
afford to remain at his work until it is finished, and is not compelled to leave it
incomplete while he searches for the necessary means of subsistence. If there were no
accumulated fund upon which the labourer could rely, no man could remain for a
single day exclusively engaged in any other occupation than those which relate to the
supply of his primary wants. Besides these wants, he should also from time to time
search for the materials on which he was to work."
These passages imply, as it seems to me, a clear insight into the nature and purposes
of capital, except that the writers have not with sufficient boldness followed out the
consequences of their notion. If we take a comprehensive view of the subject, it will
be seen that not only the chief but the sole purpose of capital is as above described.
Capital simply allows us to expend labour in advance. Thus, to raise corn we need to
turn over the surface of the soil. If we proceed straight to the work, and use the
implements with which nature has furnished us—our fingers—we should spend an
enormous amount of painful labour with very little result. It is far better, therefore, to
spend the first part of our labour in making a spade or other implement to assist the
rest of our labour. This spade represents so much labour which has been invested, and
so far spent; but if it lasts three years, its cost may be considered as repaid gradually
during those three years. This labour, like that of digging, has for its object the raising
of corn, and the only essential difference is that it has to precede the production of
corn by a longer interval. The average interval of time for which labour will remain
invested in the spade is half of the three years. Similarly, if we possess a larger
capital, and expend it in making a plough, which will last for twenty years, we invest
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at the beginning a great deal of labour which is only gradually repaid during those
twenty years, and which is therefore, on the average, invested for about ten years.
It is true that in modern industry we should seldom or never find the same man
making the spade or plough, and afterwards using the implement. The division of
labour enables me, with much advantage, to expend a portion of my capital in
purchasing the implement from some one who devotes his attention to the
manufacture, and probably expends capital previously in facilitating the work. But
this does not alter the principles of the matter. What capital I give for the spade
merely replaces what the manufacturer had already invested in the expectation that the
spade would be needed. Exactly the same considerations may be applied to much
more complicated applications of capital. The ultimate object of all industry engaged
with cotton is the production of cotton goods. But the complete process of producing
those goods is divided into many parts; and it is necessary to begin the spending of
labour a long time before any goods can be finished.
In the first place, labour will be required to till the land which is to bear the cotton
plants, and probably two years at least will elapse between the time when the ground
is first broken and the time when the cotton reaches the mills. A cotton mill, again,
must be a very strong and durable structure, and must contain machinery of a very
costly character, which can only repay its owner by a long course of use. We might
spin and weave cotton goods as in former times, or as it is done in Cashmere, with a
very small use of capital; but then the labour required would be enormously greater in
proportion to the produce. It is far more economical in the end to spend a vast amount
of labour and capital in building a substantial mill and filling it with the best
machinery, which will then go on working with unimpaired efficiency for thirty years
or more. This means that, in addition to the labour spent in superintending the
machines at the moment when goods are produced, a great quantity of labour has been
spent from one to thirty years in advance, or, on the average, fifteen years in advance.
This expenditure is repaid by an annuity of profit extending over those thirty years.
The interval elapsing between the first exertion of labour and the enjoyment of the
result is further increased by any time during which the raw material may lie in
warehouses before reaching the machines; and by the time employed in distributing
the goods to retail dealers, and through them to the consumers. It may even happen
that the consumer finds it desirable to keep a certain stock on hand, so that the time
when the real object of the goods is fulfilled becomes still further deferred. During
this time, also, capital seems to me to be invested, and only as actual utilisation takes
place is expenditure repaid by corresponding utility enjoyed.
I would say, then, in the most general manner, that whatever improvements in the
supply of commodities lengthen the average interval between the moment when
labour is exerted and its ultimate result or purpose accomplished, such improvements
depend upon the use of capital. And I would add that this is the sole use of capital.
Whenever we overlook the irrelevant complications introduced by the division of
labour and the frequency of exchange, all employments of capital resolve themselves
into the fact of time elapsing between the beginning and the end of industry.
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Quantitative Notions Concerning Capital.
One main point which has to be clearly brought before the mind in this subject is the
difference between the amount of capital invested and the amount of investment of
capital. The first is a quantity of one dimension only—the quantity of capital; the
second is a quantity of two dimensions, namely, the quantity of capital, and the length
of time during which it remains invested. If one day's labour remains invested for two
years, the capital is only that equivalent to one day; but it is locked up twice as long as
if it were invested for only one year. Now all questions in which we consider the most
advantageous employment of capital turn upon the length of investment quite as much
as upon the amount. The same capital will serve for twice as much industry if it be
absorbed or invested for only half the time.
The amount of investment of capital will evidently be determined by multiplying each
portion of capital invested at any moment by the length of time for which it remains
invested. One pound invested for five years gives the same result as five pounds
invested for one year, the product being five pound-years. Most commonly, however,
investment proceeds continuously or at intervals, and we must form clear notions on
the subject. Thus, if a workman be employed during one year on any work, the result
of which is complete, and enjoyed at the end of that time, the absorption of capital
will be found by multiplying each day's wages by the days remaining till the end of
the year, and adding all the results together. If the daily wages be four shillings, then
we have
We may also represent the investment by a diagram such as Fig. X. The length along
the line ox indicates the duration of investment, and the height
attained at any point, a, is the amount of capital invested. But it is the whole area of
the rectangles up to any point, a, which measures the amount of investment during the
time oa.
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The whole result of continued labour is not often consumed and enjoyed in a moment;
the result generally lasts for a certain length of time. We must then conceive the
capital as being progressively uninvested. Let us, for sake of simple illustration,
imagine the labour of producing the harvest to be continuously and equally expended
between the first of September in one year and the same day in the next. Let the
harvest be then completely gathered, and its consumption begin immediately and
continue equally during the succeeding twelve months. Then the amount of
investment of capital will be represented by the area of an isosceles triangle, as in Fig.
XI., the base of which corresponds to two years
of duration. Now the area of a triangle is equal to the height multiplied by half the
base; and as the height represents the greatest amount invested, that upon the first of
September, when the harvest is gathered; half the base, or one year, is the average
time of investment of the whole amount.
In the 37th proposition of the first book of Euclid it is proved that all triangles upon
the same base and between the same parallels are equal in area. Hence we may draw
the conclusion that, provided capital be invested and uninvested continuously and in
simple proportion to the time, we need only regard the greatest amount invested and
the greatest time of investment. Whether it be all invested suddenly, and then
gradually withdrawn; or gradually invested and suddenly withdrawn; or gradually
invested and gradually withdrawn; the amount of investment will be in every case the
greatest amount of capital multiplied by half the time elapsing from the beginning to
the end of the investment.
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Expression For Amount Of Investment.
To render our notions of the subject still more exact and general, let us resort once
more to mathematical symbols.
Let Dp = amount of capital supposed to be invested in the time Dt; let t = time
elapsing before its result is enjoyed, the enjoyment taking place in an interval of time
Dt, which may be disregarded in comparison with t. Then t · Dp is the amount of
investment; and if the investment is repeated, the sum of the quantities of the nature of
t · Dp, or, in the customary mode of expression, St · Dp is the total amount of
investment. But it will seldom be possible to assign each portion of result to an
exactly corresponding portion of labour. Cotton goods are due to the aggregate
industry of those who tilled the ground, grew the cotton, plucked, transported,
cleaned, spun, wove, and dyed it; we cannot distinguish the moment when each
labourer's work is separately repaid. To avoid this difficulty, we must fix on some
moment of time when the whole transaction is closed, all labour upon the ground
repaid, the mill and machinery worn out and sold, and the cotton goods consumed.
Let t now denote the time elapsing from any moment up to this final moment of
closing the accounts. Let Dp be as before an increment of capital invested, and let Dq
be an increment of capital uninvested by the sale of the products and their enjoyment
by the consumer. Thus it will be pretty obvious that the sum of the quantities t · Dp,
less by the sum of the quantities t · Dq will be the total investment of capital, or
expressed in symbols
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Dimensions Of Capital, Credit And Debit.
As the subject presents itself to me at present, I apprehend that capital is to be
regarded simply as commodity. If so, the dimension of capital will be represented by
M, and the amount of investment of capital, possessing the additional dimension of
time, will have the symbol MT. How then are we to determine the quantitative nature
of what Senior called Abstinence, that temporary sacrifice of enjoyment which is
essential to the existence of capital? Senior thus explicitly defined what he meant by
the word:1 "By the word Abstinence, we wish to express that agent, distinct from
labour and the agency of nature, the concurrence of which is necessary to the
existence of capital, and which stands in the same relation to profit as labour does to
wages." He goes on to explain that abstinence, though usually accompanying labour,
is distinct from it. A careful consideration of Senior's remarks shows that in reality
abstinence is the endurance of want, the abstaining from the enjoyment of utility
which might be enjoyed. Now the degree or intensity of want is measured by the
degree of utility of commodity if it were consumed. Great degree of utility simply
means great want, so that one dimension of abstinence must be U, and time being also
obviously an element of abstinence, the required symbolic statement of its dimensions
will be UT. This result satisfactorily corresponds with Senior's definition, for he says
that abstinence is to profit as labour is to wages. Now profit or interest is clearly
symbolised by M, and wages also by M, both consisting simply of quantities of
commodity. Thus UT bears just the same relation to M that ET does to M, for E
signifies the degree of painfulness of labour, and can barely be distinguished from U,
except in sign.
The relation of abstinence, UT, to total utility, MU, also confirms our result. For if we
convert abstinence into satisfaction, by giving a supply of commodity for
consumption, this action is symbolically represented by multiplying UT into MT-1,
which yields MU, or utility.
It will need no argument to show that the dimension of debit and credit, having regard
only to what is borrowed and owed, will be the dimension of commodity simply, or
M. According to the practice of commerce, a contract of debt is a contract to return a
certain physically defined quantity of a specified substance, such as an ounce of gold,
a ton of pig-iron, a hogshead of palm oil. No attempt is made to define quantities of
utility, so that the debt when repaid shall yield utility equal to what it possessed when
lent. The borrower and lender either take their chance about this, or provide for it in
the rate of interest to be paid. It is equally obvious that in another sense the amount of
credit or debit will be proportional to the duration of the operation, and will have the
dimensions MT.
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Effect Of The Duration Of Work.
Perhaps the most interesting point in the Theory of Capital is the advantage arising
from the rapid performance of work, if it is capable of being done with convenience
and with the same ultimate result. To investigate this point, suppose that = the
whole amount of wages which it is requisite to pay in building a house, and that this
does not alter when we vary, within certain limits, the time employed in the work,
denoted by t. If the work goes on continuously, we shall, during each unit of time,
have an amount invested equal to the tth part of ****w. The whole amount of
investment of capital will therefore be represented by the area of a triangle whose
base is t and height w; that is, the investment is ½ tw. Thus when the whole
expenditure is ultimately the same, the amount of investment is simply proportional to
the time. The result would be more serious if the accumulation of compound interest
during the time were taken into account; but the consideration of compound interest
would render the formulæ very complex, and is not requisite for the purpose in view.
