French philosopher, mathematician and economist, 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 work on modern economics
can hardly be overstated.

Augustin Cournot was born in the small town of Gray (Haute-Sa(ﾟne). 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 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, 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 ノtudes.
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 (Fig. 1). 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 Ch. 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" method 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 ノtudes*. 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", etc.
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 model (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, 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 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 ・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, Engl. 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'ag鐫re 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: ノtudes des données de las science en philosophie*, 1875.*Revue sommaire des doctrines économiques*, 1877.*Souvenirs, 1760-1860*, 1913*A. A. Cournot, Oeuvres Compl鑼es*. 5 vols, 1973.

- HET Pages: Phases of the Marginalist Revolution
- "Théorie
des Richesses: revue de
*Théories mathématiques de la richesse sociale*par Léon Walras et*Recherches sur les principes mathématiques de la théorie des richesses*par Augustin Cournot", by Joseph Bertrand, 1883,*Journal des Savants* - "La metaphysique d'inspiration et la metaphysique
scientifique. MM. Dumesnil et Cournot", 1862,
*L'année littéraire et dramatique* - "Les questions d'actualit・élevées ・l'état de thèses scientifiques et de dogmes
philosophiques -- MM. Cournot et J. Simon" 1865,
*L'année littéraire et dramatique* - "Review of Cournot's
*Considérations sur la marche des idées*" by H. Chotard, 1872,*Revue critique d'histoire et de littérature*. - "Un Géom鑼re
Philosophe: Antoine-Augustin Cournot" by Louis Liard, 1877,
*Revue des deux mondes*. - "MM. Cournot, Naudon,
Boutrot", in Paul Janet, 1879,
*La philosophie française contemporaine*. - " Philosophes
contemporains: M. Cournot"
by T.V. Charpentier, 1881,
*Revue philosophique de la France et de l'étranger* - "Ravaisson on
Cournot", in Félix Ravaisson, 1889,
*La**philosophie en France au XIXe siècle*, 1889, Paris: Hachette. - "Le Hasard chez Aristote et chez
Cournot" by Gaston Milhaud, 1902,
*Revue de métaphysique et de morale* - "Review of F.
Mentr・
*Cournot et la renaissance du probabilisme*", by A. Penjon, 1909,*Revue philosophique de la France et de l'étranger*, 6 fasc.. Année 34. p.67-75. -
*Etudes sur Cournot*by Gaston Milhaud, 1927 - "Cournot,
Bertrand and Modern Game Theory" by Clarence C. Morrison, 1998,
*Atlantic EJ* - "Cournot, Bertrand, and Game Theory: A Further Note"
by Robert W. Dimand and Mohammed H. I. Dore, 1999,
*Atlantic EJ* - "Dimand-Dore on
Cournot-Bertrand: A Reply and More" by Clarence C. Morrison, 1999,
*Atlantic EJ* - "Numéro spécialement consacr・
Cournot" (Symposium on Cournot), 1905,
*Revue de métaphysique et de morale* - Cournot Page at Gallica.
- Bibliographie Cournot at Univ. Franche-Comte.
- Biography of Cournot at MacTutor Mathematics Archive
- "Teaching Cournot without Derivatives" by Martin Dufwenberg, 1999
- Cournot Oligopoly at Illinois
- Cournot entry at Bartleby
- Cournot Page at Laura Forgette

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