Abstract
Cournot’s Researches into the Mathematical Principles of the Theory of Wealth (1838) was a major breakthrough towards modern economics. It was so both in form and content. With respect to form, it was the first rigorous and extensive mathematical model using advanced calculus to explore key economic issues. With respect to the content, it initiated the representation of demand and supply as well-shaped functions, from which an equilibrium could be determined. Cournot went further, exploring how different equilibria correspond to different market structures. In that process, through the examination of the case of duopoly he introduced the concept of a non-cooperative solution based on the “reaction functions” of the competitors, providing a first insight of what would be revisited over a century later as a Nash-equilibrium. Besides a reminder of these major results, this chapter examines personal as well as contextual factors that could explain this radical transformation in economic analysis. It also discusses why this book was ignored for decades before being rediscovered by the founders of the marginal revolution and fully integrated into modern economics. To sum up, this chapter demonstrates that Cournot was a radical innovator whose contribution remains refreshing reading.
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Notes
- 1.
From now on, all references to Researches are to the English translation by Nathaniel Bacon, with a preface by Irving Fisher (who initiated the project of this translation).
- 2.
He passed away in March 1877 in Paris. This is to say that in his lifetime he went through four revolutionary periods: the Napoleonic regime in the aftermath of the French revolution of 1789, the revolutions of 1830 and 1848; and the invasion of Prussia followed by the ‘Commune de Paris’ in 1870–1871.
- 3.
Partially related to the emergence of a large urban-working class population in relation to the development of the industry.
- 4.
This textbook (as well as his main dissertation and a few short papers published in the late 1820s) shows that Cournot was well informed and knowledgeable about the progress of mathematics of his time. However, his appointment in Lyon also meant addressing an audience including notables from that city with little familiarity with mathematics but expecting insights that could be helpful in the running of their businesses. One must be aware that universities at that time also played a role of social venues to build networks. This suggests that Cournot had to find illustrations from the business world, something he mentions in his Souvenirs ([13]; published posthumously in 1913).
- 5.
“Jusqu’à présent on n’a guère appliqué le calcul des chances qu’à des problèmes sur les jeux, problèmes purement spéculatifs ou d’un médiocre intérêt pratique, et à des faits de statistique sociale dont les causes se dérobent par leur complication à toute investigation mathématique, et pour lesquels nous n’avons d’autres données que celles de l’expérience” (Addition, #7, p. 504).
- 6.
John Maynard Keynes highly regarded and was influenced by the Exposition [22].
- 7.
His friend Hachette, who was becoming a major scientific publisher, continuously pushed Cournot – distracted by his increasing administrative responsibilities – to wrap up his scientific books while apparently considering that Researches should not be a priority. He nevertheless secured its publication.
- 8.
Among his later publications, two books help understanding Cournot’s approach to economics: Principes de la Théorie des Richesses [11]; Revue Sommaire des Doctrines Economiques [12]. Cournot suggested that they can be read, particularly the one from 1863, as Researches revisited …without mathematics (see Souvenirs, [13]). They are actually quite different in many aspects from the rigorous approach that prevailed in his Researches.
- 9.
Among this generation, besides Cournot, we find Jules Dupuit (1804–1866) and Adolphe Quételet (1796–1874) among others.
- 10.
From now on and if not otherwise specified all references to paragraph numbers are those used in Researches.
- 11.
“The abstract idea of wealth or of value in exchange, a definite idea, and consequently susceptible of a rigorous treatment in combinations, must be carefully distinguished from the accessory ideas of utility, scarcity, and suitability to the needs and enjoyment of mankind, which the world wealth still suggests in common speech” (#3).
- 12.
Cournot’s exact expression states that a market designates “the entire territory of which the parts are so united by the relations of unrestricted commerce that prices there take the same level throughout, with ease and rapidity” (#23).
- 13.
- 14.
An interesting indication of their relationship is provided in Poisson’s letter to Cournot from January 26, 1836, quoted in [11, pages VI–VII].
- 15.
Two other conditions are actually needed: a mathematical one (the sufficient condition requires a certain shape of the demand curve, an issue discussed in #24), and an economic one (there should be no radical changes in the markets for inputs or in the production system since such changes would alter the conditions shaping demand).
- 16.
To make the idea more concrete to his readers, Cournot suggested that p could denote “the annual average price” for a certain homogenous good (#23).
