COURNOT, Augustin.

Recherches sur les principes mathématiques de la théorie des richesses. Paris: Chez L. Hachette, Libraire de l’Université Royale de France, Rue Pierre‑Sarrazin, No 12, 1838. [Bound with:] URBAIN, Nestor. Introduction à l’étude de l’économie politique. Paris: Bossange Père, 1835.

Paris: Chez L. Hachette, 1838.

First edition of Cournot’s masterpiece, the foundational work of mathematical economics and one of the most remarkable achievements in nineteenth-century social science. With its appearance, Cournot established the analytical framework that would become the basis of modern microeconomic theory. A mathematician by training and Inspector General of Studies by profession, he brought to political economy the methods of analysis developed by Laplace and Poisson, using mathematics not for numerical computation but as a language of logical precision. By reducing questions of price formation and competition to quantitative relations among observable magnitudes—price, quantity, and cost—he created a new scientific idiom for economics.

Cournot’s contemporaries scarcely noticed the book. It sold poorly and was dismissed by the dominant French Liberal School as a mathematical curiosity. Yet his achievement was extraordinary. Decades before Jevons and Walras, Cournot formulated the essential concepts of modern theory: the demand function, the profit-maximising firm, and the equilibrium of interacting producers. Schumpeter would later call him “one of the men who wrote above their time,” and Mark Blaug described the Recherches as “for sheer originality and boldness of conception, without equal in the history of economic thought.”

The opening chapters of the Recherches set out Cournot’s method and purpose. Mathematics, he insists, serves only to guide reasoning and ensure rigour: it does not yield empirical numbers but clarifies relations between variables. He explicitly rejects attempts to base economics on the indeterminate notions of utility or pleasure. Scientific theory, he argues, must rest on observable facts. His starting point is therefore the relationship between market price and the quantity of goods exchanged—the “law of demand,” or loi de débit.

In Chapter 4, Cournot gives the first formal definition of the demand function, writing it in general form as $D = F(p)$D=F(p), the quantity sold as a function of price. He assumes continuity and a negative slope, treating the function as an empirical law rather than a psychological construct. The accompanying folding plate presents what is perhaps the first demand curve in price–quantity space, establishing the graphical language that remains standard to this day. Cournot notes that the functional form of demand depends on such factors as the utility of the article, the customs of the people, and the distribution of wealth, but he deliberately avoids speculative assumptions about individual motives. The emphasis is on measurable relationships.

The analysis of monopoly in Chapter 5 represents the first rigorous application of calculus to economic behaviour. Cournot defines total cost as $f(D)$f(D) and profit as $pD - f(D)$pD−f(D), and demonstrates that the producer’s optimal output is found where marginal revenue equals marginal cost. To prove the existence and uniqueness of this maximum, he applies the first and second derivative tests—conditions that have become canonical. The diagram on the folding plate illustrates this tangency, marking the point of equilibrium that later economists named “Cournot’s point.” In Chapter 6 he examines how excise taxes, ad valorem taxes, and bounties alter equilibrium price and quantity, analysing for the first time the incidence of taxation on producers and consumers.

The celebrated duopoly model, presented in Chapter 7, was Cournot’s most original contribution. Two firms producing a homogeneous product each choose an output level, recognising that their profits depend on the total quantity placed on the market. Each firm therefore reacts to its rival’s decision, and equilibrium occurs when both have correctly anticipated each other’s choice. Cournot derived the solution geometrically as the intersection of two reaction curves—fonctions de réaction—whose crossing defines a stable “Cournot point.” He demonstrated that, under duopoly, price falls and total output rises relative to monopoly, and that as the number of firms increases, price approaches marginal cost. Chapter 8 generalises this to “unlimited competition,” showing mathematically that in the limiting case of innumerable small producers, price must equal marginal cost—the defining condition of perfect competition.

Having established the theory of market equilibrium, Cournot turned in the later chapters to what he called the “communication of markets,” the integration of regional economies through trade. In Chapter 10 he analyses two countries producing the same commodity: when trade opens, prices equalise, the lower-cost region exports to the higher-cost region, and total welfare changes according to the shape of the demand functions. He further studies how tariffs, transport costs, and subsidies disturb this balance. In Chapter 12 he acknowledges that his method is partial, applying to one market at a time, and concedes that a complete theory encompassing all interdependent markets would “surpass the powers of mathematical analysis.” That challenge would be met by Walras forty years later, using Cournot’s notation and logic.

