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Robustness of the Uniqueness of Walrasian Equilibrium with Cobb-Douglas Utilities

Author

Listed:
  • David Cass

    () (Department of Economics, University of Pennsylvania)

  • Abhinash Borah

    () (Department of Economics, University of Pennsylvania)

  • Kyungmin Kim

    () (Department of Economics, University of Pennsylvania)

  • Maxym Kryshko

    () (Department of Economics, University of Pennsylvania)

  • Antonio Penta

    () (Department of Economics, University of Pennsylvania)

  • Jonathan Pogach

    () (Department of Economics, University of Pennsylvania)

Abstract

The majority of results in the literature on general equilibrium are not for an economy (i.e. given an endowment and preferences), but rather, for a set of economies (i.e. a set of endowments given preferences). Therefore, we argue that the most appropriate robustness result requires perturbing economies uniformly over the space of endowments for which the result is obtained. In this paper, we examine the robustness of the uniqueness of Walrasian endowment economies with Cobb-Douglas utility functions under this interpretation of robustness. Namely, we prove that for economies described by Cobb-Douglas utilities and all endowments in a fixed set, uniqueness of equilibrium is robust to perturbations of the utility functions.

Suggested Citation

  • David Cass & Abhinash Borah & Kyungmin Kim & Maxym Kryshko & Antonio Penta & Jonathan Pogach, 2009. "Robustness of the Uniqueness of Walrasian Equilibrium with Cobb-Douglas Utilities," PIER Working Paper Archive 09-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:09-038
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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/09-038.pdf
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    References listed on IDEAS

    as
    1. Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
    2. Balasko, Yves, 1975. "Some results on uniqueness and on stability of equilibrium in general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 95-118.
    3. Allen, Beth, 1981. "Utility perturbations and the equilibrium price set," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 277-307, October.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Walrasian Equilibrium; Uniqueness; Robustness;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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