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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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    1. Donald J. Brown & Chris Shannon, 2000. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," Econometrica, Econometric Society, vol. 68(6), pages 1529-1540, November.
    2. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    3. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
    4. 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.
    5. Geanakoplos, John & Walsh, Kieran James, 2018. "Uniqueness and stability of equilibrium in economies with two goods," Journal of Economic Theory, Elsevier, vol. 174(C), pages 261-272.
    6. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    7. Alexis Akira Toda & Kieran James Walsh & Stijn Van Nieuwerburgh, 2020. "The Equity Premium and the One Percent [Stock return predictability: Is it there?]," The Review of Financial Studies, Society for Financial Studies, vol. 33(8), pages 3583-3623.
    8. Alexis Akira Toda & Kieran James Walsh, 2017. "Edgeworth box economies with multiple equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 65-80, April.
    9. John Chipman, 2010. "Multiple equilibrium under CES preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 129-145, October.
    10. Bhagwati, Jagdish N & Brecher, Richard A & Hatta, Tatsuo, 1983. "The Generalized Theory of Transfers and Welfare: Bilateral Transfers in a Multilateral World," American Economic Review, American Economic Association, vol. 73(4), pages 606-618, September.
    11. Chipman, John S. & Moore, James C., 1979. "On social welfare functions and the aggregation of preferences," Journal of Economic Theory, Elsevier, vol. 21(1), pages 111-139, August.
    12. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    13. Robert T. Jensen & Nolan H. Miller, 2008. "Giffen Behavior and Subsistence Consumption," American Economic Review, American Economic Association, vol. 98(4), pages 1553-1577, September.
    14. Felix Kubler & Larry Selden & Xiao Wei, 2013. "Inferior Good and Giffen Behavior for Investing and Borrowing," American Economic Review, American Economic Association, vol. 103(2), pages 1034-1053, April.
    15. Hens, Thorsten & Loeffler, Andras, 1995. "Gross substitution in financial markets," Economics Letters, Elsevier, vol. 49(1), pages 39-43, July.
    16. Giménez, Eduardo L., 2022. "Offer curves and uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 98(C).
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    Cited by:

    1. Alexis Akira Toda & Kieran James Walsh, 2024. "Recent Advances on Uniqueness of Competitive Equilibrium," Papers 2402.00998, arXiv.org.

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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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