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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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  1. 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.
  2. Chichilnisky, G. & Zhou, Y., 1996. "Smooth Infinite Economies," Discussion Papers 1996_14, Columbia University, Department of Economics.
  3. repec:fth:coluec:9596-17 is not listed on IDEAS
  4. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  5. Yves Balasko, 1995. "Equilibrium Analysis of the Infinite Horizon Model with Smooth Discounted Utility Functions," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 95.04, Institut d'Economie et Econométrie, Université de Genève.
  6. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
  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.
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