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Determinacy of equilibria of smooth infinite economies

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Author Info
Covarrubias, Enrique

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Abstract

This paper deals with generic determinacy of equilibria for infinite dimensional consumption spaces. Our work could be seen as an infinite-dimensional analogue of Dierker and Dierker (1972), by characterising equilibria of an economy as a zero of the aggregate excess demand, and studying its transversality. In this case, we can use extensions of the transversality density theorem. Assuming separable utilities, we give a new proof of generic determinacy of equilibria. We define regular price systems in this setting and show that an economy is regular if and only if its associated excess demand function only has regular equilibrium prices. We also define the infinite equilibrium manifold and show that it has the structure of a Banach manifold.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9437.

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Date of creation: 2008
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Handle: RePEc:pra:mprapa:9437

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Related research
Keywords: Determinacy; equilibria; infinite economies; Fredholm maps; equilibrium manifold; Banach manifolds;

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Find related papers by JEL classification:
D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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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. 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. [Downloadable!] (restricted)
  2. Chris Shannon, 1996. "Determinacy of Competitive Equilibria in Economies with Many Commodities," GE, Growth, Math methods 9610002, EconWPA. [Downloadable!]
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  3. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January. [Downloadable!] (restricted)
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  4. Balasko, Yves, 1997. "The natural projection approach to the infinite-horizon model," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 251-263, April. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
  6. 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. [Downloadable!] (restricted)
  7. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March. [Downloadable!] (restricted)
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  1. Covarrubias, Enrique, 2008. "The number of equilibria of smooth infinite economies with separable utilities," MPRA Paper 11099, University Library of Munich, Germany. [Downloadable!]
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