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Quadratic Concavity and Determinacy of Equilibrium

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  • Chris Shannon

    () (Dept. of Economics, 549 Evans Hall, University of California, Berkeley, Berkeley, CA 94720, U.S.A.)

  • William R. Zame

    () (Dept. of Economics, Bunche Hall, UCLA, 405 Hilgard Ave., Los Angeles, CA 90095, U.S.A.)

Abstract

One of the central features of classical models of competitive markets is the generic determinacy of competitive equilibria. For smooth economies with a finite number of commodities and a finite number of consumers, almost all initial endowments admit only a finite number of competitive equilibria, and these equilibria vary (locally) smoothly with endowments; thus equilibrium comparative statics are locally determinate. This paper establishes parallel results for economies with finitely many consumers and infinitely many commodities. The most important new condition we introduce, quadratic concavity, rules out preferences in which goods are perfect substitutes globally, locally, or asymptotically. Our framework is sufficiently general to encompass many of the models that have proved important in the study of continuous-time trading in financial markets, trading over an infinite time horizon, and trading of finely differentiated commodities. Copyright The Econometric Society 2002.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 70 (2002)
Issue (Month): 2 (March)
Pages: 631-662
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Handle: RePEc:ecm:emetrp:v:70:y:2002:i:2:p:631-662

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References

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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. Robert M. Anderson & William R. Zame, 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, Berkeley Electronic Press, vol. 0(1), pages 1.
  3. Chichilnisky, G. & Zhou, Y., 1996. "Smooth Infinite Economies," Discussion Papers 1996_14, Columbia University, Department of Economics.
  4. 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.
  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. 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.
  7. repec:fth:coluec:9596-17 is not listed on IDEAS
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Citations

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Cited by:
  1. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
  2. repec:cdl:econwp:1244 is not listed on IDEAS
  3. Covarrubias, Enrique, 2008. "The number of equilibria of smooth infinite economies with separable utilities," MPRA Paper 11099, University Library of Munich, Germany.
  4. Riedel, Frank, 2002. "Generic Determinacy of Equilibria with Local Substitution," Department of Economics, Working Paper Series qt1727r74c, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  5. Enrique Covarrubias, 2007. "Regular Infinite Economies," Levine's Working Paper Archive 843644000000000034, David K. Levine.
  6. Enrique Covarrubias, 2011. "The Number of Equilibria of Smooth Infinite Economies," Working Papers 2011-02, Banco de México.
  7. H. Polemarchakis & S. Demichelis, 2002. "Frequency of Trade and the Determinancy of Equilibrium Paths: Logarithmic Economies of Overlapping Generations Under Certainty," Working Papers 2002-16, Brown University, Department of Economics.
  8. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation for Research in Economics, Yale University.
  9. DEMICHELIS, Stefano & POLEMARCHAKIS, Heracles & ,, 2000. "Life-span and the determinacy of equilibrium in economies of overlapping generations," CORE Discussion Papers 2000034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Herrendorf, Berthold & Valentinyi, Akos, 2006. "On the stability of the two-sector neoclassical growth model with externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1339-1361, August.
  11. Frank Riedel, 2003. "Generic Determinacy of Equilibria with Local Substitution," GE, Growth, Math methods 0303001, EconWPA.
  12. Berthold Herrendorf & Akos Valentinyi, 2002. "Neoclassical Growth Model with Externalities," IEHAS Discussion Papers 0203, Institute of Economics, Hungarian Academy of Sciences.
  13. Covarrubias, Enrique, 2008. "Determinacy of equilibria of smooth infinite economies," MPRA Paper 9437, University Library of Munich, Germany.
  14. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Levine's Working Paper Archive 122247000000002225, David K. Levine.
  15. Eric Bond & Kazumichi Iwasa & Kazuo Nishimura, 2011. "A dynamic two country Heckscher–Ohlin model with non-homothetic preferences," Economic Theory, Springer, vol. 48(1), pages 171-204, September.
  16. Donald J. Brown & Ravi Kannan, 2003. "Indeterminacy, Nonparametric Calibration and Counterfactual Equilibria," Cowles Foundation Discussion Papers 1426, Cowles Foundation for Research in Economics, Yale University.

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