We must clearly distinguish the case treated above, in which the amount of labour is
the same, but spread over a longer time, from other cases where the labour increases
in proportion to the time. The investment of capital, then, grows in an exceedingly
rapid manner. Neglecting the first cost of tools, materials, and other preparations, let
the first day's labour cost a; during the second day this remains invested, and the
amount of capital a is added; on each following day a like addition is made. The
amount of capital invested is evidently
At beginningof second daya,
At beginningof third daya + a,
At beginningof fourth daya + a + a;
and so on. If the work lasts during n + 1 days, the total amount of investment of
capital will be
a + 2 a + 3 a + 4 a +... n a.
The sum of the series is
which increases by a term involving the square of the time. The employment of
capital thus grows in proportion to the triangular numbers
1, 3, 6, 10, 15, 21, etc.
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If we regard the investment as taking place continuously, the whole absorption of
capital is represented
by the area of a right-angled triangle (Fig. XII.), in which ob
1
, b
1
, b
2
, b
2
b
3
, etc., are
the successive units of time. The heights of the lines a
1
b
1
, a
2
b
2
represent the amounts
invested at the ends of the times. The daily investment being a, the total amount of
investment will be
, increasing as the square of the time.
Cases of this kind continually occur, as in sinking a deep mine, of which the requisite
depth cannot be previously known with accuracy. Any large work, such as a
breakwater, an embankment, the foundations of a great bridge, a dock, a long tunnel,
the dredging of a channel, involves a problem of a similar nature; for it is seldom
known what amount of labour and capital will be required; and if the work lasts much
longer than was expected, the result is usually a financial disaster.
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Illustrations Of The Investment Of Capital.
The time during which capital remains invested, and the circumstances of its
investment and reproduction, are exceedingly various in different employments. If a
person plants cabbages, they will be ready in the course of a few months, and the
labour of planting and tending them, together with a part of the labour of preparing
and manuring the soil, yields its results with very little delay. In planting a forest tree,
however, a certain amount of labour is expended, and no result obtained until after the
lapse of thirty, forty, or fifty years. The first cost of enclosing, preparing, and planting
a plantation is considerable; and though, after a time, the loppings and thinnings of the
trees repay the cost of superintendence and repairs, yet the absorption of capital is
great, and we may thus account for the small amount of planting which goes on. The
ageing of wine is a somewhat similar case. A certain amount of labour is expended
without result for ten or fifteen years, and the cost of storage is incurred during the
whole time. To estimate the real cost of the articles at the end of the time, we must, in
all such cases, add compound interest, and this grows in a rapid manner. Every pound
invested at the commencement of a business becomes 1·63 pounds at the end of ten
years, 11·47 pounds at the end of fifty years, and no less than 131·50 pounds at the
end of a century, the rate of interest being taken at five per cent. Thus it cannot be
profitable to store wine for fifty years, unless it become about twelve times as
valuable as it was when new. It cannot pay to plant an oak and let it live a century,
unless the timber then repays the cost of planting 132 times.
If an annual charge, however small, has to be incurred (for instance, the cost of
storage and superintendence), the expense mounts up in a still more alarming manner.
Thus, if the cost of any investment is one pound per annum, the amount invested, with
compound interest at five per cent, becomes 12·58 pounds at the end of ten years,
209·35 pounds at the end of fifty years, and the enormous amount of 2610·03 at the
end of a century. We shall almost always have to take into account both the original
and continuous cost of an investment. Thus if a stock of wine worth £100 be laid by
for fifty years, and the cost of storage be £1 per annum, the total cost at the end of the
time will be £1147·0 on account of original cost, and £209·35 for storage, or in all
£1356·35.
It is to be feared that the rapid accumulation of compound interest is often overlooked
in estimating the cost of public works and other undertakings of considerable
duration. A great fort, breakwater, or canal (the Caledonian Canal, for instance) is
often not completed for twenty years after its commencement, and in the meantime it
may be of little or no use. Suppose that its cost has been £10,000 each year; then the
aggregate cost would seem to be £200,000, but allowing for interest at five per cent it
is really £330,000. The French engineer and economist, Minard,1 fully understood
this point of finance, and showed that in the case of some public works, such as the
great digue of Cherbourg harbour, and canals, the execution of which is allowed
sometimes to drag on for half a century before any adequate result is returned, the real
cost is incomparably greater than it is represented to be by merely stating the sums of
money expended. In some cases, such as the first canal of Saint Quentin, a work, after
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being long prosecuted, is abandoned, and the loss by first cost and interest becomes
enormous. The Guernsey Harbour is a case in point, and the English dockyards would
supply abundance of similar facts.
An interesting example of the investment of capital occurs in the case of gold and
silver, a large stock of which is maintained either in the form of money, or plate and
jewellery. Labour is spent in the digging or mining of the metals, which is gradually
repaid by the use or satisfaction arising from the possession of the metals during the
whole time for which they continue in use. Hence the investment of capital extends
over the average duration of the metals. Now, if the stock of gold requires one per
cent of its amount to maintain it undiminished, it will be apparent that each particle of
gold remains in use 100 years on the average; if ½ per cent is sufficient, the average
duration will be 200 years. We may state the result thus:
Loss of gold or silver annually.Average duration of each particle in use.
1 per cent 100 years
½ per cent 200 years
¼ per cent 400 years
1/10 per cent 1000 years
The wear and loss of the precious metals in a civilised country is probably not more
than part annually, including plate, jewellery, and money in the estimate, so
that the average investment will be for 200 years. It is curious that, if we regard a
quantity of gold as wearing away annually by a fixed percentage of what remains, the
duration of some part is infinite, and yet the average duration is finite. Some of the
gold possessed by the Romans is doubtless mixed with what we now possess; and
some small part of it will be handed down as long as the human race exists.
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Fixed And Circulating Capital.
Economists have long been accustomed to distinguish capital into the two kinds, fixed
and circulating. Adam Smith called that circulating which passes from hand to hand,
and yields a revenue by being parted with. The fact of being frequently exchanged is,
however, an accidental circumstance which leads to no results of importance. Ricardo
altered the use of the terms, applying the name circulating to that which is frequently
destroyed and has to be reproduced. He says unequivocally:1 "In proportion as fixed
capital is less durable, it approaches to the nature of circulating capital. It will be
consumed, and its value reproduced in a shorter time, in order to preserve the capital
of the manufacturer." Accepting this doctrine, and carrying it out to the full extent, we
must say that no precise line can be drawn between the two kinds. The difference is
one of amount and degree. The duration of capital may vary from a day to several
hundred years; the most circulating is the least durable; the most fixed the most
durable.
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Free And Invested Capital.
I believe that the clear explanation of the doctrine of capital requires the use of a term
free capital, which has not been hitherto recognised by economists. By free capital I
mean the wages of labour, either in its transitory form of money, or its real form of
food and other necessaries of life. The ordinary sustenance requisite to support
labourers of all ranks when engaged upon their work is really the true form of capital.
It is quite in agreement with the ordinary language of commercial men to say, not that
a factory, or dock, or railway, or ship, is capital, but that it represents so much capital
sunk in the enterprise. To invest capital is to spend money, or the food and
maintenance which money purchases, upon the completion of some work. The capital
remains invested or sunk until the work has returned profit, equivalent to the first cost,
with interest.
Much clearness would result from making the language of Economics more nearly
coincident with that of commerce. Accordingly, I would not say that a railway is fixed
capital, but that capital is fixed in the railway. The capital is not the railway, but the
food of those who made the railway. Abundance of free capital in a country means
that there are copious stocks of food, clothing, and every article which people insist
upon having—that, in short, everything is so arranged that abundant subsistence and
conveniences of every kind are forth-coming without the labour of the country being
much taxed to provide them. In such circumstances it is possible that a part of the
labourers of the country can be employed on works of which the utility is distant, and
yet no one will feel scarcity in the present.
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Uniformity Of The Rate Of Interest.
A most important principle of this subject is, that free capital can be indifferently
employed in any branch or kind of industry. Free capital, as we have just seen,
consists of a suitable assortment of all kinds of food, clothing, utensils, furniture, and
other articles which a community requires for its ordinary sustenance. Men and
families consume much the same kind of commodities, whatever may be the branch
of manufacture or trade by which they earn a living. Hence there is nothing in the
nature of free capital to determine its employment to one kind of industry rather than
another. The very same wages, whether we regard the money wages, or the real wages
purchased with the money, will support a man whether he be a mechanic, a weaver, a
coal miner, a carpenter, a mason, or any other kind of labourer.
The necessary result is, that the rate of interest for free capital will tend to and closely
attain uniformity in all employments. The market for capital is like all other markets:
there can be but one price for one article at one time. It is a case of the Law of
Indifference (p. 90). Now the article in question is the same, so that its price must be
the same. Accordingly, as is well known, the rate of interest, when freed from
considerations of risk, trouble, and other interfering causes, is the same in all trades;
and every trade will employ capital up to the point at which it just yields the current
interest. If any manufacturer or trader employs so much capital in supporting a certain
amount of labour that the return is less than in other trades, he will lose; for he might
have obtained the current rate by lending it to other traders.
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General Expression For The Rate Of Interest.
We may obtain a general expression for the rate of interest yielded by capital in any
employment provided that we may suppose the produce for the same amount of
labour to vary as some continuous function of the time elapsing between the
expenditure of the labour and the enjoyment of the result. Let the time in question be
t, and the produce for the same amount of labour the function of t denoted by Ft,
which may be supposed always to increase with t. If we now extend the time to t + Dt,
the produce will be F (t + Dt), and the increment of produce F (t + Dt) - Ft. The ratio
which this increment bears to the increment of investment of capital will determine
the rate of interest. Now, at the end of the time t, we might receive the product Ft, and
this is the amount of capital which remains invested when we extend the time by Dt.
Hence the amount of increased investment of capital is Dt · Ft; and, dividing the
increment of produce by this last expression, we have
When we reduce the magnitude of Dt infinitely, the limit of the first factor of the
above expression is the differential coefficient of Ft, so that we find the rate of
interest to be represented by
The interest of capital is, in other words, the rate of increase of the produce divided by
the whole produce; but this is a quantity which must rapidly approach to zero, unless
means can be found of continually maintaining the rate of increase. Unless a body
moves with a rapidly increasing speed, the space it moves over in any unit of time
must ultimately become inconsiderable compared with the whole space passed over
from the commencement. There is no reason to suppose that industry, generally
speaking, is capable of returning any such vastly increasing produce from the greater
application of capital. Every new machine or other great invention will usually require
a fixation of capital for a certain average time, and may be capable of paying interest
upon it; but when this average time is reached, it fails to afford a return to more
prolonged investments.
