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Quadratic Concavity and Determinacy of Equilibrium

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  • Shannon, Chris
  • Zame, William R.

Abstract

One of the central features of classical models of competitive markets is the generic determinacy of competitive equilibria. For smooth economies with a finite number of commodities and a finite number of consumers, almost all initial endowments admit only a finite number of competitive equilibria, and these equilibria vary (locally) smoothly with endowments; thus equilibrium comparative statics are locally determinate. This paper establishes parallel results for economies with finitely many consumers and infinitely many commodities. The most important new condition we introduce, quadratic concavity, rules out preferences in which goods are perfect substitutes globally, locally, or asymptotically. Our framework is sufficiently general to encompass many of the models that have proved important in the study of continuous-time trading in financial markets, trading over an infinite time horizon, and trading of finely differentiated commodities. Copyright The Econometric Society 2002.
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Suggested Citation

  • Shannon, Chris & Zame, William R., 1999. "Quadratic Concavity and Determinacy of Equilibrium," Department of Economics, Working Paper Series qt3fv586x6, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    • Handle: RePEc:cdl:econwp:qt3fv586x6
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    References listed on IDEAS

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    Cited by:

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    2. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    3. Riedel, Frank, 2005. "Generic determinacy of equilibria with local substitution," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 603-616, August.
    4. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    5. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    6. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation for Research in Economics, Yale University.
    7. DEMICHELIS, Stefano & POLEMARCHAKIS, Heracles, 2000. "Life-span and the determinacy of equilibrium in economies of overlapping generations," LIDAM Discussion Papers CORE 2000034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Accinelli, E. & Covarrubias, E., 2014. "An extension of the Sard–Smale Theorem to convex domains with an empty interior," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 123-128.
    9. Herrendorf, Berthold & Valentinyi, Akos, 2006. "On the stability of the two-sector neoclassical growth model with externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1339-1361, August.
    10. Berthold Herrendorf & Akos Valentinyi, 2002. "Neoclassical Growth Model with Externalities," CERS-IE WORKING PAPERS 0203, Institute of Economics, Centre for Economic and Regional Studies.
    11. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Levine's Working Paper Archive 122247000000002225, David K. Levine.
    12. Anat Bracha & Donald Brown, 2013. "(Ir)rational Exuberance: Optimism, Ambiguity, and Risk," Levine's Working Paper Archive 786969000000000782, David K. Levine.
    13. Anat Bracha & Donald J. Brown, 2013. "Keynesian Utilities: Bulls and Bears," Cowles Foundation Discussion Papers 1891, Cowles Foundation for Research in Economics, Yale University.
    14. Bloise, Gaetano & Reichlin, Pietro, 2011. "Asset prices, debt constraints and inefficiency," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1520-1546, July.
    15. Gorokhovsky, Alexander & Rubinchik, Anna, 2022. "Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models," Journal of Economic Theory, Elsevier, vol. 204(C).
    16. Rubinchik, Anna, 2015. "The chase of a multi-armed economist for the elusive social discount rate," Working Papers WP2015/8, University of Haifa, Department of Economics, revised 18 Nov 2015.
    17. Accinelli, Elvio, 2013. "The equilibrium set of infinite dimensional Walrasian economies and the natural projection," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 435-440.
    18. Molina-Abraldes, Antonio & Pintos-Clapés, Juan, 2008. "Pareto optimality in continuous-time OLG economies," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 933-950, September.
    19. H. Polemarchakis & S. Demichelis, 2002. "Frequency of Trade and the Determinancy of Equilibrium Paths: Logarithmic Economies of Overlapping Generations Under Certainty," Working Papers 2002-16, Brown University, Department of Economics.
    20. Mertens, Jean-François & Rubinchik, Anna, 2014. "Essential properties of Lp,q spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 187-196.
    21. Eric Bond & Kazumichi Iwasa & Kazuo Nishimura, 2011. "A dynamic two country Heckscher–Ohlin model with non-homothetic preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 171-204, September.
    22. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.
    23. Donald J. Brown & Ravi Kannan, 2003. "Indeterminacy, Nonparametric Calibration and Counterfactual Equilibria," Cowles Foundation Discussion Papers 1426, Cowles Foundation for Research in Economics, Yale University.

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    More about this item

    Keywords

    determinacy; infinite-dimensional commodity spaces; competitive equilibria; continuous-time finance; commodity differentiation; infinite horizon economies; Lipschitz economies; Social and Behavioral Sciences;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • 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

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