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Uniqueness and stability of equilibrium in economies with two goods

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  • Geanakoplos, John
  • Walsh, Kieran James

Abstract

We offer new sufficient conditions ensuring demand is downward sloping local to equilibrium. It follows that equilibrium is unique and stable in the sense that rising supply implies falling prices. In our setting, there are two goods, which we interpret as consumption in different time periods, and many impatience types. Agents have the same Bernoulli utility function, but the types differ arbitrarily in time preference. Our main result is that if endowments are identical and utility displays nonincreasing absolute risk aversion, then market demand is strictly downward sloping local to equilibrium. We discuss implications for the literature surrounding Diamond and Dybvig (1983).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:174:y:2018:i:c:p:261-272
    DOI: 10.1016/j.jet.2017.12.005
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    References listed on IDEAS

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    1. Havranek, Tomas & Horvath, Roman & Irsova, Zuzana & Rusnak, Marek, 2015. "Cross-country heterogeneity in intertemporal substitution," Journal of International Economics, Elsevier, vol. 96(1), pages 100-118.
    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. Emmanuel Farhi & Mikhail Golosov & Aleh Tsyvinski, 2009. "A Theory of Liquidity and Regulation of Financial Intermediation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 973-992.
    4. 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.
    5. John Geanakoplos & Kieran James Walsh, 2017. "Inefficient Liquidity Provision," Cowles Foundation Discussion Papers 2077, Cowles Foundation for Research in Economics, Yale University.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    7. Pierre Yared, 2013. "Public Debt Under Limited Private Credit," Journal of the European Economic Association, European Economic Association, vol. 11(2), pages 229-245, April.
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    Cited by:

    1. Bar Light, 2019. "General equilibrium in a heterogeneous-agent incomplete-market economy with many consumption goods and a risk-free bond," Papers 1906.06810, arXiv.org, revised Mar 2021.
    2. Giménez, Eduardo L., 2022. "Offer curves and uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    3. Won, Dong Chul, 2023. "A new approach to the uniqueness of equilibrium with CRRA preferences," Journal of Economic Theory, Elsevier, vol. 208(C).
    4. Andrea Loi & Stefano Matta, 2023. "Endowments, patience types, and uniqueness in two-good HARA utility economies," Papers 2308.09347, arXiv.org.
    5. Andrea Loi & Stefano Matta, 2021. "Risk aversion and uniqueness of equilibrium: a polynomial approach," Papers 2107.01947, arXiv.org, revised Oct 2021.
    6. Bar Light, 2020. "Uniqueness of equilibrium in a Bewley–Aiyagari model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 435-450, March.

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    More about this item

    Keywords

    Uniqueness of equilibrium; Absolute risk aversion; Excess demand functions; Stability of equilibrium; Diamond–Dybvig models;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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