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Abraham Wald's equilibrium existence proof reconsidered

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Author Info
Reinhard John () (Wirtschaftstheoretische Abteilung II, UniversitÄt Bonn, Adenauerallee 24-42, D-53113 Bonn, GERMANY)
Abstract

For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption.

In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution.

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Publisher Info
Article provided by Springer in its journal Economic Theory.

Volume (Year): 13 (1999)
Issue (Month): 2 ()
Pages: 417-428
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Handle: RePEc:spr:joecth:v:13:y:1999:i:2:p:417-428

Note: Received: July 22, 1997; revised version: December 11, 1997
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Related research
Keywords: Abraham Wald · Existence of equilibrium · Pseudomonotonicity · Variational inequality problem.

Find related papers by JEL classification:
B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium

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  1. John K.-H. Quah, 2004. "The existence of equilibrium when excess demand obeys the weak axiom," Economics Papers 2004-W07, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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