Excess Demand Functions, Equilibrium Prices, and Existence of Equilibrium

Abstract

For continuous excess demand functions, the existing literature (e.g. Sonnenschein [1972, 1973], Mantel [1974], Debreu [1974], Mas-Colell [1977], etc.) achieves a complete characterization only when the functions are defined on special subsets of positive prices. In this paper, we allow the functions to be defined on a larger class of price sets, (allowing, for example the closed unit simplex, including its boundary). Besides characterizing excess demands for a larger class of economies, it is also a useful tool for proving other results. It allows us to characterize the equilibrium price set for a larger class of economies. It also permits extending Uzawa's observation [1962] by showing that Brouwer's Fixed-Point Theorem is implied by the Arrow-Debreu Equilibrium Existence Theorem ([1954], Thm. I.).