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Quadratic Concavity and Determinacy of Equilibrium

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Chris Shannon and William R. Zame.

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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.

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Paper provided by University of California at Berkeley in its series Economics Working Papers with number E99-271.

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Date of creation: 01 Dec 1999
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Handle: RePEc:ucb:calbwp:e99-271

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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. Covarrubias, Enrique, 2008. "Determinacy of equilibria of smooth infinite economies," MPRA Paper 9437, University Library of Munich, Germany. [Downloadable!]
  2. Frank Riedel, 2002. "Generic Determinacy of Equilibria with Local Substitution," Department of Economics, Working Paper Series 1044, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
    Other versions:
  3. V. Filipe Martins-da-Rocha & Frank Riedel, 2008. "On equilibrium prices in continuous time," Working Papers 397, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
    Other versions:
  4. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Levine's Bibliography 122247000000002225, UCLA Department of Economics. [Downloadable!]
  5. Covarrubias, Enrique, 2008. "The number of equilibria of smooth infinite economies with separable utilities," MPRA Paper 11099, University Library of Munich, Germany. [Downloadable!]
  6. Herrendorf, Berthold & Valentinyi, Akos, 2002. "On the Stability of the Two-Sector Neoclassical Growth Model with Externalities," CEPR Discussion Papers 3435, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  7. Enrique Covarrubias, 2007. "Regular Infinite Economies," Levine's Working Paper Archive 843644000000000034, David K. Levine. [Downloadable!]
  8. 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!]
  9. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation, Yale University. [Downloadable!]
  10. Donald J. Brown & Ravi Kannan, 2003. "Indeterminacy, Nonparametric Calibration and Counterfactual Equilibria," Cowles Foundation Discussion Papers 1426, Cowles Foundation, Yale University. [Downloadable!]
  11. Berthold Herrendorf & Akos Valentinyi, 2002. "Neoclassical Growth Model with Externalities," IEHAS Discussion Papers 0203, Institute of Economics, Hungarian Academy of Sciences. [Downloadable!]
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