Excess demand functions, equilibrium prices, and existence of equilibrium

Kam-Chau Wong
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Kam-Chau Wong: Department of Economics, Chinese University of Hong Kong, Shatin, HONG KONG

Economic Theory, 1997, vol. 10, issue 1, 39-54

Abstract: For continuous aggregate excess demand functions of economies, 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, our extension provides 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, Theorem I).

JEL-codes: D11 D50 D51 (search for similar items in EconPapers)
Date: 1997
Note: Received: October 18, 1995; revised version June 28, 1996
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