Antoine Augustin Cournot (1801-1877)

French philosopher, mathematician and economist, Antoine Augustin Cournot has been rightly hailed as one of the greatest of the Proto-Marginalists. The unique insights of his major economics work, Researches into the Mathematical Principles of Wealth (1838) were without parallel. Although neglected in his time, the impact of Cournot’s work on modern economics can hardly be overstated.

Antoine Augustin Cournot was born in the small town of Gray (Haute-Saône). He was educated in the schools of Gray until he was fifteen. Subsequently, for the next four years, he worked haphazardly as a clerk in a lawyer’s office. Cournot directed his own studies throughout this time, mostly centered around philosophy and law. Inspired by the work of Laplace, Cournot realized that he had to learn mathematics if he was to pursue his philosophical aspirations. So, at the relatively ripe age of nineteen, he enrolled in a mathematical preparatory course at a school in Besançon. He subsequently won entry into the École Normale Supérieure in Paris in 1821.

For political reasons, the ENS was closed down in 1822 and so Cournot transferred to the Sorbonne, obtaining a lecentiate in mathematics in 1823. He threw himself wholeheartedly into the stimulating intellectual and scientific atmosphere of Paris, attending the seminars at the Academie des Sciences and the salon of the economist Joseph Droz. Among his main intellectual influences were Laplace, Lagrange and Hachette, a former disciple of MARIE ANTOINE CONDORCET, who imbibed in him the principles of mathematique sociale, i.e. the idea that the social sciences, like the natural, could be dealt with mathematically. Cournot counted the young mathematician Lejeune Dirichlet as a close friend.

From 1823, Antoine Augustin Cournot was employed as a literary advisor to Marshal Gouvoin Saint Cyr and a tutor to his son. For the next ten years, Cournot would remain in Paris in this leisurely capacity, pursuing his studies and research in his own way. In 1829, Cournot acquired a doctorate in sciences, focusing on mechanics and astronomy. After Saint Cyr’s death in 1830, Cournot took it upon himself to edit and publish the remaining volumes of his late employer’s memoirs.

Cournot’s thesis and a few of his articles brought him to the attention of the mathematician Siméon-Denis Poisson who urged him to return to academia. Cournot refused at first but, after his engagement with the Saint Cyr family ended in 1833, he took up a temporary appointment at the Academy in Paris. It was during this time that he translated John Herschel’s Astronomy (1834) and Dionysus Lardner’s Mechanics (1835).

In 1834, through the good offices of Poisson, Cournot found a permanent appointment as professor of analysis and mechanics at Lyons. A year later, Poisson secured him a rectorship at the Academy of Grenoble. Although his duties were mostly administrative, Cournot excelled at them. In 1838, (again, at the instigation of the loyal Poisson), Cournot was called to Paris as Inspecteur Général des Études. In that same year, he was made a Knight of the Légion d’honneur (he was elevated to an Officer in 1845).

It was in this year that Cournot published his economics masterpiece, the Recherches (1838). Cournot begins with some preliminary remarks on the role of mathematics applied to the social sciences. His announces that his purpose in using mathematics is merely to guide his reasoning and illustrate his argument rather than lead to any numerical calculations. He acknowledges (and disparages) N.F. Canard as his only predecessor.

In his first three chapters, he runs through the definition of wealth, absolute vs. relative prices and the law of one price. Then, in Chapter 4, he unveils his demand function. He writes it in general form as D = F(p). He assumes that F(.) is continuous and takes it as an empirical proposition that the demand function is downward-sloping (the loi de débit, “law of demand”) and proceeds to draw it in price-quantity space. He also introduces the idea of “elasticity”, but does not write it down in a mathematical formula.

It is important to note that Cournot’s “demand function” is not a demand schedule in the modern sense. His curve, D = F(p) merely summarizes the empirical relationship between price and quantity sold, rather than the conceptual relationship between price and the quantity sought by buyers. Cournot refuses to derive demand from any “utility”-based theories of individual behavior. As he notes, the “accessory ideas of utility, scarcity, and suitability to the needs and enjoyments of mankind…are variable and by nature indeterminate, and consequently ill suited for the foundation of a scientific theory” (Cournot, 1838: p.10). He satisfies himself with merely acknowledging that the functional form of F(.) depends on “the utility of the article, the nature of the services it can render or the enjoyments it can procure, on the habits and customs of the people, on the average wealth, and on the scale on which wealth is distributed.” (1838: p.47).

