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Smooth infinite economies

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  • Chichilnisky, Graciela
  • Zhou, Yuqing

Abstract

Equilibrium conditions in smooth infinite economies with separable utilities are described by Fredholm maps, which are Frechet differentiable. Therefore, Smale's extension of Sard's theorem can be used to studying infinite economies. We study structural and local uniqueness of equilibrium in smooth infinite economies and relate the theory of markets to modern Fredholm theory.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 29 (1998)
Issue (Month): 1 (January)
Pages: 27-42

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Handle: RePEc:eee:mateco:v:29:y:1998:i:1:p:27-42

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  1. Chris Shannon., 1994. "Determinacy in Infinite Horizon Exchange Economies," Economics Working Papers, University of California at Berkeley 94-233, University of California at Berkeley.
  2. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 21(6), pages 577-606.
  3. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(3), pages 514-540, June.
  4. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
  5. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 353-94, March.
  6. 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.
  7. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 38(3), pages 387-92, May.
  8. Huang, Chi-fu, 1987. "An Intertemporal General Equilibrium Asset Pricing Model: The Case of Diffusion Information," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 117-42, January.
  9. Duffie, J Darrell & Huang, Chi-fu, 1985. "Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-lived Securities," Econometrica, Econometric Society, Econometric Society, vol. 53(6), pages 1337-56, November.
  10. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
  11. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
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Citations

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Cited by:
  1. Elvio Accinelli, 2007. "Structural stability, Morse's lemma and singular economies," Documentos de Trabajo (working papers), Department of Economics - dECON 0607, Department of Economics - dECON.
  2. Chichilnisky, Graciela, 2009. "Avoiding Extinction: Equal Treatment of the Present and the Future," Economics Discussion Papers, Kiel Institute for the World Economy 2009-8, Kiel Institute for the World Economy.
  3. Covarrubias, Enrique, 2008. "The number of equilibria of smooth infinite economies with separable utilities," MPRA Paper 11099, University Library of Munich, Germany.
  4. Elvio Accinelli & Martín Puchet, 2001. "A characterization of Walrasian economies of infinity dimension," Documentos de Trabajo (working papers), Department of Economics - dECON 0701, Department of Economics - dECON.
  5. Enrique Covarrubias, 2010. "Regular Infinite Economies," Working Papers, Banco de México 2010-03, Banco de México.
  6. Accinelli, Elvio, 2013. "The equilibrium set of infinite dimensional Walrasian economies and the natural projection," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 49(6), pages 435-440.
  7. Chris Shannon and William R. Zame., 1999. "Quadratic Concavity and Determinacy of Equilibrium," Economics Working Papers, University of California at Berkeley E99-271, University of California at Berkeley.
  8. Enrique Covarrubias, 2010. "The Equilibrium Set of Economies with a Continuous Consumption Space," Working Papers, Banco de México 2010-10, Banco de México.
  9. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.
  10. Chichilnisky, G., 1996. "Topology and Invertible Maps," Discussion Papers, Columbia University, Department of Economics 1996_15, Columbia University, Department of Economics.
  11. Hervé Crès & Tobias Markeprand & Mich Tvede, 2009. "Incomplete Financial Markets and Jumps in Asset Prices," Discussion Papers, University of Copenhagen. Department of Economics 09-12, University of Copenhagen. Department of Economics.
  12. Covarrubias, Enrique, 2008. "Determinacy of equilibria of smooth infinite economies," MPRA Paper 9437, University Library of Munich, Germany.
  13. Chris Shannon & William R. Zame, 1999. "Quadratic Concavity and the Determinancy of Equilibrium," UCLA Economics Working Papers, UCLA Department of Economics 791, UCLA Department of Economics.

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