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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

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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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Publisher Info
Article provided by University of Chile, Department of Economics in its journal Estudios de Economia.

Volume (Year): 26 (1999)
Issue (Month): 1 Year 1999 (June)
Pages: 45-61
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Handle: RePEc:udc:esteco:v:26:y:1999:i:1:p:45-61

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Keywords: Equilibrium; complete markets.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Mas-Colell, Andreu, 1991. "Indeterminacy in Incomplete Market Economies," Economic Theory, Springer, vol. 1(1), pages 45-61, January.
  3. Kehoe, Timothy J., 1991. "Computation and multiplicity of equilibria," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 38, pages 2049-2144 Elsevier. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  6. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Elvio Accinelli & Alfredo Piria & Martín Puchet, 2001. "Tastes and Singular Economies," Documentos de Trabajo (working papers) 1301, Department of Economics - dECON. [Downloadable!]
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