研究ノート：一般均衡解の存在証明に係る分析ツールの概観

Abstract

In the Walras-Cassel type general equilibrium system, the coincidence of the number of equations and the number of unknown variables was regarded as the existence condition of the equilibrium solution. On the other hand, Wald, Schlesinger, von Neumann and others have investigated the mathematical conditions ensuring the existence of equilibrium solutions, especially focusing on a non-negative solution. Also, with the advent of Brauwer and Kakutaniʼs fixed point theorem, the discussions for the existence of competitive equilibrium solutions were brilliantly developed by applying topology. With the theme of general equilibrium analysis, this paper traces the historical lineage of theories surrounding the conditions for the existence of competitive equilibrium solutions, focusing mainly on the mathematical content of analytical tools, and attempts to give an overview of them.