In Chapter 5, Cournot jumps immediately into an analysis of monopoly. Here, the concept of a profit-maximizing producer is introduced. Cournot introduces the cost function f(D) and discusses decreasing, constant and increasing costs to scale. He shows mathematically how a producer will choose to produce at a quantity where marginal revenue is equal to marginal cost (he re-expresses marginal cost as a function of price in its own right, f'(D(p)) = y(p)). In Chapter 6, he examines the impact of various forms of taxes and bounties on price and quantity produced, as well as their impact on the income of producers and consumers.

In Chapter 7, Cournot presents his famous duopoly model. He sets up a mathematical model with two rival producers of a homogeneous product. Each producer is conscious that his rival’s quantity decision will also impact the price he faces and thus his profits. Consequently, each producer chooses a quantity that maximizes his profits subject to the quantity reactions of his rival. Cournot mathematically derives a deterministic solution as the quantities chosen by the rival producers are in accordance with each other’s anticipated reactions. Cournot showed how this equilibrium can be drawn as the intersection of two “reaction curves”. He depicts a stable and an unstable equilibrium in Figures 2 and 3 respectively.

Comparing solutions, Cournot notes that under duopoly, the price is lower and the total quantity produced greater than under monopoly. He runs with this insight, showing that as the number of producers increases, the quantity becomes greater and the price lower. In Chapter 8, he introduces the case of unlimited competition, i.e. where the quantity of producers is so great that the entry or departure of a individual producer has a negligible effect on the total quantity produced. He goes on to derive the prices and quantities in this “perfectly competitive” situation, in particular showing that, at the solution, price is equal to marginal cost.

In the remainder of his book, Cournot takes up what he calls the “communication of markets”, or trade of a single good between regions. In Chapter 10, he analyzes two isolated countries and one homogeneous product. He shows that the impact of opening trade between the two countries leads to the equalization of prices, with the lower cost producer exporting to the higher cost country. Cournot tries to prove that there are conditions where the opening of trade will lead to a decline in the quantity of the good and lower revenue. He then proceeds to discuss the impact of import and export taxes and subsidies (and algebraic error here was spotted later by Edgeworth (1894)) . On account of this, Cournot raises doubts in Chapter 12 about the “gains from trade” and defends the profitability of import duties.

Finally, Cournot also acknowledges that the solutions obtained via his partial equilibrium theory are incomplete. He recognizes the need to take multiple markets into account and trying to solve for the general equilibrium, but ‘this would surpass the powers of mathematical analysis’ (Cournot, 1838: p.127).

Cournot’s 1838 work received hardly any response when it came out. The denizens of the French Liberal School, who dominated the economics profession in France at the time, took no notice of it, leaving Cournot crushed and bitter. In 1839, plagued by ill-health, Poisson asked Cournot to represent him at the concours d’agrégation de mathématiques at the Conseil Royal. After Poisson died in 1840, Cournot continued on at the Conseil as a deputy to Poisson’s successor, the mathematician Louis Poinsot.

In 1841, Cournot published his lecture notes on analysis from Lyons, dedicating the resulting Traité to Possion. In 1843, he made his first stab at probability theory in his Exposition. He differentiated between three types of probabilities: objective, subjective and philosophical. The former two follow their standard ontological and epistemological definitions. The third category refers to probabilities “which depend mainly on the idea that we have of the simplicity of the laws of nature.” (1843: p.440).

After the 1848 Revolution, Cournot was appointed to the Commission des Hautes Études. It was during this time that he wrote his first treatise on the philosophy of science (1851). In 1854, he became rector of the Academy at Dijon. However, Cournot’s lifelong eye-sight problem began getting worse. Cournot retired from teaching in 1862 and moved back to Paris.

