A prominent French mathematician, Joseph Bertrand studied and taught at the École Polytéchnique in Paris. From 1862 to 1900, he held a chair at the prestigious Collège de France. He was also a member of the influential Académie des Sciences.

For philosophical reasons, Bertrand was generally opposed to the application
of mathematical reasoning to psychology, sensations, and other elusive
components of human behavior. As a result, he was very dismissive Léon Walras's
pretentious claim that economics was merely a branch of applied
mathematics. As he put it once to Walras, it was like "undertaking
the study of hydraulics with muddy liquids." In 1875, as a referee
for the *Revue des Deux Mondes*, Bertrand rejected a Walras paper (later
published in the *Giornale*) on this topic. In 1877, Walras sent Bertrand a
draft of his *Théorie mathématique de la richesse sociale*, but Bertrand
did not reply. In 1883, Bertrand finally decided to publish a review of
Walras's book in the *Journal des Savants*. Although negative in
general, Bertrand's review had some kind words for Walras. Bertrand
disputed the realism of the *t穰onnement* process and argued that
out-of-equilibrium exchange must be allowed and thus price indeterminacy.
He also disputed the utility-maximization hypothesis, arguing that merchants
were mainly interested in money profits, not utility.

In that same 1883 *Journal des Savant *article, Bertrand took the
opportunity to also review the long-neglected 1838 work of Augustin Cournot.
Here, Bertrand's assessment was damning. He argued that Cournot's work *deserved*
to be neglected because its algebraic argument was faulty and that, as a result,
Cournot had reached the wrong conclusions on questions like the incidence of tax
on monopoly price, the determinacy of duopoly price and the effects of free
trade.

On the constructive side, Bertrand (1883) "reworked" the Cournot duopoly model with prices, rather than quantities, as the strategic variables. In this case, Bertrand showed, prices will be driven immediately down to the perfectly competitive solution. Later on, F.Y. Edgeworth (1897) drew attention to the limitations of Bertrand's solution, in particular that he relied on firms having no capacity constraints and thus operating under constant marginal cost. In its stead, Edgeworth introduced capacity constraints and showed that the solution was indeterminate.

**Major works of Joseph L.F. Bertrand**

*Trait élémentaire d'alg鐫re*, 1851 - (1878 edition: vol. 1, vol. 2)*Traité de calcul différentiel et de calcul intégral*, Vol. 1, Vol. 2, 1864-70,*Rapport sur les progrès les plus récents de l'analyse mathématique*, 1867- "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", 1883,*Journal des Savants* *Thermodynamique*, 1887.*Leçons sur la théorie mathématique de l'électricit・/em>**, 1890**Eloges Academiques*, 1902

- Biography of Bertrand at MacTutor
- Bertrand Page at Gallica
- "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*

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