Economic Equilibrium

Abstract

The three problems of the theory of economic equilibrium with which these four lectures are concerned are 1) the existence of an equilibrium, 2) the connection between an equilibrium and a Pareto optimum, 3) the connection between the set of equilibria and the core. For each one of these problems, a prototype solution will be presented. Initially the simple case of a finite number of commodities and of a finite number of agents will be treated. Extensions to infinite-dimensional commodity spaces and to measure spaces of agents will then be made. The latter of these extensions, which was called for by the solution of the third problem, has established an important link between the theory of economic equilibrium and the theory of optimal control in the use that they both make of the mathematical theory of integration of correspondences. By a correspondence from a set E to a set F is meant here a function from E to the set of nonempty subsets of F.