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Excess demand functions, equilibrium prices, and existence of equilibrium

Author

Listed:
  • Kam-Chau Wong

    (Department of Economics, Chinese University of Hong Kong, Shatin, HONG KONG)

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).

Suggested Citation

  • Kam-Chau Wong, 1997. "Excess demand functions, equilibrium prices, and existence of equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 39-54.
    • Handle: RePEc:spr:joecth:v:10:y:1997:i:1:p:39-54
    Note: Received: October 18, 1995; revised version June 28, 1996
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    Cited by:

    1. Guoqiang Tian, 2016. "On the existence of price equilibrium in economies with excess demand functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 5-16, April.
    2. Maćkowiak, Piotr, 2011. "Some Equivalents of Brouwer's Fixed Point Theorem and the Existence of Economic Equilibrium," MPRA Paper 42461, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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