Introduction

A pioneer of mathematical economics, most of Cournot’s contribution was over­looked by his fellow economists in his time. He will later be vindicated by none other than William Stanley Jevons and Leon Walras, particularly for his analysis of the demand function and his study of monopoly and duopoly.

Life and background

Antoine-Augustin Cournot¹ was born on 28 August 1801, in Gray, in Franche- Comte. He was admitted in Ecole Normale Superieure at the age of 20, but the school was closed in 1822 for political reasons. He then studied at the Faculty of Sciences in Paris where he defended his main doctoral thesis in mechanics and a secondary thesis in astronomy in 1829.

The mathematical papers he published attracted the attention of French math­ematician Simeon-Denis Poisson and, with his help, Cournot became professor of mechanics and analysis at the Faculty of Sciences in Lyon in 1834. In Octo­ber 1835, he became “Recteur” of the Academie of Grenoble while teaching math­ematics at the Faculty. The following year, he replaced Andre-Marie Ampere as general inspector of education. While occupying these three positions, he wrote his first economic publication, Recherches sur les principes mathematiques de la theo- rie des richesses, published in 1838. He refocused on mathematics and published Traite elementaire de la theorie des fonctions et du calcul infinitesimal (1841) fol­lowed by a book on probability theory, Exposition de la theorie des chances et des probabilites (1843). Cournot’s visual faculties soon started to deteriorate, forcing

1 For more information about Cournot’s life and works, see, for instance, Theocharis (1983), Menard (1978), Martin (1996) and Deschamps and Martin (2020).

DOI: 10.4324/9780429202407-5 him to stop using mathematics²; he then turned his attention to the philosophy of sciences with his Essai sur les fondements de nos connaissances et sur les car- acteres de la critiquephilosophique (1851) and Traite de l^,enchainement des idees fondamentales dans les sciences et dans l'histoire (1861). From 1854, he served as “Recteur” of the Academie of Dijon but, because of his blindness, he stepped down in 1862. He continued his research until his death. Cournot returned to econom­ics by publishing Principes de la theorie des richesses (1863) which presented in literary form the ideas advanced in 1838. However, the book signalled a change in his views and the influence of John Stuart Mill and Friedrich List. Cournot’s dissatisfaction with liberalism became more evident. The idea that “the greatest good for society must necessarily be the result of the forces generated by private interests” (1863, 275) seemed ill-founded.^[54] His criticisms were twofold: on the one hand, the notion of optimum was not clearly defined, and, on the other hand, it was impossible to prove that individual interests necessarily led to a collective well-being. Cournot died in Paris on 31 March 1877. That year saw the publica­tion of his Revue sommaire des doctrines economiques in which he criticised both liberalism and socialism.

Mathematics, economics and philosophy

Cournot was a mathematician, an economist and a philosopher (Martin 1996). The challenge is to examine to what extent his views on probability theory and the his­tory and philosophy of sciences informed his economic analyses.

In Exposition de la Theorie des chances et des probabilites (1843), Cournot stressed that “nothing is more important than carefully distinguishing between the two meanings of the term probability, either used in an objective or a subjective sense, if we want to avoid confusion and errors” (Cournot 1843, 148). What char­acterised his approach of random markets was the rejection of Bernoulli’s solution to the Saint Petersburg paradox.

In L'enchainement des idees fondamentales dans les sciences et dans l'histoire (1861), he studied economic optimism and maintained that the idea that the great­est general good necessarily resulted from conflicting private interests was not sus­ceptible of a logical proof. The motto Laissez faire, laissez passer must triumph in the end, not because of a theoretical proof, but because it naturally came to the

2 In a letter sent to Leon Walras, Cournot (1873, vol. 1: 331) wrote:

I must confess that for the past 30 years, I have been compelled to appeal to a reader... I have not been able to find someone who is capable of reading mathematics... I cannot read mathematics with my ears, let alone dictate... and this is the reason why I was forced to stop using mathemat­ics for the past 30 years. mind of individuals, and because only artificial and arbitrary rules were proposed against it.

At first sight, the 1863 Principes was a non-mathematical restatement of the 1838 Recherches. But there is more. In the book, Cournot returned to his initial economic approach, but he also drew upon his Essai sur le fondement de nos connaissances (1851) and upon the analysis he made of the Platonic opposition between science and opinion. From this point of view, political economy was in an ambiguous position. Cournot (1863, 326) stated “that it does not admit and will never completely admit the regular, systematic and always progressive con­struction, which belong to the sciences... and never completely rely on unshak­able and universally accepted bases”. First, while some propositions of the theory of wealth could be rigorously proved, their meaning depended on considerations drawn from social economics,^[55] but this field was based on opinion, not science.

The mathematical apparatus... lead us unfortunately to think that one confer to these hypotheses a value that they effectively have in the interpretation of natural phenomena, but that they cannot have to the same degree in the interpretation of social phenomena.

(1863, 329-30)

Although he considered political economy a positive discipline, and though he admitted that most individuals relied on experience to solve the most salient ques­tions with regard to private and public affairs, Cournot underlined the importance of theory. He thus decided to study political economy only from a theoretical standpoint.

Cournot’s theoretical political economy was conceived of through the lens of mathematics. In the preface to his Recherches, he wrote that he intended to apply to the theory of wealth “the forms and symbols of mathematical analysis” (1838, 3). He was led to use the theory of continuous functions and of infinitesimal cal­culus, of which he gave an elementary exposition a few years later (1841). For Cournot (1838, viii), “it is natural to use mathematical symbols... to discuss the relationships between variables”. To do so, Cournot drew upon authors known today as classical economists.

There are authors, such as Smith and Say, who wrote on political economy in a pure literary form; but there are others, like Ricardo, who studied more abstract issues or seeking greater precision, could not avoid algebra, but only ended up disguising it with long and tedious arithmetic.

(1838, 4-5)

Cournot warned the reader against a false idea regarding the application of math­ematics to the theory of wealth. “Some believed that using signs and formulas had no other purpose than numerical calculus” (1838, 4). Indeed, using mathematics could lead to errors, or could even be perceived as lazy or pretentious. Therefore, rather than using basic algebra, Cournot favoured the theory of functions, differen­tial calculus and integrals. He avoided being too specific about the algebraic for­mulation of the functions employed, merely stating that they were continuous and derivable. Cournot’s analysis of the demand function serves as a perfect illustration of his methodology. By making the demand of a good a continuous and derivable function with respect to its price, Cournot aimed to show that greater analytical rigour could be attained, without specifying the mathematical form of the function, which he thought was impossible to do.

2.