Differentiability of Equilibria for Linear Exchange Economies

Jean-Marc Bonnisseau, Michael Florig () and Alejandro Jofré
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Michael Florig: CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Alejandro Jofré: CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago] - UCHILE - Universidad de Chile = University of Chile [Santiago] - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: The purpose of this paper is to study the differentiability properties of equilibrium prices and allocations in a linear exchange economy when the initial endowments and utility vectors vary. We characterize an open dense subset of full measure of the initial endowment and utility vector space on which the equilibrium price vector is a real analytic function, hence infinitely differentiable function. We provide an explicit formula to compute the equilibrium price and allocation around a point where it is known. We also show that the equilibrium price is a locally Lipschitzian mapping on the whole space. Finally, using the notion of the Clarke generalized gradient, we prove that linear exchange economies satisfy a property of gross substitution.

Keywords: general equilibrium; linear utility functions; equilibrium manifold; sensitivity analysis (search for similar items in EconPapers)
Date: 2001
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Published in Journal of Optimization Theory and Applications, 2001, 109 (2), pp.265-288. ⟨10.1023/A:1017558204399⟩

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Related works:
Journal Article: Differentiability of Equilibria for Linear Exchange Economies (2001)
Working Paper: Differentiability of Equilibria for Linear Exchange Economies (2001)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00265685

DOI: 10.1023/A:1017558204399

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