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Global invertibility of excess demand functions

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  • Covarrubias, Enrique

Abstract

In this paper we provide necessary and sufficient conditions for the excess demand function of a pure exchange economy to be globally invertible so that there is a unique equilibrium. Indeed, we show that an excess demand function is globally invertible if and only if its Jacobian never vanishes and it is a proper map. Our result includes as special cases many partial results found in the literature that imply global uniqueness including Gale-Nikaido conditions and properties related to stability of equilibria. Furthermore, by showing that the condition is necessary, we are implicitly finding the weakest possible condition.

Suggested Citation

  • Covarrubias, Enrique, 2013. "Global invertibility of excess demand functions," MPRA Paper 47300, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:47300
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    References listed on IDEAS

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    1. Debreu, Gerard, 1984. "Economic Theory in the Mathematical Mode," American Economic Review, American Economic Association, vol. 74(3), pages 267-278, June.
    2. Wagstaff, Peter, 1975. "A Uniqueness Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 521-524, June.
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    9. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
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    More about this item

    Keywords

    Uniqueness Equilibrium;

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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