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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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  2. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & William Zame, 1989. "Determinacy of Equilibrium in Large Square Economies," Levine's Working Paper Archive 46, David K. Levine.
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  4. Chichilnisky, G & Zhou, Y, 1996. "Smooth Infinite Economiesq," Discussion Papers 1996_30, Columbia University, Department of Economics.
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  8. 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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  11. Antoine Mandel, 2007. "An index formula for production economies with externalities," Documents de travail du Centre d'Economie de la Sorbonne b07026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
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  13. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Zame, William R., 1989. "Determinacy of equilibrium in large-scale economies," Journal of Mathematical Economics, Elsevier, vol. 18(3), pages 231-262, June.
  14. GIRAUD, Gaël, 2000. "An algebraic index theorem for non-smooth economies," CORE Discussion Papers 2000016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  17. Chris Shannon., 1996. "Determinacy of Competitive Equilibria in Economies with Many Commodities," Economics Working Papers 96-249, University of California at Berkeley.
  18. Covarrubias, Enrique, 2008. "Determinacy of equilibria of smooth infinite economies," MPRA Paper 9437, University Library of Munich, Germany.
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  22. Hervé Crès & Tobias Markeprand & Mich Tvede, 2009. "Incomplete Financial Markets and Jumps in Asset Prices," Discussion Papers 09-12, University of Copenhagen. Department of Economics.
  23. Jouini, Elyès, 1992. "An index theorem for nonconvex production economies," Economics Papers from University Paris Dauphine 123456789/5638, Paris Dauphine University.
  24. Anderson, Robert M. & Raimondo, Roberto C., 2007. "Incomplete markets with no Hart points," Theoretical Economics, Econometric Society, vol. 2(2), June.
  25. Mas-Colell, Andreu, 1991. "Indeterminacy in Incomplete Market Economies," Economic Theory, Springer, vol. 1(1), pages 45-61, January.
  26. Enrique Covarrubias, 2010. "Regular Infinite Economies," Working Papers 2010-03, Banco de México.
  27. 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.
  28. 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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Cited by:
  1. Enrique Covarrubias, 2010. "The Equilibrium Set of Economies with a Continuous Consumption Space," Working Papers 2010-10, Banco de México.

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