In 1859, Cournot wrote his Souvenirs, a haunting autobiographical memoir (published posthumously in 1913). Despite the dark pessimism about the decline of his creative powers, he wasn’t quite yet finished. He published two more philosophical treatises in 1861 and 1872 which sealed his fame in the French philosophy community, but did nothing to advance his economics. He took another stab at economics with his Principes (1863), which, on the whole, was merely a restatement of the 1838 Recherches without the math and in more popular prose. Once again, it was completely neglected. A Journal des économistes review churlishly claimed that Cournot had “not gone beyond Ricardo”, and Cournot’s bitterness increased accordingly.

However, by this time the Marginalist Revolution had already started. Léon Walras (1874), who had read Cournot’s work early on, argued that his own theory was but a multi-market generalization of Cournot’s partial equilibrium theory (indeed, the notation is almost identical). W. Stanley Jevons, who had not read him, nonetheless hailed him as a predecessor in later editions of his Theory (1871). Francis Ysidro Edgeworth (1881) went to Cournot to pick up his theory of perfect competition. Alfred Marshall claimed to have read him as far back as 1868, and extensively acknowledged Cournot’s influence in his 1890 textbook, particularly in his discussion of the theory of the firm.

Cournot lived long enough to greet the works of Walras and Jevons with a warm sense of vindication. This is evident in Cournot’s Revue sommaire (1877), a long, non-mathematical statement of his earlier work. He seemed particularly grateful that Walras had bravely climbed the steps of the Institute de France and accused the academicians of injustice towards Cournot. He died that same year.

Walras, Jevons and the other young blades complained loudly that Cournot had been unjustly neglected by his contemporaries. So, in 1883, the French mathematician Joseph Bertrand took it upon himself to finally provide the first review of the Cournot’s Recherches (jointly with a Walras book) in the Journal des savants. It was not a kind review. Bertrand argued that Cournot had reached the wrong conclusion on practically everything, and reworked Cournot’s duopoly model with prices, rather than quantities, as the strategic variables – and obtained the competitive solution immediately. Edgeworth (1897) revisited the model and assailed both Cournot and Bertrand for obtaining deterministic solutions, arguing that the equilibrium solution in the case of a small number of producers should always be indeterminate.

The development of monopolistic competition in the 1930s drew much inspiration from Cournot’s work. As the theory of games advanced in the 1950s, Mayberry, JOHN NASH and Shubik (1953) restated Cournot’s duopoly theory as a non-cooperative game with quantities as strategic variables. They showed that Cournot’s solution was nothing other than its Nash equilibrium (Nash, 1951). Cournot’s influence on modern theory continues unabated, having been given a particular boost in the attempt to develop non-cooperative foundations for Walrasian general equilibrium theory (e.g. Novshek and Sonnenschein (1978) and the 1980 JET Symposium).

Major works of Antoine Augustin Cournot
– Translator, Traité d’astronomie, par Sir John F.-W. Herschel, 1834
– Translator, Eléments de Mechanique by Dionysus Lardner, 1835
– Mémoire sur les applications du calcul des chances à la statistique judiciaire, 1838, Journal des mathématiques pures et appliquées, 12. T. 3. p.257-334
– Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth), 1838 (1897, England trans. by N.T. Bacon)
– Traité élémentaire de la théorie des fonctions et du calcul infinitésimal, 1841
– Exposition de la théorie des chances et des probabilités, 1843
– De l’origine et des limites de la correspondence entre l’agèbre et la géométrie, 1847
– Essai sur les fondements de nos connaissances et sur les caractères de la critique philosophique, 1851 – Vol. I, Vol. II
– Traité de l’enchainement des idées fondamentales dans les sciences et dans l’histoire, 1861
– Principes de la théorie des richesses, 1863
– Les institutions d’instruction publiques en France, 1864
– Considérations sur la marche des ideées et des événements dans les temps modernes, 2 vols, 1872
– Materialisme, vitalisme, rationalisme: Études des données de las science en philosophie, 1875
– Revue sommaire des doctrines économiques, 1877
– Souvenirs, 1760-1860, 1913
– A.A. Cournot, Oeuvres Complètes. 5 vols, 1973

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