To take an instance, let us suppose that the produce of labour in some case is
proportional to the interval of abstinence t; then we have say Ft = a · t, in which a is
an unknown constant. The differential coefficient F't is now a; and the rate of interest
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or
or
; or the rate of interest varies inversely as the time of investment.
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Dimension Of Interest.
The formula which we obtained in the preceding section has been subjected to close
criticism by an eminent mathematician, who proposed several alternative formulæ,
but finally accepted my solution of the question as correct. As Professor Adamson,
however, has also raised some objections to the formula, it seems desirable to explain
its meaning and mode of derivation more fully than was done in the first edition.
In the first place, as regards the theory of dimensions the formula is clearly correct.
The rate of interest expresses the ratio which the annual sum paid per annum for the
loan of capital bears to the capital. The interest and the capital are quantities of the
same nature, their ratio being an abstract number. Dividing by length of time rate of
interest will have the dimension T -1.
Or we may put it in this way—Interest is paid per annum, or per month, or per other
unit of time, and the less the magnitude of this unit, the less must be the numerical
expression of the rate of interest. Simple interest at five per cent per annum is 0.416...
per cent per month, and so on. Hence time enters negatively, and the dimension of the
rate of interest will be T -1. Or, again, we may state it thus symbolically—The capital
advanced may be taken as having the dimension M; the annual return has the
dimensions MT. Dividing the former by the latter we obtain
Now the formula
clearly agrees with this result; for the denominator is a certain unknown function of
the time of advance of the capital t. We may assume that it can be expressed in a finite
series of the powers of t, and the numerator, being the differential coefficient of the
same function, will be of one degree of power less than Ft. Hence the dimensions of
the formula will be
It must be carefully remembered that it is the rate of interest which has the dimension
T -1, not interest itself, which, being simply commodity of some kind, has the
dimension of commodity, namely M, of the same nature, and having the same
dimensions.
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The function of capital is simply this, that labour which would produce certain
commodity m
1
, if that commodity were needed immediately for the satisfaction of
wants, is applied so as to produce m
2
after the lapse of the time t. The reason for this
deferment is that m
2
usually exceeds m
1
, and the difference or interest m
2
- m
1
is
commodity having the same dimensions as m
1
. Hence the rate of interest, apart from
the question of time, would be m
2
- m
1
divided by m
1
, and the quantities being of the
same nature, the ratio will be an abstract number devoid of dimensions. But the time
for which the results of labour are foregone is as important a matter as the quantity of
commodity. The amount of deferment is m
1
t, so that the rate of interest is m
2
- m
1
divided by m
1
t, which will have the dimension T -1.
Exactly the same result would be obtained, however, if we regarded the use of capital
from a different point of view. Capital and deferment of consumption are not needed
only in order to increase production, that is to say, the manufacture of goods; they are
needed also to equalise consumption, and to allow commodity to be consumed when
its utility is at the highest point. Now, when certain commodity is consumed within an
interval of time, the utility produced will, as we have seen, possess the dimensions
MUT -1 T, or MU. Suppose that instead of being consumed within that interval, the
commodity is held in hand for a time before being consumed at all. Then the amount
of deferment of utility will be proportional both to the interval of time over which it is
deferred, and to the utility which is deferred. Thus the amount of deferment will have
the dimensions MUT. The increase of utility due to deferment will clearly have the
same dimensions as were previously determined, namely MU. Hence the ratio of this
increase to the amount of deferment will have the dimensions or T -1, and
this result corresponds with the dimension of the rate of interest as otherwise reached.
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Peacock On The Dimensions Of Interest.
The need of some care in forming our conceptions of these quantities is strikingly
illustrated by the fact that not quite fifty years ago so profound and philosophic a
mathematician as the late Dean Peacock completely misapprehended the matter. In
the first edition of his celebrated and invaluable Treatise on Algebra, published in
1830, he gives (§111, p. 91) the interest of money as an example of a quantity of three
dimensions, and one which may be represented by a solid. He says: "If p represent the
principal or sum of money lent or forborne, r the rate of interest (of £1 for one year),
and t the number of years, then the interest accumulated or due will be represented by
prt; for if r be the interest of £1 for one year, pr will be the interest of a sum of money
denoted by p for one year, and therefore prt will be the amount of this interest in t
years, no interest being reckoned upon interest due: such would be the result
according to the principles of Arithmetical Algebra.
"If we now suppose prt represented respectively by lines which form the adjacent
edges of a parallelopipedon, the solid thus formed will represent the interest
accumulated or due: in other words, it will represent whatever is represented by the
general formula prt when specific values and significations are given to its symbols:
for in whatever manner we may suppose any one of the symbols of prt to vary, the
solid will vary in the same proportion.
"The lines which we assume to represent units of p,r, and t, are perfectly arbitrary,
whether they are made equal to each other or not: this is clearly the case with p and t,
which are quantities of a different nature: and the third quantity is likewise different
from the other two, being an abstract numerical quantity: for it expresses the relation
between the interest of £1 and £1, or between the interest of £100 and £100, which is
the quotient of the division of one quantity by another of the same nature: thus, if the
interest be five per cent, then : if four per cent, then
: and similarly in other cases: the line, therefore, which is
assumed to represent the abstract unit to which r is referred, is independent of the
lines which represent units of p and of t, and may therefore be assumed at pleasure,
equally with those lines.
"The lines which represent p and t form a rectangular area, which is the geometrical
representation of their product: the third quantity r, being merely numerical, may
either be represented by a line, as in the case just considered, when a solid
parallelopipedon is made the representative of prt: or we may consider the area pt as
representing the product prt when r = 1, and that this product in any other case is
represented by a rectangle which bears to the rectangle pt the ratio of r to 1: this may
be effected by increasing or diminishing one of the sides of the rectangle in the
required ratio: the product prt may therefore be correctly represented either by a solid
or an area, when one of the factors is an abstract number."
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The conclusion at which he arrives is a lame one, for he thinks that the same kind of
quantity may be represented indifferently by a solid or an area. The fact is that
Peacock confused a product of three factors with a quantity of three dimensions. He
took these dimensions as if they were, say M = money, R = rate of interest, and T =
time. If we simply multiply these together, as Peacock first does, we get a quantity
apparently of three dimensions, MRT. If, according to Peacock's subsequent idea, we
take R to be an abstract numerical quantity, then we have two dimensions left,
namely, MT. He overlooks the fact that the rate of interest involves time negatively,
although he describes r as "the rate of interest (of £1 for one year)." Correctly stated,
the dimensions of prt, the quantity of interest are M × T -1 × T or M, that is simply the
dimension of the money advanced.
If you say, for instance, that the simple interest of £300 at five per cent per annum for
five years is £75, there remains no reference in this result to time: £75 is simply £75,
and is of exactly the same nature as the £300 which bore the interest.
That Peacock subsequently discovered error, or at least difficulty, in this section, is
rendered probable by the fact that he omitted the illustration altogether in his second
edition; but he does not, so far as I have observed, give any explanation.
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Tendency Of Profits To A Minimum.
It is one of the favourite doctrines of economists since the time of Adam Smith, that
as society progresses and capital accumulates, the rate of profit, or more strictly
speaking, the rate of interest, tends to fall. The rate will always ultimately sink so low,
they think, that the inducements to further accumulation will cease. This doctrine is in
striking agreement with the result of the somewhat abstract analytical investigation
given above. Our formula for the rate of interest shows that unless there be constant
progress in the arts, the rate must tend to sink towards zero, supposing accumulation
of capital to go on. There are sufficient statistical facts, too, to confirm this conclusion
historically. The only question that can arise is as to the actual cause of this tendency.
Adam Smith vaguely attributed it to the competition of capitalists, saying: "The
increase of stock which raises wages, tends to lower profit. When the stocks of many
rich merchants are turned into the same trade, their mutual competition naturally tends
to lower its profit; and when there is a like increase of stock in all the different trades
carried on in the same society, the same competition must produce the same effect in
them all."1
Later economists have entertained different views. They attributed the fall of interest
to the rise in the cost of labour. The produce of labour, they said, is divided between
capitalists and labourers, and if it is necessary to give more to labour, there must be
less left to capital, and the rate of profit will fall. I shall discuss the validity of this
theory in the final chapter, and will only remark here, that it is not in agreement with
the view which I have ventured to take concerning the origin of interest. I consider
that interest is determined by the increment of produce which it enables a labourer to
obtain, and is altogether independent of the total return which he receives for this
labour. Our formula (p. 245) shows that the rate of interest will be greater as the
whole produce Ft is less, if the advantage of more capital, measured by F't, remains
unchanged. In many ill-governed countries, where the land is wretchedly tilled, the
average produce is small, and yet the rate of interest is high, simply because the want
of security prevents the due supply of capital: hence more capital is urgently needed,
and its price is high. In America and the British Colonies the produce is often high,
and yet interest is high, because there is not sufficient capital accumulated to meet all
the demands. In England and other old countries the rate of interest is generally lower
because there is an abundance of capital, and the urgent need of more is not actually
felt.
I conceive that the returns to capital and labour are independent of each other. If the
soil yields little, and capital will not make it yield more, then both wages and interest
will be low, provided that the capital be not attracted away to more profitable
employment. If the soil yields much, and capital will make it yield more, then both
wages and interest will be high; if the soil yields much, and capital will not make it
yield more, then wages will be high and interest low, unless the capital finds other
investments. But the subject is much complicated by the interference of rent. When
we speak of the soil yielding much, we must distinguish between the whole yield and
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the final rate of yield. In the Western States of America the land yields a large total,
and all at a high final rate, so that the labourer enjoys the result. In England there is a
large total yield, but a small final yield, so that the landowner receives a large rent and
the labourer small wages. The more fertile land having here been long in cultivation,
the wages of the labourer are measured by what he can earn by cultivating sterile land
which it only just pays to take into cultivation.
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Advantage Of Capital To Industry.
