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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 stability 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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Web page: http://www.elsevier.com/locate/jmateco

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

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Cited by:
  1. Covarrubias, Enrique, 2011. "The equilibrium set of economies with a continuous consumption space," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 137-142, March.
  2. Chichilnisky, Graciela, 2009. "Avoiding extinction: equal treatment of the present and the future," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 3(32), pages 1-25.
  3. Elvio Accinelli & Martín Puchet, 2001. "A characterization of Walrasian economies of infinity dimension," Documentos de Trabajo (working papers) 0701, Department of Economics - dECON.
  4. Enrique Covarrubias, 2007. "Regular Infinite Economies," Levine's Working Paper Archive 843644000000000034, David K. Levine.
  5. Chris Shannon and William R. Zame., 1999. "Quadratic Concavity and Determinacy of Equilibrium," Economics Working Papers E99-271, University of California at Berkeley.
  6. Chichilnisky, G., 1996. "Topology and Invertible Maps," Discussion Papers 1996_15, Columbia University, Department of Economics.
  7. 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.
  8. Elvio Accinelli, 2007. "Structural stability, Morse's lemma and singular economies," Documentos de Trabajo (working papers) 0607, Department of Economics - dECON.
  9. Chris Shannon & William R. Zame, 1999. "Quadratic Concavity and the Determinancy of Equilibrium," UCLA Economics Working Papers 791, UCLA Department of Economics.
  10. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.
  11. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
  12. Accinelli, Elvio, 2013. "The equilibrium set of infinite dimensional Walrasian economies and the natural projection," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 435-440.

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