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Quadratic Concavity and Determinacy of Equilibrium

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Author Info
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.)

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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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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. 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. [Downloadable!] (restricted)
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  2. Robert Anderson & William Zame, 2001. "Genericity with Infinitely Many Parameters," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 1(advances/), pages 1003-1003. [Downloadable!] (restricted)
  3. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May. [Downloadable!] (restricted)
  4. 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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  5. 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)
  6. repec:fth:coluec:9596-17 is not listed on IDEAS
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  1. Enrique Covarrubias, 2007. "Regular Infinite Economies," Levine's Working Paper Archive 843644000000000034, UCLA Department of Economics. [Downloadable!]
  2. 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. [Downloadable!]
  3. Frank Riedel, 2003. "Generic Determinacy of Equilibria with Local Substitution," GE, Growth, Math methods 0303001, EconWPA. [Downloadable!]
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  4. Berthold Herrendorf & Akos Valentinyi, . "On the Stability of the Two-Sector Neoclassical Growth Model with Externalities," Working Papers 2167721, Department of Economics, W. P. Carey School of Business, Arizona State University. [Downloadable!]
    Other versions:
  5. Donald J. Brown & Ravi Kannan, 2003. "Indeterminacy, Nonparametric Calibration and Counterfactual Equilibria," Cowles Foundation Discussion Papers 1426, Cowles Foundation, Yale University. [Downloadable!]
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