We must take great care not to confuse the rate of interest on capital with the whole
advantage which it confers on industry. The rate of interest depends on the advantage
of the last increment of capital, and the advantages of previous increments may be
greater in almost any ratio. In considering the laws of utility, we found that an article
possessing an immensely great total utility, for instance corn or water, might have a
very low final degree of utility, because our need of it was almost entirely satisfied;
yet the ratio of exchange always depends upon the final, not the previous degree of
utility. The case is the same with capital. Some capital may be indispensable to a
manufacture; hence the benefit conferred by the capital is indefinitely great, and were
there no more capital to be had, the rate of interest which could be demanded,
assuming the article manufactured to be necessary, would be almost unlimited. But as
soon as ever a larger supply of capital becomes available, the prior benefit of capital is
overlooked. As free capital is always the same in quality, the second portion may be
made to replace the first if needful: hence capitalists can never exact from labourers
the whole advantages which their capital confers—they can exact only a rate
determined by the advantage of the last increment. A lender of capital cannot say to a
borrower who wants £3000: "I know that £1000 is indispensable to your business, and
therefore will charge you 100 per cent interest upon it; for the second £1000, which is
less necessary, I will charge twenty per cent; and as upon the third £1000 you can
only earn the common profit, I will only ask five percent." The answer would be, that
there are many people only earning five per cent on their capital who would be glad to
lend enough at a small advance of interest; and it is a matter of indifference who is the
lender.
The general result of the tendency to uniformity of interest is, that employers of
capital always get it at the lowest prevailing rate; they always borrow the capital
which is least necessary to others, and
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either the labourers themselves, or the public generally as consumers, gather all the
excess of advantage. To illustrate this result, let distances along the line ox, in Fig.
XIII., mark quantities of capital employing in any branch of industry a fixed number
of labourers. Let the area of the curve denote the whole produce of labour and capital.
Thus to the capital, on, results a produce measured by the area of the curvilinear
figure between the upright lines oy and qn. But the amount of increased produce
which would be due to an increment of capital would be measured by the line qn, so
that this will represent F't (p. 245). The interest of the capital will be its amount, on,
multiplied by the rate qn, or the area of the rectangle oq. The remainder of the
produce, pqry, will belong to the labourer. But had less capital been available, say not
more than om, its rate of interest would have been measured by pm, the amount of
interest by the rectangle op, while the labourer must have remained contented with the
smaller share, psy. I will not say that the above diagram represents with strict
accuracy the relations of capital, produce, wages, rate of interest, and amount of
interest; but it may serve roughly to illustrate their relations. I see no way of
representing exactly the theory of capital in the form of a diagram.
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Are Articles In The Consumers' Hands Capital?
The views of the nature of capital expressed in this chapter generally agree with those
entertained by Ricardo and various other economists; but there is one point in which
the theory leads me to a result at variance with the opinions of almost all writers. I
feel quite unable to adopt the opinion that the moment goods pass into the possession
of the consumer they cease altogether to have the attributes of capital. This doctrine
descends to us from the time of Adam Smith, and has generally received the
undoubting assent of his followers. The latter, indeed, have generally omitted all
notice of such goods, treating them as if no longer under the view of the economist.
Adam Smith, although he denied the possessions of a consumer the name of capital,
took care to enumerate them as part of the stock of the community. He divides into
three portions the general stock of a country, and while the second and third portions
are fixed and circulating capital, the first is described as follows:—1
"The first is that portion which is reserved for immediate consumption, and of which
the characteristic is, that it affords no revenue or profit. It consists in the stock of
food, clothes, household furniture, etc., which have been purchased by their proper
consumers, but which are not yet entirely consumed. The whole stock of mere
dwelling-houses too subsisting at any one time in the country make a part of this first
portion. The stock that is laid out in a house, if it is to be the dwelling-house of the
proprietor, ceases from that moment to serve in the function of a capital, or to afford
any revenue to its owner. A dwelling-house, as such, contributes nothing to the
revenue of its inhabitant; and though it is, no doubt, extremely useful to him, it is as
his clothes and household furniture are useful to him, which, however, make a part of
his expense, and not of his revenue."
MacCulloch, indeed, in his edition of the Wealth of Nations, p. 121, has remarked
upon this passage, that "the capital laid out in building houses for such persons is
employed as much for the public advantage as if it were vested in the tools or
instruments they make use of in their respective businesses." He appears, in fact, to
reject the doctrine, and it is surprising that economists have generally acquiesced in
Adam Smith's view, though it leads to manifest contradictions. It leads to the absurd
conclusion that the very same thing fulfilling the very same purposes will be capital or
not according to its accidental ownership. To procure good port wine it is necessary to
keep it for a number of years, and Adam Smith would not deny that a stock of wine
kept in the wine merchant's possession for this purpose is capital, because it yields
him revenue. If a consumer buys it when new, and keeps it to improve, it will not be
capital, although it is evident that he gains the same profit as the merchant by buying
it at a lower price. If a coal merchant lays in a stock of coal when cheap, to sell when
dear, it is capital; but if a consumer lays in a stock, it is not.
Adam Smith's views seem to be founded upon a notion that capital ought to give an
annual revenue or increase of wealth like a field yields a crop of corn or grass.
Speaking of a dwelling-house, he says: "If it is to be let to a tenant for rent, as the
house itself can produce nothing, the tenant must always pay the rent out of some
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other revenue, which he derives either from labour, or stock, or land. Though a house,
therefore, may yield a revenue to its proprietor, and thereby serve in the function of a
capital to him, it cannot yield any to the public, nor serve in the function of a capital
to it, and the revenue of the whole body of the people can never be in the smallest
degree increased by it. Clothes and house-hold furniture, in the same manner,
sometimes yield a revenue, and thereby serve in the function of a capital to particular
persons. In countries where masquerades are common, it is a trade to let out mas-
querade dresses for a night. Upholsterers frequently let furniture by the month or by
the year. Undertakers let the furniture of funerals by the day and by the week. Many
people let furnished houses, and get a rent, not only for the use of the house, but for
that of the furniture. The revenue, however, which is derived from such things, must
always be ultimately drawn from some other source of revenue."1
This notion that people live upon a kind of net revenue flowing in to them appears to
be derived from the old French economists, and plays no part in modern Economics.
Nothing is more requisite than a dwelling-house, and if a person cannot hire a house
at the required spot, he must find capital to build it. I think that no economist would
refuse to count among the fixed capital of the country that which is sunk in dwelling-
houses. Capital is sunk in farming that we may have bread, in cotton mills that we
may be clothed, and why not in houses that we may be lodged? If land yields an
annual revenue of corn and wool, milk, beef, and other necessaries, houses yield a
revenue of shelter and comfort. The sole end of all industry is to satisfy our wants;
and if capital is requisite to supply shelter, and furniture and useful utensils, as it
undoubtedly is, why refuse it the name which it bears in all other employments?
Can we deny that the property of a hotel-keeper is capital and yields a revenue to its
owner? Yet it is invested in pots and pans, and beds, and all kinds of common
furniture. In America it is not uncommon for people to live all their lives in hotels or
boarding-houses; and we might readily conceive the system to advance until no one
would undertake housekeeping except as a profession. Now if we allow to what is
invested in hotels, hired furnished houses, lodgings, and the like, the nature of capital,
I do not see how we can refuse it to common houses. We should thus be led into all
kinds of absurdities.
For instance, if two people live in their own houses, these are not, according to
present opinion, capital; if they find it convenient to exchange houses and pay rent
each to the other, the houses are capital. At great watering-places like Brighton it is a
regular business to lease houses, fill them with furniture, and then let them for short
periods as furnished houses: surely it is capital which is embarked in the trade. If a
private individual happens to own a furnished house which he does not at the time
want, and lets it, can we refuse to regard his house and furniture as capital? Whenever
one person provides the articles and another uses them and pays rent, there is capital.
Surely, then, if the same person uses and owns them, the nature of the things is not
fundamentally different. There is no need for a money payment to pass; but every
person who keeps accurate accounts should debit those accounts with an annual
charge for interest and depreciation on what he has invested in house and furniture.
Housekeeping is an occupation involving wages, capital and interest, like any other
business, except that the owner consumes the whole result.
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By accepting this view of the subject, we shall avoid endless difficulties. What, for
instance, shall we say to a theatre? Is it not the product of capital? Can it be erected
without capital? Does it not return interest, if successful, like any cotton mill or steam
vessel? If the economist agrees to this, he must allow, on similar grounds, that a very
large part of the aggregate capital of the country is invested in theatres, hotels,
schools, lecture rooms, and institutions of various kinds which do not belong to the
industry of the country, taken in a narrow sense, but which none the less contribute to
the wants of its inhabitants, which is the sole object of all industry.
I may add that even the food, clothes, and many other possessions of extensive classes
are often indubitable capital; they are bought upon credit, and interest is undoubtedly
paid for the capital sunk in them by the dealers. There is hardly, I suppose, a man of
fashion in London who walks in his own clothes, and the tailors find in the practice a
very profitable investment for capital. Except among the poorer classes, and often
among them, food is seldom paid for until after it is consumed. Interest must be paid
one way or another upon the capital thus absorbed. Whether or not these articles in the
consumers' hands are capital, at any rate they have capital invested in them—that is,
labour has been spent upon them of which the whole benefit is not enjoyed at once.
I might also point out at almost any length, that the stock of food, clothing, and other
requisite articles of subsistence in the country are a main part of capital according to
the statements of J. S. Mill, Professor Fawcett, and most other economists. Now what
does it really matter if these articles happen to lie in the warehouses of traders or in
private houses, so long as there is a stock? At present it is the practice for farmers and
corn merchants to hold the produce of the harvest until the public buys and consumes
it. Surely the stock of corn is capital. But if it were the practice of every housekeeper
to buy up corn in the autumn and keep it in a private granary, would it not serve in
exactly the same way to subsist the population? Would not everything go on exactly
the same, except that every one would be his own capitalist in regard to corn in place
of paying farmers and corn merchants for doing the business?
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CHAPTER VIII
CONCLUDING REMARKS
The Doctrine Of Population.
IT is no part of my purpose in this work to attempt to trace out, with any approach to
completeness, the results of the theory given in the preceding chapters. When the
views of the nature of Value, and the general method of treating the subject by the
application of the fluxional calculus, have received some recognition and acceptance,
it will be time to think of results. I shall therefore only occupy a few more pages in
pointing out the branches of economic doctrine which have been passed over, and in
indicating their connection with the theory.
The doctrine of population has been conspicuously absent, not because I doubt in the
least its truth and vast importance, but because it forms no part of the direct problem
of Economics. I do not remember to have seen it remarked that it is an inversion of
the problem to treat labour as a varying quantity, when we originally start with labour
as the first element of production, and aim at the most economical employment of that
labour. The problem of Economics may, as it seems to me, be stated thus:—Given, a
certain population, with various needs and powers of production, in possession of
certain lands and other sources of material: required, the mode of employing their
labour which will maximise the utility of the produce. It is what mathematicians
would call a change of the variable, afterwards to treat that labour as variable which
was originally a fixed quantity. It really amounts to altering the conditions of the
problem so as to create at each change a new problem. The same results, however,
would generally be obtained by supposing the other conditions to vary. Given, a
certain population, we may imagine the land and capital at their disposal to be greater
or less, and may then trace out the results which will, in many respects, be applicable
respectively to a less or greater population with the original land and capital.