- 17.
Cournot is well aware that some goods may not fulfill the conditions justifying continuity (e.g., luxury goods) but he considers that they are either exceptions or that these “exceptional cases” will tend to be “suppressed” by “the extension of commerce” (conclusion of #22).
- 18.
Notation slightly modified. Cournot does not have the concept of budget constraint; the maximum value p′ is determined through a purely mathematical reasoning.
- 19.
The idea of a utility function clearly did not occur to Cournot, who considered the very idea of “utility” in economics as “accessory” (#3).
- 20.
The term “tâtonnement” became dear to Walras, but took a very different meaning in economics (see [19]). In the general equilibrium model that Walras initiated [36], the term “tâtonnement” refers to a price-adjustment process leading to equilibrium and (that is the main point) without any transaction out of equilibrium. I am grateful to Professor Maruyama for having reminded me of this important difference between the two models (Walras vs Cournot).
- 21.
Italics are from Cournot. In French, the term is “insensible”, which would be better translated by “unnoticeable” (in modern terminology: “marginal”).
- 22.
For a discussion on how close Cournot came to a general equilibrium model, see Dos Santos Fereira [16: 85 sq]. However, Cournot remained pessimistic about the possibility to build a rigorous model of interdependent markets (and a general equilibrium) because of the complexities involved.
- 23.
- 24.
The exact expression used by Cournot is “adjusting the price.” Bacon’s translation slightly differs, emphasizing that each party is price-maker, although conditional on what the other one is doing.
- 25.
For decades Cournot needed the help of a personal secretary and he was almost blind when he passed away.
- 26.
“C’est ce que j’ai essayé de faire dans mon volume de 1863, qui a eu encore moins de succès chez tous les économistes que ma plaquette de 1838” (italics from Cournot; see Jaffe (ed.), [20, Vol. I, pp. 331–332]).
- 27.
Cournot does not seem to be aware of Whewell’s contributions.
- 28.
Significantly, although Cournot refers to the “statistiques sociales,” I could not find any reference, even in 1843, to the term “mathématique sociale,” even when discussing Condorcet.
- 29.
See the following statement in the addendum to Herschel [18, p. 504]: “Jusqu’à présent on n’a guère appliqué le calcul des chances qu’à des problèmes sur les jeux … et à des faits de statistique sociale dont les causes se dérobent par leur complication à toute investigation mathématique et pour lesquels nous n’avons d’autres données que celles de l’expérience.».
- 30.
For a detailed discussion of the relation of Cournot to statistics, see Menard [28].
- 31.
See Bru [4] for a comment on the mathematical significance of this terminology at the time.
- 32.
“Pourquoi vous êtes-vous amusé à nous parler en hiéroglyphes effarouchants …” (italics are from de Fontenay).
- 33.
- 34.
“Mais je tremble que vos courbes “d’utilité intensive et extensive” ne vous mènent au pur laissez-faire, c’est-à-dire, en économie nationale, au déboisement du sol, et en économie internationale, à l’étouffement de la plèbe des races par une race privilégiée conformément à la théorie de M. Darwin.” (Letter to Walras from September 3, 1873; in Jaffe ed., [20, vol. 1, p. 332].).
- 35.
In a very different perspective, Cournot has also had a significant influence on philosophy in France, and particularly on the philosophy of sciences. See Deschamps and Martin (ed.) [15].
- 36.
For a detailed analysis, see Menard [27].
- 37.
However, Cournot never considered utility or scarcity as relevant foundations to the analysis of equilibrium (see his letter to Walras, Sept. 3, 1873).
- 38.
Leonard [24] is right in pointing out that interpreting Cournot’s analysis in terms of a Nash equilibrium is a retrospective reading that can be distortive. Reading Cournot in terms of game theory required … the development of game theory and the demonstration by Nash of the equilibrium associated with his name!
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Special thanks to Professor Toru Maruyama for his invitation to contribute to this volume and for his highly inspiring insights.
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Menard, C. (2023). Toward the Marginal Revolution: The Foundational Status of Antoine-Augustin Cournot. In: Maruyama, T. (eds) Marginal Revolution in Economics. Monographs in Mathematical Economics, vol 6. Springer, Singapore. https://doi.org/10.1007/978-981-99-4342-5_2
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