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Competitive equilibria in semi-algebraic economies

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  • Kubler, Felix
  • Schmedders, Karl

Abstract

This paper develops a method to compute the equilibrium correspondence for exchange economies with semi-algebraic preferences. Given a class of semi-algebraic exchange economies parameterized by individual endowments and possibly other exogenous variables such as preference parameters or asset payoffs, there exists a semi-algebraic correspondence that maps parameters to positive numbers such that for generic parameters each competitive equilibrium can be associated with an element of the correspondence and each endogenous variable (i.e. prices and consumptions) is a rational function of that value of the correspondence and the parameters. This correspondence can be characterized as zeros of a univariate polynomial equation that satisfy additional polynomial inequalities. This polynomial as well as the rational functions that determine equilibrium can be computed using versions of Buchberger's algorithm which is part of most computer algebra systems. The computation is exact whenever the input data (i.e. preference parameters etc.) are rational. Therefore, the result provides theoretical foundations for a systematic analysis of multiplicity in applied general equilibrium.

Suggested Citation

  • Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:301-330
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    Cited by:

    1. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    2. Michal Fabinger & E. Glen Weyl, 2018. "Functional Forms for Tractable Economic Models and the Cost Structure of International Trade," CIRJE F-Series CIRJE-F-1092, CIRJE, Faculty of Economics, University of Tokyo.
    3. Arias-R., Omar Fdo., 2014. "A condition for determinacy of optimal strategies in zero-sum convex polynomial games," MPRA Paper 57099, University Library of Munich, Germany.
    4. Michal Fabinger & E. Glen Weyl, 2016. "The Average-Marginal Relationship and Tractable Equilibrium Forms," CIRJE F-Series CIRJE-F-1028, CIRJE, Faculty of Economics, University of Tokyo.
    5. E. Weyl & Michal Fabinger, 2015. "A Tractable Approach to Pass-Through Patterns," 2015 Meeting Papers 747, Society for Economic Dynamics.
    6. Felix Kubler & Karl Schmedders, 2010. "Tackling Multiplicity of Equilibria with Gröbner Bases," Operations Research, INFORMS, vol. 58(4-part-2), pages 1037-1050, August.
    7. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    8. Soares, Helena & Sequeira, Tiago Neves & Marques, Pedro Macias & Gomes, Orlando & Ferreira-Lopes, Alexandra, 2018. "Social infrastructure and the preservation of physical capital: Equilibria and transitional dynamics," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 614-632.
    9. Orrego, Fabrizio, 2011. "Demografía y precios de activos," Revista Estudios Económicos, Banco Central de Reserva del Perú, issue 22, pages 83-101.
    10. Li, Xiaoliang & Wang, Dongming, 2014. "Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 48-58.
    11. Arias-R., Omar Fdo., 2014. "On the pseudo-equilibrium manifold in semi-algebraic economies with real financial assets," MPRA Paper 54297, University Library of Munich, Germany.
    12. Michal Fabinger & E. Glen Weyl, 2016. "Functional Forms for Tractable Economic Models and the Cost Structure of International Trade," Papers 1611.02270, arXiv.org, revised Aug 2018.
    13. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    14. Charles Gauthier & Raghav Malhotra & Agustin Troccoli Moretti, 2022. "Finite Tests from Functional Characterizations," Papers 2208.03737, arXiv.org, revised Jul 2024.
    15. Orrego, Fabrizio, 2010. "Demography, stock prices and interest rates: The Easterlin hypothesis revisited," Working Papers 2010-012, Banco Central de Reserva del Perú.
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    More about this item

    Keywords

    Semi-algebraic preferences Equilibrium correspondence Polynomial equations Grobner bases Equilibrium multiplicity;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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