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The Equilibrium Set of Economies with a Continuous Consumption Space

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  • Enrique Covarrubias

Abstract

We study global properties of the equilibrium set of economies with a continuous consumption space. This framework is important in intertemporal allocation problems (continuous or infinite time), financial markets with uncertainty (continuous states of nature) and commodity differentiation. We show that the equilibrium set is contractible which implies that (i) there is a continuous economic policy linking any two equilibrium states, and (ii) any two such economic policies can be continuously deformed one into the other. We also give three equivalent formulations of the problem of global uniqueness of equilibria in terms of the projection map from the equilibrium set to the space of parameters. We finally study the local and global effects that the existence of critical economies has on the equilibrium set.

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File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7B82090083-8040-261A-F80B-584AE25191BA%7D.pdf
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Bibliographic Info

Paper provided by Banco de México in its series Working Papers with number 2010-10.

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Date of creation: Jul 2010
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Handle: RePEc:bdm:wpaper:2010-10

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Keywords: General equilibrium; infinite economies; intertemporal choice; uncertainty.;

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  1. 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.
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  3. Enrique Covarrubias, 2010. "Regular Infinite Economies," Working Papers 2010-03, Banco de México.
  4. 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.
  5. 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.
  6. Covarrubias, Enrique, 2008. "The number of equilibria of smooth infinite economies with separable utilities," MPRA Paper 11099, University Library of Munich, Germany.
  7. Balasko, Yves, 1997. "The natural projection approach to the infinite-horizon model," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 251-263, April.
  8. Covarrubias, Enrique, 2008. "Determinacy of equilibria of smooth infinite economies," MPRA Paper 9437, University Library of Munich, Germany.
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Cited by:
  1. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.

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