[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v70y2002i2p631-662.html
   My bibliography  Save this article

Quadratic Concavity and Determinacy of Equilibrium

Author

Listed:
  • Chris Shannon

    (Dept. of Economics, 549 Evans Hall, University of California, Berkeley, Berkeley, CA 94720, U.S.A.)

  • William R. Zame

    (Dept. of Economics, Bunche Hall, UCLA, 405 Hilgard Ave., Los Angeles, CA 90095, U.S.A.)

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.

Suggested Citation

  • Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
    • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:2:p:631-662
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    2. Kehoe, Timothy J. & Levine, David K. & Romer, Paul M., 1990. "Determinacy of equilibria in dynamic models with finitely many consumers," Journal of Economic Theory, Elsevier, vol. 50(1), pages 1-21, February.
    3. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
    4. Mas-Colell, Andreu & Richard, Scott F., 1991. "A new approach to the existence of equilibria in vector lattices," Journal of Economic Theory, Elsevier, vol. 53(1), pages 1-11, February.
    5. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    6. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
    7. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    8. Hindy, Ayman & Huang, Chi-fu, 1992. "Intertemporal Preferences for Uncertain Consumption: A Continuous Time Approach," Econometrica, Econometric Society, vol. 60(4), pages 781-801, July.
    9. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
    10. Balasko, Yves, 1997. "Equilibrium analysis of the infinite horizon model with smooth discounted utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 783-829, May.
    11. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
    12. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Zame, William R., 1989. "Determinacy of equilibrium in large-scale economies," Journal of Mathematical Economics, Elsevier, vol. 18(3), pages 231-262, June.
    13. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & William Zame, 1989. "Determinacy of Equilibrium in Large Square Economies," Levine's Working Paper Archive 46, David K. Levine.
    14. Jones, Larry E, 1984. "A Competitive Model of Commodity Differentiation," Econometrica, Econometric Society, vol. 52(2), pages 507-530, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    2. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    3. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation for Research in Economics, Yale University.
    4. 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.
    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," Levine's Working Paper Archive 122247000000002225, David K. Levine.
    7. Anat Bracha & Donald Brown, 2013. "(Ir)rational Exuberance: Optimism, Ambiguity, and Risk," Levine's Working Paper Archive 786969000000000782, David K. Levine.
    8. Riedel, Frank, 2005. "Generic determinacy of equilibria with local substitution," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 603-616, August.
    9. 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.
    10. Bloise, Gaetano & Reichlin, Pietro, 2011. "Asset prices, debt constraints and inefficiency," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1520-1546, July.
    11. 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.
    12. 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).
    13. Anat Bracha & Donald Brown, 2013. "Keynesian Utilities: Bulls and Bears," Levine's Working Paper Archive 786969000000000792, David K. Levine.
    14. 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).
    15. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    16. 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.
    17. Berthold Herrendorf & Akos Valentinyi, 2002. "Neoclassical Growth Model with Externalities," CERS-IE WORKING PAPERS 0203, Institute of Economics, Centre for Economic and Regional Studies.
    18. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Riedel, Frank, 2002. "Generic Determinancy of Equilibria with Local Substitution," Department of Economics, Working Paper Series qt43j2n5f5, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    2. Riedel, Frank, 2002. "Generic Determinacy of Equilibria with Local Substitution," Department of Economics, Working Paper Series qt1727r74c, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    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. Anderson, Robert M. & Raimondo, Roberto C., 2007. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Department of Economics, Working Paper Series qt0zq6v5gd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    5. 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.
    6. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.
    7. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    8. Kehoe, Timothy J & Levine, David K & Romer, Paul M, 1992. "On Characterizing Equilibria of Economies with Externalities and Taxes as Solutions to Optimization Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 43-68, January.
    9. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    10. Covarrubias, Enrique, 2011. "The equilibrium set of economies with a continuous consumption space," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 137-142, March.
    11. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    12. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    13. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    14. Balasko, Yves, 1997. "Equilibrium analysis of the infinite horizon model with smooth discounted utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 783-829, May.
    15. 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).
    16. 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.
    17. Kehoe, Timothy J. & Levine, David K. & Romer, Paul M., 1990. "Determinacy of equilibria in dynamic models with finitely many consumers," Journal of Economic Theory, Elsevier, vol. 50(1), pages 1-21, February.
    18. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    19. 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).
    20. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & William Zame, 1989. "Determinacy of Equilibrium in Large Square Economies," Levine's Working Paper Archive 46, David K. Levine.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:70:y:2002:i:2:p:631-662. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.