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The Number of Equilibria of Smooth Infinite Economies

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  • Enrique Covarrubias

Abstract

We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.

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File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7B14EE8887-387E-251D-7F06-0A9631F55808%7D.pdf
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Bibliographic Info

Paper provided by Banco de México in its series Working Papers with number 2011-02.

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Date of creation: May 2011
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Handle: RePEc:bdm:wpaper:2011-02

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Web page: http://www.banxico.org.mx
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Keywords: Uniqueness; determinacy; equilibria; infinite economy; Fredholm map; equilibrium manifold; index theorem; Z-Rothe vector field.;

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References

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  1. GIRAUD, Gaël, 2000. "An algebraic index theorem for non-smooth economies," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2000016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  21. Hervés-Beloso, C. & Monteiro, P.K., 2010. "Strictly monotonic preferences on continuum of goods commodity spaces," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 725-727, September.
  22. Kehoe, Timothy J, 1983. "Regularity and Index Theory for Economies with Smooth Production Technologies," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 895-917, July.
  23. Hervés-Beloso, Carlos & Monteiro, Paulo Klinger, 2009. "Existence, continuity and utility representation of strictly monotonic preferences on continuum of goods commodity spaces," MPRA Paper 15157, University Library of Munich, Germany.
  24. Mas-Colell, Andreu, 1991. "Indeterminacy in Incomplete Market Economies," Economic Theory, Springer, Springer, vol. 1(1), pages 45-61, January.
  25. Momi, Takeshi, 2003. "The index theorem for a GEI economy when the degree of incompleteness is even," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 273-297, June.
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Cited by:
  1. Covarrubias, Enrique, 2011. "The equilibrium set of economies with a continuous consumption space," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 137-142, March.

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