SFB 303 Discussion Paper No. A - 540
Author: John, Reinhard
Title: Abraham Wald's Equilibrium Existence Proof Reconsidered
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.
Keywords: Existence of Equilibrium, Pseudomonotonicity, Variational Inequality
Problem
JEL-Classification-Number: C62
Creation-Date: December 1996, revised:February 1997
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