Joseph Louis François Bertrand(1822 … - 經濟

※ [本文轉錄自 Math 看板]

作者: fizeau (.) 看板: Math
標題: [名人] Joseph Louis François Bertrand(1822-1900)
時間: Tue Apr 29 21:39:52 2008

http://cepa.newschool.edu/het/profiles/bertrand.htm

A prominent French mathematician, Joseph Bertrand studied and taught at the É
cole 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 Acadé
mie 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 of 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 Thé
orie 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 tâ
tonnement 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 determinancy 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.




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