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- Title
Research note: An Overview of Analytical Tools for Proving the Existence of General Equilibrium Solutions.
- 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 Kakutani's 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.
- Subjects
FIXED point theory; LEAST fixed point (Mathematics); TOPOLOGY; WALRAS, Leon, 1834-1910; CASSEL, Gustav, 1866-1945
- Publication
Fukuoka Jo Gakuin University Bulletin. Faculty of International Career Development, 2023, Vol 9, p55
- ISSN
2189-3942
- Publication type
Article