Gradients,subgradients, and economic equilibria |
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| Authors: | Philippe Artzner Joseph M Ostroy |
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| Institution: | Institut de Recherche Mathématique Avancée, Université Louis Pasteur, Strasbourg, France;Department of Economics, University of California, Los Angeles, Los Angeles, California 90024 U.S.A. |
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| Abstract: | Two concepts of differentiability are shown to underlie two concepts of equilibrium for nonatomic economies. The weaker concept of subdifferentiability corresponds to Walrasian equilibrium and the stronger concept of Fréchet differentiability to product-exhaustion. Product-exhaustion is shown to be equivalent to a definition of economic equilibrium in terms of the rationality of price-taking. |
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