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Regular Infinite Economies

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  • Enrique Covarrubias

Abstract

The main contribution of this paper is to place smooth infinite economies in the setting of the equilibrium manifold and the natural projection map à la Balasko. We show that smooth infinite economies have an equilibrium set that has the structure of a Banach manifold and that the natural projection map is smooth. We define regular and critical economies, and regular and critical prices, and we show that the set of regular economies coincides with the set of economies whose excess demand function has only regular prices. Generic determinacy of equilibria follows as a by-product.

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File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7BA37473DF-33D5-931D-8227-69C026162C03%7D.pdf
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Bibliographic Info

Paper provided by Banco de México in its series Working Papers with number 2010-03.

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Date of creation: Mar 2010
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Handle: RePEc:bdm:wpaper:2010-03

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Web page: http://www.banxico.org.mx
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Keywords: General equilibrium; Infinite economies; Intertemporal choice; Uncertainty.;

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References

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  1. Elvio Accinelli, 2003. "About manifolds and determinacy in general equilibrium theory," Estudios de Economia, University of Chile, Department of Economics, vol. 30(2 Year 20), pages 169-177, December.
  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.
  3. Chris Shannon & William R. Zame, 2000. "Quadratic Concavity and Determinacy of Equilibrium," GE, Growth, Math methods 9912001, EconWPA.
  4. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September.
  5. Araujo, A., 1988. "The non-existence of smooth demand in general banach spaces," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 309-319, September.
  6. Balasko, Yves, 1997. "The natural projection approach to the infinite-horizon model," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 251-263, April.
  7. 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.
  8. Mas-Colell, Andreu, 1991. "Indeterminacy in Incomplete Market Economies," Economic Theory, Springer, vol. 1(1), pages 45-61, January.
  9. Chris Shannon, 1996. "Determinacy of Competitive Equilibria in Economies with Many Commodities," GE, Growth, Math methods 9610002, EconWPA.
  10. 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.
  11. 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.
  12. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
  13. Balasko, Yves, 1997. "Equilibrium analysis of the infinite horizon model with smooth discounted utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 783-829, May.
  14. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-81, September.
  15. Dierker, Egbert, 1993. "Regular economies," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 17, pages 795-830 Elsevier.
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Cited by:
  1. Enrique Covarrubias, 2011. "The Number of Equilibria of Smooth Infinite Economies," Working Papers 2011-02, Banco de México.
  2. Enrique Covarrubias, 2010. "The Equilibrium Set of Economies with a Continuous Consumption Space," Working Papers 2010-10, Banco de México.
  3. 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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