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On uniqueness of equilibrium for complete markets with infinitely many goods and in finance models

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  • Elvio Accinelli

Abstract

Our concern in this paper is to obtain conditions for the uniqueness of equilibria, with, commodity bundles as consumption patterns which depend on the state of the world. In the first section we consider an economy with complete markets, where consumption spaces are a finite product of measurable function spaces, with separable and proper utility functions and with strictly positive endowments. Using the excess utility function the infinite dimensional problem stated above is reduced to a finite dimensional one. We obtain local uniqueness. The degree theory, and specially the Poincaré-Hopf theorem applied to this excess utility function, allow us to characterize the cardinality of the equilibrium set, and we find conditions for the global uniqueness of this set. On the other hand, we obtain conditions for the uniqueness in economies with incomplete markets and only one good available in each state of the world. When markets are incomplete, equilibrium allocations are typically not Pareto efficient;

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  • Elvio Accinelli, 1999. "On uniqueness of equilibrium for complete markets with infinitely many goods and in finance models," Estudios de Economia, University of Chile, Department of Economics, vol. 26(1 Year 19), pages 45-61, June.
  • Handle: RePEc:udc:esteco:v:26:y:1999:i:1:p:45-61
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    1. Mas-Colell, Andreu, 1991. "Indeterminacy in Incomplete Market Economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 45-61, January.
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    3. Mas-Colell, Andreu & Monteiro, Paulo K., 1996. "Self-fulfilling equilibria: An existence theorem for a general state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 51-62.
    4. Dana, Rose-Anne, 1993. "Existence, uniqueness and determinacy of Arrow-Debreu equilibria in finance models," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 563-579.
    5. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
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    1. Elvio Accinelli & Alfredo Piria & Martín Puchet, 2003. "Taste And Singular Economies," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 2(1), pages 35-48, Marzo 200.

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    Keywords

    Equilibrium; complete markets.;

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