Cournot, Antoine Augustin
Cournot, Antoine Augustin
Antoine Augustin Cournot (1801–1877), French mathematician, economist, and philosopher, was born at Gray (Haute-Saône), the son of a notary. He came from a family of farmers who had lived in Franche-Comté since at least the middle of the sixteenth century. Until age 15, Cournot attended the collége at Gray; then, for the next four years, he read a great deal on his own, especially works by scientists and philosophers, such as Laplace and Leibniz. After preparing at Besançon, Cournot was admitted in 1821 to the scientific section of the École Normale Supérieure, in Paris. The school was closed by the reactionary regime the following year, but Cournot stayed in Paris and in 1823 received the licentiate in sciences. He attended sessions at the Académie des Sciences and associated with the principal scholars of the day; it was through one of them that he met Proudhon. In October 1823, Cournot entered the household of Marshal Gouvion Saint-Cyr in the double capacity of literary adviser to the marshal, who wanted to complete some unfinished manuscripts, and tutor to the marshal’s son.
Cournot spent ten years with the marshal, all the while continuing his scientific studies. In 1829 he received a doctorate in science, writing a main thesis in mechanics and a supplementary one in astronomy. He also studied law. A series of articles that he published on scientific questions attracted the attention of the great mathematician Poisson, who was then professor at the École Polytechnique and later at the University of Paris. Poisson was then in charge of the instruction in mathematics throughout France and arranged Cournot’s appointment to the chair of mathematical analysis in the faculty of sciences at Lyon. Cournot taught for only one year, however; subsequently, most of his life was spent in university administration, in which he was very successful. He became, successively, rector of the Academie de Grenoble in 1835, inspector general of the University of Dijon, and rector of the Academie de Dijon from 1854 to 1862. Cournot then accepted no further public positions and returned to Paris, where he died just as he was about to apply for membership in the Institut de France. Toward the end of his life he was nearly blind.
Cournot’s administrative work left him ample time for a great deal of scientific writing. Unfortunately, his books suffer from a lack of the stimulation that contact with an audience gives to teachers. Ten of his works appeared between 1838 and 1877. These books have three major themes: (1) algebra, infinitesimal analysis, and calculus of probabilities; (2) the theory of wealth; and (3) the philosophy of science, the philosophy of history, and even general philosophy. These themes were interdependent in Cournot’s work, and although the economic side will be stressed here, the profound unity of his thought must be remembered. Cournot started with mathematics, was then attracted to economics, and ended with a general interpretation of the world that was infused with his profound understanding of probabilities. It is the concept of probability that integrates the three parts of his work.
Cournot’s rather melancholic and solitary temperament considerably delayed the influence he was ultimately to have. Modest and self-effacing, he did nothing to make his books attractive. They tend to be austere, crowded with facts and proofs. Even the titles he chose reflect his modesty: Researches, Essay, and Considerations. It is not surprising, then, that he is less well known in the field of probability than Laplace and Poisson, less appreciated among economists than Bastiat, Say, or Proudhon (to mention only French economists), and less quoted in philosophy than Comte or Spencer. And yet Cournot, having the rare knowledge required to use the language of all of these authors, combined many of their qualities and made a quasi-prophetic synthesis of their ideas.
Mathematics and probability theory. Cournot’s mathematical works, econometrics aside, appeared between 1840 and 1850. In his Exposition de la theorie des chances et des probabilités (1843), he put forward a definition of statistics as that science which deals with collecting and coordinating numerous facts of every kind, in such a way as to obtain numerical relationships that are markedly independent of the anomalies of chance, and that manifest the existence of uniformly operating causes whose effects have been confounded, however, with other, accidental effects.
Cournot, living in the first half of the nineteenth century, stood at the crossroads of two ways of mathematical endeavor: the one originated with Pascal and Fermat and led to the work of Jacques Bernoulli, Gauss, Laplace, and Poisson on the doctrine of chances; the other, renouncing the mathematical study of chance and uncertainty, focused on the mathematics of rigorous determinations by algorithms that admit no margin of uncertainty— as if science were perfectly deterministic. This concept that the perfect is the determined was to play a major role in the development of the early science of economics, as one can see from the still current term “perfect competition.” Cournot fore-saw that science could not be intrinsically and definitively tied to such determinism. He believed that a science of margins and chances is not only viable but perhaps better suited to the needs of economics than a science of absolute, exact equilibria. Nonetheless, Cournot is often regarded as having introduced into economic theory the use of deterministic mathematics.
