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On the Existence of Price Equilibrium in Economies with Excess Demand Functions

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  • Tian, Guoqiang

Abstract

This paper provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous. We introduce a very weak notion of continuity, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semicontinuity. It is shown that the condition, together with Walras’s law, guarantees the existence of price equilibrium in economies with excess demand functions. The condition is also necessary, and thus our results generalize all the existing results on the existence of price equilibrium in economies where excess demand is a function.

Suggested Citation

  • Tian, Guoqiang, 2010. "On the Existence of Price Equilibrium in Economies with Excess Demand Functions," MPRA Paper 57930, University Library of Munich, Germany, revised Jul 2014.
  • Handle: RePEc:pra:mprapa:57930
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    References listed on IDEAS

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    Cited by:

    1. Bernard Cornet, 2020. "The Gale–Nikaido–Debreu lemma with discontinuous excess demand," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 169-180, October.
    2. Pascal Gourdel & Cuong Le Van & Ngoc-Sang Pham & Cuong Tran Viet, 2023. "Hartman-Stampacchia theorem, Gale-Nikaido-Debreu lemma, and Brouwer and Kakutani fixed-point theorems," Working Papers hal-04008394, HAL.

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    More about this item

    Keywords

    Existence of price equilibrium; recursive transfer lower semi-continuity; discontinuity; excess demand function;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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