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Relation Of Wages And Profit.
There is another inversion of the problem of Economics which is generally made in
works upon the subject. Although labour is the starting-point in production, and the
interests of the labourer the very subject of the science, yet economists do not
progress far before they suddenly turn round and treat labour as a commodity which is
bought up by capitalists. Labour becomes itself the object of the laws of supply and
demand, instead of those laws acting in the distribution of the products of labour.
Economists have invented, too, a very simple theory to determine the rate at which
capital can buy up labour. The average rate of wages, they say, is found by dividing
the whole amount of capital appropriated to the payment of wages by the number of
the labourers paid; and they wish us to believe that this settles the question. But a little
consideration shows that this proposition is simply a truism.The average rate of
wages must be equal to what is appropriated to the purpose divided by the number
who share it. The whole question will consist in determining how much is
appropriated for the purpose; for it certainly need not be the whole existing amount of
circulating capital. Mill distinctly says, that because industry is limited by capital, we
are not to infer that it always reaches that limit;1 and, as a matter of fact, we often
observe that there is abundance of capital to be had at low rates of interest, while there
are also large numbers of artisans starving for want of employment. The wage-fund
theory is therefore illusory as a real solution of the problem, though I do not deny that
it may have a certain limited and truthful application, to be shortly considered.
Another part of the current doctrines of Economics determines the rate of profit of
capitalists in a very simple manner. The whole produce of industry must be divided
into the portions paid as rent, taxes, profits, and wages. We may exclude taxes as
exceptional, and not very important. Rent also may be eliminated, for it is essentially
variable, and is reduced to zero in the case of the poorest land cultivated. We thus
arrive at the simple equation—
Produce = profit + wages.
A plain result also is drawn from the formula; for we are told that if wages rise profits
must fall, and vice versâ. But such a doctrine is radically fallacious; it involves the
attempt to determine two unknown quantities from one equation. I grant that if the
produce be a fixed amount, then if wages rise profits must fall, and vice versâ.
Something might perhaps be made of this doctrine if Ricardo's theory of a natural rate
of wages, that which is just sufficient to support the labourer, held true. But I
altogether question the existence of any such rate.
The wages of working men in this kingdom vary from perhaps ten shillings a week up
to forty shillings or more; the minimum in one part of the country is not the minimum
in another. It is utterly impossible, too, to define exactly what are the necessaries of
life. I am inclined, therefore, to reject altogether the current doctrines as to the rate of
wages; and even if the theory held true of any one class of labourers separately, there
is the additional difficulty that we have to account for the very different rates which
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prevail in different trades. It is impossible that we should accept for ever Ricardo's
sweeping simplification of the subject, involved in his assumption, that there is a
natural ordinary rate of wages for common labour, and that all higher rates are merely
exceptional instances, to be explained away on other grounds.
The view which I accept concerning the rate of wages is not more difficult to
comprehend than the current one. It is that the wages of a working man are ultimately
coincident with what he produces, after the deduction of rent, taxes, and the interest
of capital. I think that in the equation
Produce = profit + wages,
the quantity of produce is essentially variable, and that profit is the part to be first
determined. If we resolve profit into wages of superintendence, insurance against risk,
and interest, the first part is really wages itself; the second equalises the result in
different employments; and the interest is, I believe, determined as stated in the last
chapter. The reader will observe the important qualification that wages are only
ultimately thus determined—that is, in the long run, and on the average of any one
branch of employment.
The fact that workmen are not their own capitalists introduces complexity into the
problem. The capitalists, or entrepreneurs, enter as a distinct interest. It is they who
project and manage a branch of production, and form estimates as to the expected
produce. It is the amount of this produce which incites them to invest capital and buy
up labour. They pay the lowest current rates for the kind of labour required; and if the
produce exceeds the average, those who are first in the field make large profits. This
soon induces competition on the part of other capitalists, who, in trying to obtain good
workmen, will raise the rate of wages. Competition will proceed until the point is
reached at which only the market rate of interest is obtained for the capital invested.
At the same time wages will have been so raised that the workmen reap the whole
excess of produce, unless indeed the price of the produce has fallen, and the public, as
consumers, have the benefit. Whether this latter result will follow or not depends
upon the number of labourers who are fitted for the work. Where much skill and
education is required, extensive competition will be impossible, and a permanently
high rate of wages will exist. But if only common labour is requisite, the price of the
goods cannot be maintained, wages will fall to their former point, and the public will
gain the advantage of cheaper supplies.
It will be observed that this account of the matter involves the temporary application
of the wage-fund theory. It is the proper function of capitalists to sustain labour before
the result is accomplished, and as many branches of industry require a large outlay
long previous to any definite result being arrived at, it follows that capitalists must
undertake the risk of any branch of industry where the ultimate profits are not
accurately known. But we now have some clue as to the amount of capital which will
be appropriated to the payment of wages in any trade. The amount of capital will
depend upon the amount of anticipated profits, and the competition to obtain proper
workmen will strongly tend to secure to the latter all their legitimate share in the
ultimate produce.
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For instance, let a number of schemes be set on foot for laying telegraphic cables. The
ultimate profits are very uncertain, depending upon the utility of the cables as
compared with their cost. If capitalists make a large estimate of those profits, they will
apply much capital to the immediate manufacture of the cables. All workmen
competent at the moment to be employed will be hired, and high wages paid if
necessary. Every man who has peculiar skill, knowledge, or experience, rendering his
assistance valuable, will be hired at any requisite cost. At this point it is the wage-
fund theory that is in operation. But, after a certain number of years, the condition of
affairs will be totally different. Capitalists will learn, by experience, exactly what the
profits of cables may be; that amount of capital will be thrown into the work which
finds the average amount of profits, and neither more nor less. The cost of
transmitting messages will be reduced by competition, so that no excessive profits
will be made by any of the parties concerned; the rate of wages, therefore, of every
species of labour will be reduced to the average proper to labour of that degree of
skill. But if there be required in any branch of the work a very special kind of skilled
and experienced labour, it will not be affected by competition in the same way, and
the wages or salary will remain high.
I think that it is in this way quite possible to reconcile theories which are at first sight
so different. The wage-fund theory acts in a wholly temporary manner. Every labourer
ultimately receives the due value of his produce after paying a proper fraction to the
capitalist for the remuneration of abstinence and risk. At the same time workers of
different degrees of skill receive very different shares according as they contribute a
common or a scarce kind of labour to the result.
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Professor Hearn's Views.
I have the more pleasure and confidence in putting forward these somewhat heretical
views concerning the general problem of Economics, inasmuch as they are nearly
identical with those arrived at by Professor Hearn, of Melbourne University. It would
be a somewhat long task to trace out exactly the coincidence of opinions between us,
but he certainly adopts the notion that the capitalist merely buys up temporarily the
prospects of the concern he manages and the labourers he employs. Thus he says: "In
place of having a share in the undertaking, the co-operator sells for a stipulated price
his labour or the use of his capital. The case therefore comes within the ordinary
conditions of exchange; and the price of labour and the price of capital are determined
in the same manner as all other questions of price are determined. Yet the general
character of the partnership is not destroyed. Although each particular transaction
amounts to a sale, yet for the continuance of the business a nearer connection arises.
Although the whole loss of the undertaking, if the undertaking be unfortunate, falls
upon the last proprietor, and the interests of the other parties have been previously
secured, yet each such loss prevents a repetition of the transaction from which it
arose. The capital which ought to have been replaced, and which if replaced would
have afforded the means of employing labour and of defraying the interest upon other
capital, has disappeared; and thus the market for labour and for capital is by so much
diminished. Both the labourer and the intermediate capitalist are therefore directly
concerned in the success of every enterprise towards which they have contributed. If it
be successful, they feel the advantage; if it be not successful, they feel in like manner
the loss. But this community of interest is no longer direct, but is indirect merely; and
it arises not from the gains or the losses of partners, but from the increased ability, or
the diminished demands, of customers."1
This passage really contains a statement of the views which I am inclined wholly to
accept; but no passages which I can select will convey an adequate notion of the
enlightened view which Professor Hearn takes of the industrial structure of society in
his admirable work on Plutology.
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The Noxious Influence Of Authority.
I have but a few lines more to add. I have ventured in the preceding pages to call in
question not a few of the favourite doctrines of economists. To me it is far more
pleasant to agree than to differ; but it is impossible that one who has any regard for
truth can long avoid protesting against doctrines which seem to him to be erroneous.
There is ever a tendency of the most hurtful kind to allow opinions to crystallise into
creeds. Especially does this tendency manifest itself when some eminent author,
enjoying power of clear and comprehensive exposition, becomes recognised as an
authority. His works may perhaps be the best which are extant upon the subject in
question; they may combine more truth with less error than we can elsewhere meet.
But "to err is human," and the best works should ever be open to criticism. If, instead
of welcoming inquiry and criticism, the admirers of a great author accept his writings
as authoritative, both in their excellences and in their defects, the most serious injury
is done to truth. In matters of philosophy and science authority has ever been the great
opponent of truth. A despotic calm is usually the triumph of error. In the republic of
the sciences sedition and even anarchy are beneficial in the long run to the greatest
happiness of the greatest number.
In the physical sciences authority has greatly lost its noxious influence. Chemistry, in
its brief existence of a century, has undergone three or four complete revolutions of
theory. In the science of light, Newton's own authority was decisively set aside,
though not until after it had retarded for nearly a century the progress of inquiry.
Astronomers have not hesitated, within the last few years, to alter their estimates of all
the dimensions of the planetary system, and of the universe, because good reasons
have been shown for calling in question the real coincidence of previous
measurements. In science and philosophy nothing must be held sacred. Truth indeed
is sacred; but, as Pilate said, "What is truth?" Show us the undoubted infallible
criterion of absolute truth, and we will hold it as a sacred inviolable thing. But in the
absence of that infallible criterion, we have all an equal right to grope about in our
search of it, and no body and no school nor clique must be allowed to set up a
standard of orthodoxy which shall bar the freedom of scientific inquiry.
I have added these words because I think there is some fear of the too great influence
of authoritative writers in Political Economy. I protest against deference for any man,
whether John Stuart Mill, or Adam Smith, or Aristotle, being allowed to check
inquiry. Our science has become far too much a stagnant one, in which opinions
rather than experience and reason are appealed to.