Economics. Cournot wrote three works in economics, in 1838, 1863, and 1877; thus, his career began and ended with writings on economics. When Recherches sur les principes mathématiques de la théorie des richesses (1838a) first appeared, it was such a fiasco that Cournot remained silent on the subject of economics for 25 years. He then wrote Principes de la théorie des richesses (1863), putting into “literary” language what he had previously said in the language of mathematics. Despite the concessions Cournot made in the form of presentation, the Principes was no better received than the Recherches; indeed, if Cournot had produced only his nonmathematical work, he would never have been recognized as anything but a minor figure.
Strictly speaking, to be sure, Cournot was not the first to have used mathematical language to express economic problems. There was Nicolas Canard, in France, whom Cournot did quote, but Canard did not have Cournot’s scope and erudition. Great erudition is needed to combine economics and mathematics, and if mathematical economics has had its setbacks, the reason is that it has not always been guided by such clear minds as Cournot’s.
Cournot’s great merit is that, without saying so explicitly, he was the first to construct a true theory of prices and markets. Chapter 4 of Recherches, entitled “Of the Law of Demand,” is the first model of its kind. Cournot was interested exclusively in the demand that is followed by an actual sale and that is, therefore, observable and measurable. He is recognized for having revealed the concept of function and for having made available to economists the immensely useful language of functional concepts. Sales are, in general, a decreasing function of price. This function is continuous, at least when the number of consumers is not limited. Moreover, the sales function is not purely abstract; it may be constructed on the basis of mean annually observed data. And since it is not merely an a priori function but an empirical, experimental one, Cournot may be considered to have made the initial step in developing econometrics.
In this econometric mode of analysis, a related idea is that of imperfection, hence of uncertainty and, in turn, of chance in measurement. Here again, Cournot’s knowledge of probabilities saved him from incorrectly associating mathematics with the idea of rigorous precision. He asserted that even if the object of numerical calculation “were unattainable, it would be nevertheless not improper to introduce the unknown law of demand into the analytical combinations, by means of an indeterminate symbol; for it is well known that one of the most important functions of analysis consists precisely in assigning determinate relations between quantities to which numerical values and even algebraic forms are absolutely unassignable” ([1838a] 1960, p. 48). We must give up trying to grasp what cannot be grasped rigorously. It is for this reason, perhaps, that we must reason mathematically “… by showing what determinate relations exist between unknown quantities, analysis reduces these unknown quantities to the smallest possible number, and guides the observer to the best observations for discovering their values. It reduces and coordinates statistical documents; and it diminishes the labour of statisticians …” (ibid., pp. 48–49).
Cournot’s first construction is worked out in this spirit: it consists in drawing up, within suitable limits, tables of correspondence between the values of the demand, D = f(p), and the price, p. In a second stage, the function pf(p), the total value of the amount sold, is considered. This becomes the crux of the theory of markets. Long before Alfred Marshall, Cournot presented a theory of elasticity: depending on whether ?D/?p D/p or ?D/?p > D/p, the price increase will make the product pf(p) larger or smaller. Hence commercial statistics should begin by dividing merchandise into two categories, depending on whether their current prices are lower or higher than the value making pf(p) a maximum. In this formulation, Cournot was truly a great innovator.
Instead of attacking the general price equilibrium directly, as Léon Walras and Vilfredo Pareto were later to do, Cournot proceeded by gradual steps. He started with monopoly, then considered competition limited to a few participants, and in the end took up the case of indefinite or unlimited competition, using the intercommunication of markets to complete his theory. This procedure has been criticized, for economists in the classical tradition follow the inverse procedure, starting with unlimited competition or, as they call it, perfect competition and ending up with monopoly. However, Cournot’s point of view has again been adopted in the modern theory of games and of the rational search for decisions. Although his theory of duopoly was criticized in 1883 by the mathematician Joseph Bertrand, the theory of bilateral monopoly was later to be erected on a similar base. The model with two parties was changed to a three-sided model (triopoly), and as the number of parties increased, the system was called oligopoly, pliopoly, and finally polypoly; the larger the number, the more closely the model approached that of classical competition. Today, makers of models no longer believe that there is an irreducible difference between models with many elements and those with few, but instead they relate the theory of markets to the general theory of economic interaction; hence their work is in the tradition of Cournot’s model, at first so poorly understood. There is still much to be learned from this 1838 model. Although Cournot has been rehabilitated, his contribution to economics has not been exhausted.
