Walras et le tâtonnement: Gauss-Seidel ou... Lagrange ?

Emeric Lendjel ()
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Emeric Lendjel: Centre d'études interdisciplinaires Walras-Pareto - UNIL - Université de Lausanne = University of Lausanne

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Abstract: This paper attempts to fill a gap in the walrasian historiography. Many scholars accord with the mathematical character of Walras' tâtonnement, but without attributing to it a precise mathematical form. Thus, this article shows that Walras did use of the Lagrange's method which he identified with his tâtonnement. This is an iterative method of resolution of equation which was widely known at the beginning of the nineteenth century. Thanks to this method, Walras demonstrates that mechanism of competition leads "in practice", by tâtonnements, to the same equilibrium solution as the one established by the theoretician when solving the system of equations. Then this interpretation is corroborated by the fact that Cournot did use the same method when dealing with the monopolistic situation. Finally, several arguments are put forth in order to disprove Uzawa's alternate hypothesis : namely, Walras' use of the Gauss-Seidel method.

Keywords: iteratives methods; Lagrange's method; Gauss-Seidel's method; Walras; tâtonnement; méthodes itératives; méthode de Lagrange; méthode de Gauss-Seidel (search for similar items in EconPapers)
Date: 2001-12
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00515345
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Published in Œconomia - History/Methodology/Philosophy, 2001, série PE (35), pp.1627-1655

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00515345

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