THE

QUARTERLY JOURNAL

OF

ECONOMICS

JANUARY, 1898

COURNOT AND MATHEMATICAL ECONOMICS.

"Cournot's genius must give a new mental activity to every one who passes through his hands."-MARSHALL.

THE appearance in English* of Cournot's Principes Mathématiques offers a suitable occasion for a review of that remarkable work and of the later developments of economic method which it foreshadowed. In the six decades since the original work was published, a decided change has taken place in the modes of conceiving and treating economic problems. For good or for ill the mathematical method has finally taken root, and is flourishing with a vigor of which both its friends and enemies little dreamed. Sixty years ago the mathematical treatise of Cournot was passed over in silence, if not contempt. To-day the equally mathematical work of Pareto is received with almost universal praise. In Cournot's time "mathematical economists" could be counted on one's fingers, or even thumbs. To-day they muster some thirty active enthusi

*Researches into the Mathematical Principles of the Theory of Wealth. By Augustin Cournot, 1838, translated by Nathaniel T. Bacon. In the "Economic Classics" series. Macmillan, 1897.

asts and a much larger number of followers and sympathizers. In 1838 there seems to have been no institution of learning besides the Academy at Grenoble, of which Cournot was rector, where "mathematical economics" were employed or approved. In 1898 there are at least a dozen such institutions, and in England alone half that number, Oxford and Cambridge among them. It is in France, the prophet's own country, where he is still without honor. When Cournot wrote, no journal existed in which such investigations as his could find a welcome. To-day the Economic Journal, the Journal of the Royal Statistical Society, the Giornale degli Economisti, and the Nationaloekonomisk Tidsskrift receive such material with more or less regularity; while, within the last eight years alone, twenty other journals have occasionally published economic articles containing mathematics. Opponents of the new method no longer venture to ignore or ridicule it, but, in academic circles at least, seek to acquaint themselves with its history and present aims as matters of necessary and professional information. In recognition of such wide-spread interest the latest Dictionary of Political Economy devotes some forty articles to the history, writings, methods, and terminology of the "mathematical school."

It may fairly be claimed that Cournot was the principal founder of this school. For this reason, if for no other, his book is an "economic classic," and as such deserves careful study. But its interest is not simply historical. The bulk of its reasoning and conclusions has never yet been superseded. Those who now read it for the first time will find it as new and fresh as any modern investigation. As the original work has long been out of print and scarce in the antiquarian market, the present edition serves the double purpose of translation and second edition. Moreover, thanks to the painstaking work of the * Cf. Walras, Théorie Mathématique de la Richesse Sociale, 1883, p. 9.

translator, it far surpasses the original in typographical accuracy, a prime requisite in a mathematical work.

Exclusive of the preface and appended bibliography, the text occupies 166 pages. Of this material, the last two chapters, making 45 pages, have only an historical interest. As we shall see, they are vitiated throughout by fallacious conceptions of income. About 18 other pages (namely, §§ 34, 39, 42, 46 (2d par.), 48, 49, 52, 54, 64, 65, 72, 73) may be omitted without loss of continuity and without great loss of substance. The remaining 103 pages are almost uniformly excellent, and will repay very thorough study by all who care for exact ideas and demonstrations in Political Economy. Furthermore, the reader will find, before he has gone far, that very thorough study is indispensable to a mastery of the subtle author. Jevons, though himself a mathematical economist, confesses, with characteristic candor, "I have by no means mastered all parts, . . . my mathematical power being insufficient to enable me to follow Cournot in all parts of his analysis." The general trend of reasoning and the final conclusions will be patent to the most non-mathematical reader, and I have heard a distinguished economist of that description say that he found the book easy reading. But a slight acquaintance with the notations of the Differential Calculus is necessary for interpreting the formulæ, and considerable familiarity for deriving them in some cases. To lift the beginner in the Calculus over the last sort of difficulties, I have appended to this article a series of notes. The work is, of course, not wholly mathematical. Of the 103 pages above mentioned, containing the essential parts, only about 70 are mathematical. The reader who will make up his mind at the outset to work his way through these pages at half-speed or quarter-speed need not chafe over *Theory of Political Economy, preface to 2d edition, p. xxix of 3d edition. . † See the Appendix.

necessary hindrances and delays, and will not regret the extra time required.

In his preface Cournot defends his method of treating economic science. Few better statements exist of the aims and merits of "deductive" and "mathematical" economics. While welcoming all study of facts, Cournot insists on a framework of theory in which those facts fit. A very few facts (such as that demand increases with a decrease of price) suffice to determine the main outlines of that theory, though its exact form depends on the specific circumstances of each particular case. He answers the alleged objection to a mathematical treatment that economic problems lack the data for numerical solution:

Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression. . . . Thus . . . theoretical mechanics furnishes to practical mechanics general theorems of most useful application, although in almost all cases recourse to experience is necessary for the numerical results which practice requires.*

Entering upon the book itself, we find that it naturally falls under three heads. The introductory chapters, treating of value, "absolute and relative," and of the foreign exchanges, are quite apart from the rest of the book. Chapters IV.-X. inclusive discuss the determination of prices under different conditions as to monopoly and competition, taxes and bounties. This portion of the work is the most distinctive and the most widely celebrated. The remaining two chapters give an ambitious but erroneous theory of "Social Income."

Chapter I. is devoted to defining wealth, which term Cournot uses in the sense of value in exchange. He carefully distinguishes this idea from utility, with which he conceives the economist has no direct concern. Here,

* Page 3.

of course, he differs materially from modern mathematical economists, beginning with Jevons and Walras. To prevent all misunderstanding, Cournot points out that, under his definition of wealth, the destruction of spices by the East India Company, though opposed to the general good, was a "real creation of wealth in the commercial sense of the word." What relations exist between wealth thus conceived and the welfare of the human race Cournot regards as too difficult a problem to admit of present solution. Yet he does not disparage efforts towards that end.

Chapter II. deals with "Changes in Value, Absolute and Relative," a subject of engaging interest in these latter days of conflicting monetary standards. The reader will be filled with surprise and admiration at Cournot's anticipations of modern thought on this difficult topic. The values of a system of commodities are compared to the positions of a system of particles. The value of each commodity is expressed relatively to other commodities, just as the position of each particle is expressed by reference to the other particles. When a change occurs in the relative values or positions, the question arises, Which term of the comparison has suffered an absolute change? Clinging to physical analogy, Cournot cites the remarkable passage in Newton's Principia in which an "absolute space is supposed as a background for mechanical motion, distinct from the "relative space" made up of the system of moving points. He does not despair of distinguishing statistically absolute and relative changes, and observes that in case all commodities except one, such as gold or silver, preserve the same relative values, the probability is greater that the one commodity has changed than that all the others have changed. Although the whole discussion lacks one of its modern elements,- the idea of utility, it must nevertheless be regarded as more profound and worthy of serious consideration than most contemporaneous treatments of the same theme.