There are valuable suggestions towards the improvement of the science contained in
the works of such writers as Senior, Cairnes, Macleod, Cliffe-Leslie, Hearn,
Shadwell, not to mention a long series of French economists from Baudeau and Le
Trosne down to Bastiat and Courcelle-Seneuil; but they are neglected in England,
because the excellence of their works was not comprehended by David Ricardo, the
two Mills, Professor Fawcett, and others who have made the orthodox Ricardian
school what it is. Under these circumstances it is a positive service to break the
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monotonous repetition of current questionable doctrines, even at the risk of new error.
I trust that the theory now given may prove accurate; but, however this may be, it will
not be useless if it cause inquiry to be directed into the true basis and form of a
science which touches so directly the material welfare of the human race.
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APPENDIX I
List of Mathematico-Economic Books, Memoirs, and other published writings.
Remarks upon the purpose and some of the contents of this list will be found in the
preface to the second edition of this book.
1711. CEVA (Joanne). De re nummaria quoad fieri potuit geometrice Nactata.
Mantuae. 4to. 60 pp.
1717. MARIOTTE (Esme). Essaie de Logique. Second edition. In collected works.
Leide. See Principe 97 and 11me Partie, Article III.
1720. HUTCHESON (Francis). An Inquiry into the Original of our Ideas of Beauty
and Virtue. London. 8vo. (3d Edition, 1729, xxii, 304 pp.)
1728. HUTCHESON (Francis). An Essay on the Nature and Conduct of the Passions
and Affections, with Illustrations on the Moral Sense. London. 8vo. xxiv, 333 pp.
[1754. FORBONNAIS. Element du Commerce, ch. ix, and passim.]
1765. BECCARIA (Cesare). Tentativo analitico sui contrabbandi. Estratto dal foglio
periodico intitolato: Il Caffè (vol. i. Brescia). Custodi's Scrittori classici Italiani di
Economia politica. Parte Moderna, vol. xii, pp. 235-241. Milano, 1804.
1771. ANONYMOUS. An Essay on the Theory of Money. London. 8vo. 161 pp.
(attributed to Major-General Henry Lloyd).
1776. CONDILLAC (Etienne Bonnot de). Le Commerce et le Gouvernement. Paris.
1781. ANONYMOUS (A. N. Isnard). Traité des Richesses. Londres et Lausanne. 2
vols. 8vo. xxiv, 344, 327 pp.
1786. CONDORCET. Vie de Turgot, pp. 162-169.
1787. English Translation, pp. 403-409.
1792. S0ILIO (Guglielmo). Saggio sull' Influenza dell' Analisi nelle scienze politiche
ed economiche. (In vol. v of the collection Nuova Raccolta d'opuscoli di Autori
Siciliani. Palermo.)
1793. LANG. Historische Entwickelung der Deutschen Steuerverfassung. Riga.
1801. CANARD (Nicolas François). Principes d'Economie Politique: Ouvrage
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1883. EDGEWORTH (F. Y.) The Method of ascertaining a Change in the Value of
Gold. Jour. Statistical Society, London, vol. xlvi, pp. 714-718.
1883. LAUNHARDT (Wilhelm). Wirthschaftliche Fragen des Eisenbahnwesens.
Centralblatt der Bauverwaltung.
1883. WALRAS (Léon). Théorie mathematique de la Richesse sociale. 253 pp. 4to.
Lausanne.
1884. EDGEWORTH (F. Y.) The Rationale of Exchange. Jour. Statistical Society,
London, vol. xlvii, pp. 164-166.
1884. POYNTING (J. H.) A Comparison of the Fluctuations in the Price of Wheat,
and in Cotton and Silk Imports into Great Britain. Jour. Statistical Society, London,
vol. xlvii, pp. 34-64.
1884. WALRAS (Léon). Monnaie d'Or avec Billon d'Argent Regulateur. Bruxelles.
8vo.
1884. PIERSON (N. G.) Leerboek der Staathuishoudkunde. Erste deel. Haarlem.
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1884. WIESER (F. von). Ueber den Ursprung und die Hauptgesetze des
wirthschaftlichen Werthes. Wien.
1884. HOUDARD (Adolphe). Théorie générale de la valeur. Journal des
Économistes.
1884. WICKSTEED (Philip H.) Das Kapitab. A criticism. Today, Oct. London.
1884. GIDE (Charles). Principes d'economie politique. Paris.
1885. WALRAS (Léon). D'une Methode de Régularisation de la Variation de Valeur
de la Monnaie. Bull. Soc. Vaud. Sc. Nat. 22 pp. 8vo.
1885. SIMON (Alfred) and WALRAS (Léon). Contribution à l'étude des variations
des prix. Bull. Soc. Vaud. Sc. Nat. 11 pp. 8vo.
1885. LAUNHARDT (Wilhelm). Mathematische Begründung der
Volkswirthschaftslehre. Leipsig. viii, 216 pp. 8vo.
1885. LAUNHARDT (Wilhelm). Das Wesen des Geldes. Leipsig. vi, 75 pp. 8vo.
1886. GROSSMAN. Die Mathematik im Dienste der National-ökonomie. 1ste
Lieferung. 80 pp. 4to. Vienna.
1886. NEWCOMB (Simon). Principles of Political Economy. 8vo. New York. xvi,
543 pp.
1886. BOEHM-BAWERK. Grundzüge der Theorie des Wirtschaftlichen Güterwerts.
Jahrbücher für Nationalökonomie und Statistik N. F. Band xiii. Jena.
1886. PIERSON (N. G.) Grondbeginselen der Staathuishoudkunde Tweede Druk.
Haarlem.
1886. FEAUVEAU (G.) Études sur les Premiers Principes de la Science Économique.
Journal des Economistes.
1886. ANTONELLI (G. B.) Sulla Teoria Mathematica della economica politica. Pisa.
1886. WALRAS (Léon). Théorie de la Monnaie in 8vo. xii, 120 pp. Lausanne.
1886. GROSSMANN (Ludwig). Die Mathematik im Dienste der Nationalökonomie.
II Lieferung. Vienna.
1887. EDGEWORTH (F. Y.) On the Method of ascertaining and measuring
Variations in the Value of the Monetary Standard. Report of the British Association
for the Advancement of Science.
1887. EDGEWORTH (F. Y.) Metritike, or the Method of measuring Probability and
Utility. London: Temple Co.
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1887. AIKIN-KAROLY. Solutions nouvelles de deux Questions Fondamentales
d'Économie Sociale. Revue d'Economie Politique.
1887. LAUNHARDT (Wilhelm). Theorie des Trassirens. Heft. I. Die kommerzielle
Trassirung. Second Edition. iv, 112 pp. Hannover.
1887. HELM (G.) Die Bisherigen Versuche, Mathematik auf Volkswirthschaftliche
Fragen anzuwenden. Ges. Isis. in Dresden. Abh. I. 13 pp.
1887. VAN DORSTEN (Dr. R. K.) Mathematische onderzoe-kingen op het gebied
der Staathuishoudkunde. Ar chief voor politieke en sociale rekenkunde, 1ste deel, 3de
en 4de aflevering.
1887. WESTERGAARD (H.) Mathematiken i Nationalökonomiens Tjeneste. In the
volume Smaaskrifter Tilegnede A. F. Krieger. Copenhagen.
1887. PANTALEONI (Maffeo). Teoria della pressione tributaria e metodi per
misurarla. Parte prima Teoria della pressione tributaria. 78 pp. Roma.
1888. EDGEWORTH (F. Y.) The Mathematical Theory of Banking. Jour. Statistical
Society, London, March 1888.
1888. WICKSTEED (Philip H.) The Alphabet of Economic Science. I. Elements of
the Theory of Value or Worth. London.
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[Back to Table of Contents]
APPENDIX II
List of works and papers upon Economical Subjects, by the author of the present
book:—
1857. Comparison of the Land and Railway Policy of New South Wales. The Public
Lands of New South Wales. Articles in the Empire newspaper, April 7 and June 23.
Sydney, New South Wales.
1862. Diagram, showing all the Weekly Accounts of the Bank of England, since the
passing of the Bank Act of 1844, with the Amount of Bank of England, Private, and
Joint Stock Bank Promissory Notes in Circulation during each week, and the Bank
Minimum Rate of Discount. London. Sheet, 20 x 30 inches, coloured.
This Diagram represents to the eye all the useful results of tables, containing about
113,000 figures.
1862. Diagram, showing the Price of the English Funds, the Price of Wheat, the
Number of Bankruptcies, and the Rate of Discount, monthly, since 1731; so far as the
same have been ascertained. London. Sheet, 20 x 30 inches, coloured.
This Diagram is drawn from tables carefully compiled for the purpose, and containing
more than 12,000 figures.
Explanatory Notes and References are appended to each Diagram.
1862. (1) On the Study of Periodic Commercial Fluctuations. With five diagrams. (2)
Notice of a general Mathematical Theory of Political Economy. Papers read in the F
section of the British Association at the Cambridge Meeting. Report. Proceedings of
Sections, pp. 157, 158.
1863. A serious Fall in the Value of Gold Ascertained, and its social effects set forth.
With two diagrams. London: Edward Stanford, Charing Cross. 8vo. 73 pp.
1865. The Coal Question; an Inquiry concerning the Progress of the Nation, and the
Probable Exhaustion of our Coal Mines. London and Cambridge: Macmillan & Co.
8vo. xix, 349 pp.
1865. On the Variation of Prices, and the Value of the Currency since 1782. Paper
read before the London Statistical Society, May 1865. Journal of the Statistical
Society, vol. xxviii, pp. 294-320. With four diagrams.
1866. On the frequent Autumnal Pressure in the Money Market, and the Action of the
Bank of England. Paper read before the Statistical Society, April 1866. Journal of the
Statistical Society of London, vol. xxix, pp. 235-253.
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1866. Brief Account of a General Mathematical Theory of Political Economy. (Read
at the British Association, 1862.) Journal of the Statistical Society of London, vol.
xxix, pp. 282-287.
1866. The Coal Question, etc. Second edition. London. 8vo. xxvi, 383 pp.
1866. An Introductory Lecture on the Importance of diffusing a Knowledge of
Political Economy. Delivered in Owens College, Manchester, at the opening of the
Session of Evening Classes, on October 12. Manchester. 12mo. 35 pp.
1867. Science Lectures for the People. Lecture IX. On Coal: its importance in
manufactures and trade. Delivered in the Carpenters' Hall, Manchester, January 16,
1867. (Science Lectures, vol. i, pp. 128-140.)
1867. On the Analogy between the Post-Office, Telegraphs, and other systems of
Conveyance of the United Kingdom, as regards Government Control. Paper read
before the Manchester Statistical Society, April 1867. Transactions, 1866-67, pp.
89-104.
1868. A Lecture on Trades' Societies: their Objects and Policy. Delivered by request
of the Trades Unionists' Political Association, March 31. Manchester. 8vo. 16 pp.
