## Recherches sur les Principes Mathématiques de la Théorie des Richesses.

Paris: Chez L. Hachette, 1838.

First edition, uncut in original printed wrappers and extremely rare thus, of Cournot’s masterpiece which inaugurated mathematical economics. “Although neglected in his time, the impact of Cournot’s work on modern economics can hardly be overstated” (*The History of Economic Thought*). “With the publication in 1838 of his *Recherches sur les principes mathématiques de la théorie des richesses*, he was a third of a century ahead of Walras and Jevons and must be considered the true founder of mathematical economics. By reducing the problem of price formation in a given market to a question of analysis, he was the first to formulate the data of the diagram of monopolistic competition, thus defining a type of solution that has remained famous as ‘Cournot’s point’ … Undoubtedly, he remains the first of the important pioneers in this field” (DSB). “Cournot, in a book that for sheer originality and boldness of conception has no equal in the history of economic thought, was the very first writer to define and to draw a demand function … To prove the existence and uniqueness of the maximum [of the total profit], Cournot employed the familiar tests of calculus: the first derivative of the total profit function must vanish and the second derivative must be negative. All this in 1838!” (Blaug, pp. 301-2). Schumpeter (p. 463) places Cournot among “The Men Who Wrote Above Their Time” – that is, men who delivered “important performances, the powerful originality of which was recognized late but which the profession completely, or almost completely, failed to recognize at the time.” Cournot himself expected that this work would not be well received – in the preface he writes, “le titre. . . indique . . . que j’ai intention d’y appliquer les formes et les symboles de l'analyse mathématique: or c’est-là, je le confesse, un plan qui doit m’attirer tout d’abord la reprobation des théoriciens accrédités” – and it was not until the 1870s that its importance began to be recognised. Today “it strikes us as an utterly modern work – underlining Schumpeter’s view of Cournot as a man above his time. It is not just that Cournot provides us with the now-standard presentations of monopoly and perfect competition much as they are found in basic microeconomics textbooks today; it is that he presents them in a thoroughly modern idiom. The ideas of Smith, Ricardo, Jevons, Marshall, and Walras live on in modern economics, but the dust of an outmoded vocabulary and defunct styles of exposition hang around the original texts. Not so with Cournot. It would hardly raise a student’s eyebrow if Cournot’s text were included on a modern graduate syllabus. Cournot invented the modern idiom of mathematical economics and remains one of its master expositors. He did not attempt to write a complete treatise on political economy in the mode of Adam Smith. Rather – in the manner of so many recent economists – he extracted from political economy just those portions that were most amenable to mathematical representation and analyzed them concisely and efficiently. In style and substance, the *Recherches* reads very much like graduate textbooks from Samuelson’s *Foundations of Economic Analysis *(1947) to the present day” (Wible & Hoover, p. 515). Only four complete copies have sold at British and American auctions in the last 30 years (the folding plate is often lacking), and only one in original printed wrappers.

“Cournot begins with some preliminary remarks on the role of mathematics applied to the social sciences. He 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, Cournot 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’). 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’ (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’ (p. 47). He proceeds to draw the demand curve in price-quantity space (Fig. 1). He also introduces the idea of ‘elasticity’ of demand, but does not write it down in a mathematical formula.

“In Chapter 5, Cournot jumps immediately into an analysis of monopoly. Here, Cournot introduces the concept of a profit-maximizing producer. He begins by positing a 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. 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 an 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. On account of this, Cournot raises doubts in Chapter 12 about the ‘gains from trade’ and defends the profitability of import duties.

“Finally, Cournot 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’ (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. Cournot was left crushed and bitter … Cournot took another stab with his *Principes de la théorie des richesses* (1863), which, on the whole, was merely a restatement of the 1838 *Recherches* in more popular prose and without the mathematics. Once again, it was completely neglected …

“However, by this time the Marginalist Revolution had already started. Léon Walras (*Éléments d'économie politique pure*, 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 *The Theory of Political Economy *(1871). Francis Ysidro Edgeworth (*Mathematical Psychics*, 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 *Principles of Economics*, 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 des doctrines économiques* (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 …

“Cournot’s *Recherches *were finally translated into English in 1898. The introduction by Irving Fisher and Henry L. Moore’s 1905 biographical pieces helped promote Cournot’s work among Anglo-American economists. The development of monopolistic competition in the 1930s drew much inspiration from Cournot’s work.

“Cournot’s influence grew by leaps and bounds in the second half of the 20th Century. As game theory advanced, Mayberry, Nash and Shubik (‘A comparison of treatments of a duopoly situation,’ *Econometrica* 21 (1953), 141-54) 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, ‘Non-cooperative games,’ *Annals of Mathematics* 54 (1951), 286-95). 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” (*The History of Economic Thought*).

Antoine Augustin Cournot was born on August 28, 1801, in the small town of Gray (Haute-Saône) in France. He was educated in the schools of Gray until he was 15. At 19, he enrolled in a mathematical preparatory course at a school in Besançon, and subsequently won entry into the École Normale Supérieure in Paris in 1821. In 1822, Cournot transferred to the Sorbonne, obtaining a licentiate in mathematics in 1823. In Paris, he attended seminars at the Académie des Sciences and the salon of the economist Joseph Droz. Among his main intellectual influences were Pierre-Simon Laplace, Joseph-Louis Lagrange and Hachette, a former disciple of Marie-Antoine Condorcet, who started him on the principles of *mathématique sociale,* i.e., the idea that the social sciences, like the natural sciences, could be dealt with mathematically. From 1823, Cournot was employed as a literary advisor to Marshal Gouvoin Saint Cyr and as a tutor to his son. In 1829, Cournot acquired a doctorate in sciences, focusing on mechanics and astronomy. In 1834, 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, and he published his masterpiece, the *Recherches*. In 1839, the sickly 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 élémentaire de la théorie des fonctions et du calcul infinitésimal *to his long-time benefactor, Poisson. In 1843, Cournot made his first stab at probability theory in his brilliant *Exposition de la théorie des chances et des probabilités*. 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,’ or what modern commentators would call ‘credal probabilities’. 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 *Essai sur les fondements de nos connaissances et sur les caractères de la critique philosophique* (1851). In 1854, he became rector of the Academy at Dijon. However, by this time, Cournot’s lifelong eye-sight problem began getting worse. In 1859, Cournot wrote his *Souvenirs*, a haunting autobiographical memoir (published posthumously in 1913). Cournot retired from teaching in 1862 and moved back to Paris. Despite the dark pessimism about the decline of his sight and his creative powers, Cournot wasn’t quite yet finished. He published two more philosophical treatises in 1861 and 1872 which sealed his fame in the French philosophy community.

Kress C4590. Blaug, *Economic Theory in Retrospect*, 1997. Schumpeter, *History of Economic Analysis*, 1954. Wible & Hoover, ‘Mathematical Economics Comes to America: Charles S. Peirce’s Engagement with Cournot’s *Recherches Sur Les Principes Mathematiques De La Théorie Des Richesses*,’ *Journal of the History of Economic Thought *37 (2015), pp. 511-36. *The History of Economic Thought* (hetwebsite.net/het/profiles/cournot.htm).

8vo (219 x 137 mm), pp. xi (including half-title), 198, [2, contents and errata], with one folding plate, diagrams in text, uncut (some foxing throughout as always with this book. Original printed wrappers (slight spotting, fraying to edges, spine worn with some loss). Housed in a modern cloth box.

Item #6159

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Price:
$28,000.00
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