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A new approach to the uniqueness of equilibrium with CRRA preferences

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  • Won, Dong Chul

Abstract

This paper investigates the uniqueness of equilibrium in the economy where agents have preferences with possibly distinct levels of relative risk aversion. Equilibrium prices exist in a price range determined by micro and macroeconomic information. Macroeconomic information is inferred from two representative-agent economies, which provide lower and upper bounds on aggregate demand, respectively. Analysis of the first and second-order price effects shows that individual demand has a unique inflection point at which the income effect maximally dominates the substitution effect. In contrast, aggregate demand may have multiple inflection points, which creates multiple equilibria. Sufficient conditions for the uniqueness of equilibrium are characterized by the local behavior of individual demand at the inflection point. They require that aggregate demand must have no more than two inflection points in the equilibrium price range. The result of this paper sheds light on the Sonnenschein-Mantel-Debreu theory that has negative implications for the uniqueness of equilibrium.

Suggested Citation

  • Won, Dong Chul, 2023. "A new approach to the uniqueness of equilibrium with CRRA preferences," Journal of Economic Theory, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:jetheo:v:208:y:2023:i:c:s0022053123000030
    DOI: 10.1016/j.jet.2023.105607
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    References listed on IDEAS

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    1. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).

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    More about this item

    Keywords

    Unique equilibrium; Constant relative risk aversion; Higher-order price effect; Quasi-convex demand; Law of demand;
    All these keywords.

    JEL classification:

    • 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
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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