1868. Lecture on the Probable Exhaustion of our Coal Mines. Royal Institution of
Great Britain. Friday Evening, March 13. 8vo. 7 pp.
1868. On the International Monetary Convention, and the Introduction of an
International Currency into this kingdom. Paper read before the Manchester Statistical
Society, May 13. Transactions, 1867-68, pp. 79-92.
1868. On the Condition of the Metallic Currency of the United Kingdom, with
reference to the Question of International Coinage. Paper read before the Statistical
Society of London, November. Journal of the Statistical Society of London, vol. xxxi,
pp. 426-464.
1869. Letter on the Value of Gold. Economist Newspaper, May 8. Reprinted in the
Journal of the Statistical Society of London, December, vol. xxxii, p. 445.
1869. On the Work of the Society in connection with the Questions of the Day.
Inaugural Address read before the Manchester Statistical Society, November 10,
1869. Transactions, 1869-70, pp. 1-14.
1870. Opening Address of the President of Section F (Economic Science and
Statistics) of the British Association for the Advancement of Science at the Fortieth
Meeting, at Liverpool, September 1870. Report. Transactions of the Sections, pp.
178-187. Journal of the Statistical Society of London, vol. xxxiii, pp. 309-326.
1870. On Industrial Partnerships. A Lecture delivered under the auspices of the
National Association for the Promotion of Social Science, April 5, 1870. London, 1
Adam Street, Adelphi. 12mo. 39 pp.
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1871. The Match Tax: a Problem in Finance. London. 8vo. 66 pp.
1871. The Theory of Political Economy. London and New York: Macmillan & Co.
8vo. xvi, 267 pp.
1874. The Progress of the Mathematical Theory of Political Economy, with an
explanation of the Principles of the Theory. Paper read before the Manchester
Statistical Society, November 11. Transactions, 1874-75, pp. 1-19, with a diagram.
Reprinted in the Journal of the Statistical Society of London, vol. xxxvii, p. 478.
1875. On the Progress of the Coal Question. British Association, Bristol, 1875.
Transactions of Sections, p. 216.
1875. The Post-Office Telegraphs and their Financial Results. Fortnightly Review,
December 1, vol. xviii, N. S., pp. 826-835.
1875. La Teorica dell' Economia Politica, esposta da W. Stanley Jevons. Biblioteca
dell' Economista. 3n serie, tome ii, pp. 175-311. (Translated under the
superintendence of Professor Gerolamo Boccardo.)
1875. Money and the Mechanism of Exchange (International Scientific Series, vol.
xvii). London: H. S. King & Co.; New York: D. Appleton & Co. Post 8vo. xviii, 349
pp.
1876. La Monnaie et le Mécanisme de l'Echange. Paris: Librairie Germer Baillière et
Cie. (Bibliothèque Scientifique Internationale, vol. xx.) 8vo. viii, 288 pp.
1876. Geld und Geldverkehr. Leipzig: F. A. Brockhaus (Internationale
Wissenschaftliche Bibliothek, xxi Band). 8vo. xvi, 359 pp.
1876. La Moneta et il Mecanismo dello Scambio. Milano: Fratelli Dumolard.
(Biblioteca Scientifica Internazionale, vol. vi.) 8vo. xxix, 319 pp.
1876. On the United Kingdom Alliance and its Prospects of Success. Paper read
before the Manchester Statistical Society, March 8. Transactions, pp. 127-142.
1876. On the Frequent Autumnal Pressure in the Money Market, and the action of the
Bank of England. Paper reprinted from the Journal of the Statistical Society of
London, 1866, in the Transactions of the Manchester Statistical Society. Appendix,
pp. 17-41.
1876. The Future of Political Economy. Introductory Lecture at the Opening of the
Session, 1876-77, at University College, London. Faculty of Arts and Laws.
Fortnightly Review, December, vol. xx, pp. 617-631. (See also Appendix I, 1877,
Jevons.)
1877. The Silver Question: A Paper read by Hamilton A. Hill, of Boston, before the
American Social Science Association at Saratoga, September 5. Boston: Published for
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the Association by A. Williams & Co., pp. 26-32. Reprinted in the London Bankers'
Magazine, December. 7 pp.
1878. Science Primers—Primer of Political Economy. London: Macmillan & Co.
18mo. 134 pp.
1878. L'Economie Politique, par W. Stanley Jevons, traduite par Henri Gravez,
Ingénieur. Paris: Librairie Germer Baillière et Cie. (Bibliothèque Utile, vol. xliv.)
18mo. 184 pp.
1878. Money and the Mechanism of Exchange. London: C. Kegan Paul & Co. Fourth
edition.
1878. The Periodicity of Commercial Crises and its Physical Explanation. Paper read
before the F section of the British Association at the Dublin Meeting, August 19.
Report. Transactions of Section F, p. 666. Published in the Journal of the Statistical
and Social Inquiry Society of Ireland, August, 1878. Vol. vii, pp. 334-342.
1878. Commercial Crises and Sun-spots. Article printed in Nature of November 14,
vol. xix, pp. 33-37.
1878. Remarks on the Statistical use of the Arithmometer. Journal of the Statistical
Society of London, vol. xli, pp. 597-601.
1879. Methods of Social Reform, No. II. A State Parcel Post. Article in the
Contemporary Review of January, vol. xxxiv, pp. 209-229.
1879. Sun-spots and Commercial Crises. Nature, April 24, vol. xix, pp. 588-590.
1881. Bimetallism. Article in Contemporary Review of May, vol. xxxix, pp. 750-757.
1884. Investigations in Currency and Finance. Edited, with Introduction, by H. S.
Foxwell, M.A. London: Macmillan & Co. 8vo. xliv, 414 pp.
Printed by R. & R. Clark, Edinburgh.
[1[1]]Principles of Political Economy, book iii. chap. vi. sec. i. l. This definition
occurs at the beginning of a carefully prepared summary of the principles of the
theory of value.
[1]Hermathena, No. iv., 1876, pp. 1-32. Republished in Mr. Leslie's collected Essays
in Political and Moral Philosophy, Dublin, 1879, pp. 216-242.
[[3]]Journal of the London Statistical Society, December 1878, vol. xli. pp. 602-629.
Journal of the Statistical and Social Inquiry Society of Ireland, August 1878, vol. vii.
Appendix. Also as a separate publication, Longmans, London, 1878.
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[1]"The Future of Political Economy," Fortnightly Review, November 1876, vol. viii.,
N. S., pp. 617-631. Translated in the Journal des Economistes, March 1877, 3me
Série, vol. xlv. p. 325.
[1]See p. ix of this edition.
[[6]]Traité d'Economie Politique... 5me ed., Paris, 1863, pp. 700-702.
[1]Some Leading Principles of Political Economy Newly Expounded, pt. 1, chap. iii.
p. 97.
[1]Book iii. chap. xviii. sec. 7.
[1]1720. Hutcheson. An Inquiry, 1729, etc., pp. 186-198.
[1]1728. Hutcheson. An Essay, etc., pp. 34-43, and elsewhere.
[1]Elemens d'Ideologie, iv., et ve Parties. Traité de la Volonté et de Ses Effets, Paris,
1815, 8vo, p. 499. Edition of 1826, p. 335. American Edition, A treatise on Political
Economy, translated from the unpublished French original. Georgetown, D.C. 1817,
p. xiii.
[2]Observations on the Effects of the Corn Laws, and of a rise or fall in the price of
Corn on the Agriculture and General Wealth of the Country. London, 1814, p. 30: 3d
ed., 1815, p. 32.
[1]Traité d'Economie Politique, Cinquième Edition, p. 701.
[2]Theorie und Geschichte der National-Oekonomik, 1858, vol. i. p. 9.
[1]A copy of Gossen's book will be found in the Library of the British Museum (Press
mark 8408, cc). It was not acquired by that institution until May 24, 1865, as shown
by the date stamped upon the copy.
[1]Transactions of the Connecticut Academy, 1877, vol. iv. pp. 151-232.
[1]"Land Systems and Industrial Economy of Ireland, England, and Continental
Countries." London, 1870. Appendix, pp. 357-379.
[2]London, 1877, Trübner.
[1]Chap. v. vol. i. p. 304.
[2]Principles of Political Economy, book iii., chap. v., sec. 2, paragraph 3.
[1]Principles of Political Economy, book iii., chap. vi., sec. 1, article 9.
[[2]]Reports of Sections, p. 158.
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[[23]]Journal of the Statistical Society, vol. xxix. p. 282.
[[24]]The large type or non-symbolic portion of the Treatise has been reprinted in a
separate volume, under the title Elements of Natural Philosophy, by Professors Sir W.
Thomson and P. G. Tait. Part I. Oxford, Clarendon Press, 1873. But the authors
appear to me to be inaccurate in describing this work, in the preface, as non-
mathematical. It is comparatively non-symbolic, but equally mathematical with the
complete Treatise.
[1]This subject of the approximate character of quantitative science is pursued, at
some length, in my Principles of Science, chap. xxi., on "The Theory of
Approximation," and elsewhere in the same work.
[[2]]Thomson and Tait's Treatise on Natural Philosophy, vol. i. p. 337.
[[1]]See Principles of Science, chap. xiii., on "The Exact Measurement of
Phenomena," 3d ed., p. 270.
[[1]]Formal Logic, p. 175.
[[1]]Chapter iv., on the "Value of a Lot of Pleasure or Pain, How to be measured,"
sec. v. 5.
[[1]]The Emotions and the Will, 1st ed., p. 447.
[[1]]Concerning the meaning and employment of Averages, see Principles of Science,
chap. xvi., on "The Method of Means."
[[2]]System of Logic, book vi., chap. ix. sec. 3.
[[1]]2d ed. (Macmillan), 1875.
[[2]]Principles of Science, chaps. vii., ix., xii., etc.
[[1]]Principles of Science, chap. xix., on "Experiment."
[[1]]Hermathena, No. iv., Dublin, 1876, p. 1.
[[2]]Statistical Journal, January 1879, vol. xli. p. 602. Also reprint by Longmans,
1878.
[[2]]Fortnightly Review, December 1876; "The Future of Political Economy."
[[1]]An Introduction to the Principles of Morals and Legislation, by Jeremy Bentham.
Edition of 1823, vol. i. p. 1.
[[2]]Principles of Moral and Political Philosophy, book i., chap. vi.
[[1]]The Emotions and the Will, 1st ed., p. 460.
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[[1]]An Introduction to the Principles of Morals and Legislation, 2d ed., 1823, vol. i.
p. 49. The earliest writer who, so far as I know, has treated Pleasure and Pain in a
definitely quantitative manner, is Francis Hutcheson, in his Essay on the Nature and
Conduct of the Passions and Affections, 1728, pp. 34-43, 126, etc.
