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Constructing pure-exchange economies with many equilibria

Author

Listed:
  • Pascal Gauthier

    (Nordic Investment Bank)

  • Timothy J. Kehoe

    (University of Minnesota
    Federal Reserve Bank of Minneapolis
    National Bureau of Economic Research)

  • Erwan Quintin

    (University of Wisconsin–Madison)

Abstract

We develop a restart algorithm based on Scarf’s (The Computation of Economic Equilibria, Yale University Press, 1973) algorithm for computing approximate Brouwer fixed points. We use the algorithm to compute all of the equilibria of a general equilibrium pure-exchange model with four consumers, four goods, and 15 equilibria. The mathematical result that motivates the algorithm is a fixed-point index theorem that provides a sufficient condition for uniqueness of equilibrium and a necessary condition for multiplicity of equilibria. Examining the structure of the model with 15 equilibria provides us with a method for constructing higher dimensional models with even more equilibria. For example, using our method, we can construct a pure-exchange economy with eight consumers and eight goods that has (at least) 255 equilibria.

Suggested Citation

  • Pascal Gauthier & Timothy J. Kehoe & Erwan Quintin, 2022. "Constructing pure-exchange economies with many equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 541-564, April.
    • Handle: RePEc:spr:joecth:v:73:y:2022:i:2:d:10.1007_s00199-021-01406-0
    DOI: 10.1007/s00199-021-01406-0
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    References listed on IDEAS

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    1. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
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    Cited by:

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    2. Won, Dong Chul, 2023. "A new approach to the uniqueness of equilibrium with CRRA preferences," Journal of Economic Theory, Elsevier, vol. 208(C).

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    More about this item

    Keywords

    Uniqueness of equilibrium; Multiplicity of equilibrium; Computation of equilibrium;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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