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Constructing Pure-Exchange Economies with Many Equilibria

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Abstract

We develop a restart algorithm based on Scarf’s (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.

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  • Pascal Gauthier & Timothy J. Kehoe & Erwan Quintin, 2021. "Constructing Pure-Exchange Economies with Many Equilibria," Staff Report 631, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:93490
    DOI: 10.21034/sr.631
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    Cited by:

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    More about this item

    Keywords

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

    JEL classification:

    • 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
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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