[[1]]Introduction, p. 50.
[[1]]1st ed., p. 30.
[[2]]See above, p. 28.
[[1]]The Emotions and the Will, 1st ed., p. 74.
[[1]]Essays on some Unsettled Questions of Political Economy, p. 132.
[[1]]Inquiry into the Nature and Origin of Public Wealth, 2d ed., 1819, p. 306 (1st ed.
1804).
[[2]]Encyclopœdia Metropolitana, art. "Political Economy," p. 133. 5th ed. of
Reprint, p. 11.
[[1]]Harmonies of Political Economy, translated by P. J. Stirling, 1860, p. 65.
[[2]]Traité Théorique et Pratique d'Economic Politique, par J. G. Courcelle-Seneuil,
2me ed., Paris, 1867, tom. i. p. 25.
[[3]]Ib., p. 33.
[[4]]2d ed., p. 11.
[[1]]The theory of dimensions of utility is fully stated in a subsequent section.
[[1]]Encyclopœdia Metropolitana, p. 133. Reprint, p. 12.
[[1]]London: Longmans.
[[2]]Cairnes is, however, an exception. See his work on The Character and Logical
Method of Political Economy. London, 1857, p. 81. 2d ed. (Macmillan), 1875, pp. 56,
110, 224 App. B.
[[1]]Pp. 96-99.
[[1]]It is used precisely in its present economical sense in the remarkable "Processe of
the Libelle of English Policie," probably written in the fifteenth century, and printed
in Hakluyt's Voyages.
[[1]]J.D. Everett's Illustrations of the Centimetre-gramme-second System of Units,
1875; Fleeming Jenkin's Text-Book of Electricity and Magnetism, 1873; Clerk
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Maxwell's Theory of Heat, or the commencement of his great Treatise on Electricity,
vol. i. p. 2.
[[1]]Condillac, Le Commerce et le Gouvernement, Seconde Partie, Introduction.
Œuvres Complètes. Paris, 1803. Tom. vii. p. 2.
[[2]]Garnier, Traité d' Economie Politique, 5me ed., p. 11.
[[1]]See chap. iv.
[[2]]See chap. vii.
[[1]]Principles of Political Economy, book iii., chap. i. sec. 1.
[[1]]Principles of Political Economy, book iii., chap. vi.
[[1]]Wealth of Nations, book i., chap. iv., near the end.
[[1]]De l'Intérêt Social, 1777, chap. i. sec. 4.
[[1]]Le Commerce et le Gouvernement, 1776; Œuvres Complètes de Condillac, 1803,
tom. 6me, p. 20.
[[1]]I find that Cournot has long since defined the economical use of the word market,
with admirable brevity and precision, but exactly to the same effect as the text above.
He incidentally says in a footnote (Récherches sur les Principes Mathématiques de la
Théorie des Richesses, Paris, 1838, p. 55), "On sait que les économistes entendent par
marché, non pas un lieu déterminé ou se consomment les achats et les ventes, mais
tout un territoire dont les parties sont unies par des rapports de libre commerce, en
sorte que les prix s'y nivellent avec facilité et promptitude."
[71.[71]]Waterston's Cyclopœdia of Commerce, ed. 1846, p. 466.
[[1]]Principles of Science, 1st ed., vol. i. p. 422; 3d ed., p. 363.
[[1]]It is, I believe, verified in the New York Stock Markets, where it is the practice to
sell Stocks by auction in successive lots, without disclosing the total amount to be put
up. When the amount offered begins to exceed what was expected, then each
successive lot brings a less price, and those who bought the earlier lots suffer. But if
the amount offered is small, the early buyers have the advantage. Such an auction sale
only exhibits in miniature what is constantly going on in the markets generally on a
large scale.
[[1]]Principles of Political Economy, book iii., chap. ii. sec. 4.
[[1]]See Magnus's Lessons, sec. 91.
[[1]]Seconde Édition, Paris, 1833, sec. 12, vol. i. p. 14.
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[[1]]Since the above was written the value of Cleopatra's Needle has actually formed
the subject of decision in the Admiralty Court, in connection with the award of
salvage. The fact, however, is that in the absence of any act of exchange concerning
such an object, the notion of value is not applicable at all. At the best the value
assigned, namely £25,000, is a mere fiction arbitrarily invented to represent what
might conceivably be given for such an object if there were a purchaser. It is,
moreover, curious that since the first edition was printed Russia has actually made an
exchange of islands with Japan.
[[1]]Thornton On Labour; its Wrongful Claims and Rightful Dues (1869), p. 58.
[[1]]See the author's "History of the Floods and Droughts of New South Wales," in
the Australian Almanack, Sydney, 1859, p. 61. Also Mr. H. C. Russell's Climate of
New South Wales.
[[1]]Serious Fall in the Value of Gold, 1863, p. 33 (reprinted in Investigations in
Currency and Finance, 1885). Money and the Mechanism of Exchange (International
Scientific Series), chap. xii. This chapter has been translated by M. H. Gravez, and
reprinted in the Bibliothèque Utile, vol. xliv. (Germer Baillière), Paris, 1878. See also
Papers on the Silver Question read before the American Social Science Association at
Saratoga, September 5, 1877, Boston, 1877, and Bankers' Magazine, December 1877
(reprinted in Investigations in Currency and Finance, 1884).
[[1]]Principles of Political Economy, book iii., chap. xviii., end of the 8th section.
[[1]]Principles of Political Economy, book v., chap. iv. sec. 6.
[[1]]See Jevons' Principles of Science, chap. xxii., new ed., pp. 487-489, and the
references there given.
[[1]]Chalmers' Christian and Economic Polity of a Nation, vol. ii. p. 240.
[[1]]Chalmers' Christian and Economic Polity of a Nation, vol. ii. p. 242.
[[1]]Ibid., p. 251.
[[1]]Chalmers' Christian and Economic Polity of a Nation, vol. ii. p. 252.
[[1]]Vol. v. p. 324, etc.
[[1]]Quoted in Lauderdale's Inquiry into the Nature and Origin of Public Wealth, 2d
ed., 1819, pp. 51, 52.
[[1]]Ibid.
[[1]]No. 200, quoted by Lauderdale, p. 50.
[[1]]The Political and Commercial Works of Charles Davenant, vol. ii. p. 163.
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[[1]]Ibid., p. 224.
[[1]]An Inquiry into the Nature and Effects of the Paper Credit of Great Britain, pp.
270, 271.
[[2]]History of Prices, vol. i. pp. 13-15.
[[1]]Six Lectures on Political Economy. Cambridge, 1862.
[[1]]History of Prices.
[[1]]Todhunter's History of the Theory of Probability, chap. xi., etc.
[[1]]Principles of Political Economy and Taxation, 3d ed., p. 2.
[[1]]On the Principles of Political Economy and Taxation, 3d ed., 1821, p. 2.
[[1]]Mr. W. L. Sargant, in his Recent Political Economy, 8vo, London, 1867, p. 99,
states that contracts have been made to manufacture the Enfield Rifle, of identically
the same pattern, at prices ranging from 70s. each down to 20s., or even lower. The
wages of the workmen varied from 40s. or 50s. down to 15s. a week. Such an instance
renders it obvious that it is scarcity which governs value, and that it is the value of the
produce which determines the wages of the producers.
[[1]]Wealth of Nations, book i., chap. v.
[[2]]Traité Théorique et Pratique d'Economie Politique, 2d ed., vol i. p. 33.
[[1]]I have altered this definition as it stood in the first edition by inserting the words
partly or wholly, and I only give it now as provisionally the best I can suggest. The
subject presents itself to me as one of great difficulty, and it is possible that the true
solution will consist in treating labour as a case of negative utility, or negative
mingled with positive utility. We should thus arrive at a higher generalisation which
appears to be foreshadowed in the remarkable work of Hermann Heinrich Gossen
described in the preface to this edition. Every act, whether of production or of
consumption, may be regarded as producing what Bentham calls a lot both of
pleasures and pains, and the distinction between the two processes will consist in the
fact that the algebraic value of the lot in the case of consumption yields a balance of
positive utility, while that of production yields a negative or painful balance, at least
in that part of the labour involving most effort. In a happy life the negative balance
involved in production is more than cleared off by the positive balance of pleasure
arising from consumption.
[[1]]Plutology, p. 24.
[[1]]Natural Elements of Political Economy, p. 119.
[[1]]Edition of 1847, pp. 454, 455.
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[[1]]Query No. 20.
[[1]]While revising this edition it seems to me probable that this, as well as some
other parts of the theory, might be more simply and generally stated, but what is given
is substantially true and correct, and it must stand for the present. [See also the Errata
for this page, which reads "for 'in this respect be taken negatively,' read 'in this
respect be taken positively.' ".—Econlib Editor.]
[[1]]Babbage, On the Economy of Machinery and Manufactures, sec. 32, p. 30.
[[1]]Vol. ii. p. 324; vol. iii. p. 289. See also Haughton's Principles of Animal
Mechanics, 1873, pp. 444-450. The subject has since been followed up with much
care and ability by Professor Francis E. Nipher, of the Washington University, St.
Louis, Missouri, U.S. Details of his experiments will be found in the American
Journal of Science, vol. ix. pp. 130-137; vol. x., etc.; Nature, vol. xi. pp. 256, 276, etc.
[[1]]Inquiry, etc., p. 45, note.
[[1]]New edition, 1839, p. 444.
[[1]]Elements, p. 17.
[[1]]Book i., chap. v. sec. I.
[[2]]Wealth of Nations, p. 445.
[[1]]Principles of Political Economy, p. 100.
[[2]]Manual of Political Economy, 2d ed., p. 47.
[[1]]Elements of Political Economy, 3d ed., 1826, p. 9.
[[1]]Plutology; or The Theory of the Efforts to Satisfy Human Wants, 1864
(Macmillan), p. 139.
[[1]]Political Economy, by Nassau W. Senior, 5th ed., 1863, p. 59.
[[1]]Minard, Annales des Ponts et Chaussées, 1850, 1er Semestre, p. 57.
[[1]]On the Principles of Political Economy and Taxation, chap. i., sec. 5, 3d ed., p.
36.
[[1]]Wealth of Nations, book i., chap. ix., second paragraph.
[[1]]Wealth of Nations, book ii., chap. i., twelfth paragraph.
[[1]]Wealth of Nations, book ii., chap. i., twelfth paragraph continued.
[[1]]Principles of Political Economy, book i., chap. v., sec. 2.
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[[1]]Plutology: or The Theory of the Efforts to satisfy Human Wants. By William
Edward Hearn, LL.D., Professor of History and Political Economy in the University
of Melbourne. London (Macmillan and Co.), 1864, p. 329.
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