Philosophy. In Cournot’s philosophical works there emerge a philosophy of order and one of history. Cournot firmly maintained that, appearances to the contrary, chance does not imply disorder. By virtue of the theory of probabilities it is possible to see regularities: it is, as it were, the point of intersection of multiple independent causal series. And it permits the joining of the sciences with philosophy. The meaning of history, for all its incoherence, and the meaning of the future, for all its unpredictability, are profoundly related. To discover the course of ideas and events is the function of knowledge and the vocation of the human mind.
Cournot was a pioneer. He did nothing to court his contemporaries, and they, in turn, not only failed to appreciate him but ignored him. By a fitting reversal, his triumph came 80 years after his death. The most advanced of the econometric school recognize him as their ancestor. The theory of probabilities, whose full import Cournot realized, is a vital component of the structure of recent science. The problems that did not interest the men of his time are those that guide the building of tomorrow’s world; Cournot had anticipated the concern with predictions and decisions that now preoccupies economists.
Henri Guitton
[For the historical context of Cournot’s work, see biographies of theBernoulli family; Gauss; Laplace; Poisson. For discussion of the subsequent development of his ideas, seeDemand and supply; Oligopoly; Probability.]
WORKS BY COURNOT
1829 Mémoire sur le mouvement d’un corps rigide soutenu par un plan fixe. Paris: Hachette.
(1838a) 1960 Researches Into the Mathematical Principles of the Theory of Wealth. New York: Kelley. ? First published in French.
1838b Mémoire sur les applications du calcul des chances à la statistique judiciaire. Journal de mathématiques pures et appliquées 3:257–334. ? This is an early example of work on what is now called “latent structure.”
(1841) 1857 Traité élémentaire de la théorie des fonctions et du calcul infinitésimal. 2d ed. Paris: Hachette.
1843 Exposition de la théorie des chances et des probabilités. Paris: Hachette.
1847 De I’origine et des limites de la correspondance entre Valgebre et la géométric. Paris: Hachette.
(1851) 1956 An Essay on the Foundations of Our Knowledge. New York: Liberal Arts Press. ? First published in French.
(1861) 1911 Traité de I’enchaînement des idées fondamentales dans les sciences et dans I’histoire. New ed. Paris: Hachette.
1863 Principes de la théorie des richesses. Paris: Hachette.
(1872) 1934 Considérations sur la marche des idées et des èvènements dans les temps modernes. 2 vols. Paris: Boivin.
(1875) 1923 Matérialisme, vitalisme, rationalisme: Études des données de la science en philosophie. Paris: Hachette.
1877 Revue sommaire des doctrines économiques. Paris: Hachette.
1913 Souvenirs (1760–1860). With an introduction by E. P. Bottinelli. Paris: Hachette. ? Published posthumously.
SUPPLEMENTARY BIBLIOGRAPHY
[A. A. Cournot.] 1905 Revue de métaphysique et de morale 13:291–343. ? The entire issue is devoted to Cournot.
Bertrand, J. 1883 [Book Reviews of] Théories mathematiques de la richesse sociale, par Léon Walras; Recherches sur les principes mathematiques de la théorie de la richesse, par Augustin Cournot. Journal des savants [1883]: 499–508.
Bompaire, FranÇois 1931 Du principe de liberté économique dans I’oeuvre de Cournot et dans celle de I’école de Lausanne (Walras, Pareto). Paris: Sirey.
Bottinelli, E. P. 1913 A. Cournot: Métaphysicien de la connaissance. Paris: Hachette.
Edgeworth, F. Y. (1894)1963 Antoine Augustin Cournot. Volume 1, pages 445–447 in Robert H. I. Palgrave, Palgrave’s Dictionary of Political Economy. New York: Kelley.
Liefmann-Kiel, Elisabeth 1937 Die wissenschaftliche Methode und das Gesamtwerk Cournots. Archiv für mathematische Wirtschafts- und Sozialforschung 3: 238–251.
Loiseau, Georges 1913 Les doctrines économiques de Cournot. Paris: Rousseau.
MentrÉ, FranÇois 1908 Cournot et la renaissance du probabilisme au XIXe siécle. Paris: Riviere.
MentrÉ, FranÇois 1927 Pour qu’on Use Cournot. Paris: Beauchesne.
Milhaud, Gaston S. (1902–1911) 1927 Études sur Cournot. Paris: Vrin.
Roy, RenÉ 1933 Cournot et I’école mathématique. Econometrica 1:13–22.
Second, J. 1911 Cournot et la psychologie vitaliste. Paris: Alcan.