Cournot’s mathematical economy was too far ahead of its time to find readers. The economists of his generation, still trained in literary and moral discourse, regarded algebraic reasoning as pedantic and obscure. Only after the 1870s did the Recherches receive its due. Walras, who read it early, declared that his own Éléments d’économie politique pure was nothing more than the generalisation of Cournot’s partial equilibrium model. Jevons hailed him as a forerunner, Edgeworth built on his theory of perfect competition, and Marshall openly acknowledged his influence in the Principles of Economics (1890). The first English translation, issued in 1898 with an introduction by Irving Fisher, brought the book to an Anglo-American audience and secured Cournot’s reputation as the founder of mathematical economics.

The twentieth century deepened that recognition. As game theory emerged, Cournot’s duopoly was reinterpreted in strategic terms. Mayberry, Nash, and Shubik demonstrated in 1953 that the Cournot equilibrium coincides precisely with the Nash equilibrium of a non-cooperative game where quantities are the strategic variables. Industrial-organisation theory, the analysis of imperfect competition, and modern studies of taxation and welfare all continue to operate within the framework Cournot devised. His concepts of reaction curves, comparative statics, and market integration remain embedded in the structure of economic analysis.

The folding plate included in the Recherches distils the work’s geometrical insight. It contains ten figures showing the demand curve, the decomposition of revenue into average and marginal components, the monopoly tangency condition, and the intersecting reaction curves of duopoly, with examples of both stable and unstable equilibria. The final figures illustrate the progressive convergence toward perfect competition as the number of firms increases. Far from decorative, these diagrams form a visual summary of Cournot’s system—a compact map of the logic of markets that would later fill entire textbooks.

Antoine Augustin Cournot was born in 1801 at Gray in Haute-Saône. Trained in mathematics at the École Normale and later at the Sorbonne, where he studied under Laplace and Poisson, he devoted his early career to teaching analysis and mechanics at Lyon before being appointed rector of the Academy of Grenoble. In 1838, the year of the Recherches, he became Inspecteur Général des Études and a chevalier of the Légion d’honneur. His later writings extended the methods of mathematical reasoning to probability, epistemology, and the philosophy of science. The Exposition de la théorie des chances et des probabilités (1843) distinguished between objective, subjective, and philosophical probability; his Essai sur les fondements de nos connaissances (1851) explored the limits of human understanding. Despite failing eyesight and growing pessimism, Cournot continued to write until his death in 1877.

The Recherches sur les principes mathématiques de la théorie des richesses stands today as the first systematic attempt to apply the language of analysis to the behaviour of markets. In tone and structure it is astonishingly modern: concise, logical, and free of rhetorical flourish. Cournot did not aspire to the encyclopaedic sweep of Adam Smith but, like the economists of a century later, extracted from political economy only what could be stated with mathematical clarity. Reading him now is to encounter the idiom of Samuelson and Debreu in embryonic form. As Blaug observed, “Cournot invented the modern idiom of mathematical economics and remains one of its master expositors.”

Bound before Cournot’s text, lies Nestor Urbain’s Introduction à l’étude de l’économie politique (Paris, 1835), a short pedagogical survey typical of the French academic style of the 1830s. It defines the elementary vocabulary of production, exchange, and taxation and would have served as a convenient primer for readers approaching Cournot’s far more demanding treatise. Its presence here, together with several dozen blank leaves once reserved for notes, forms an instructive historical pairing—but it is Cournot’s Recherches, self-contained and revolutionary, that remains the true centrepiece, the work that transformed political economy into a mathematical science.

References: Kress C4590; Blaug, Economic Theory in Retrospect (1997); Schumpeter, History of Economic Analysis (1954); Wible & Hoover, “Mathematical Economics Comes to America,” Journal of the History of Economic Thought 37 (2015); The History of Economic Thought (hetwebsite.net/het/profiles/cournot.htm).

Two works bound in one, 8vo (205 x 130 mm), Urbain: pp [VIII] [1] 2-259 [260: blank]; Cournot: pp [I-V] VI-XI [XII], [1] 2-198 [199-200: chapter table and errata] and 1 engraved folding plate. Contemporary French half calf over marbled boards, smooth gilt spine tooled in an elegant rococo palette and lettered Économie Politique; sprinkled edges. A well‑preserved copy, the binding lightly rubbed at extremities, scattered faint foxing to the text as usual, the large plate clean and without tears.

Item #6486

Price: $18,000.00