IDEAS home Printed from https://ideas.repec.org/p/ecm/wc2000/0437.html

The Weak Axiom and Comparative Statics

Author

Listed:
  • John K.-H. Quah

    (Oxford University)

Abstract

This paper examines conditions which guarantee that the excess demand function of an exchange economy will satisfy the weak axiom in an open neighborhood of a given equilibrium price. This property ensures that the equilibrium is locally stable with respect to Walras' tatonnement. A related issue is the possibility of local comparative statics; in particular, the paper examines conditions which guarantee that when an economy's endowment is perturbed, the equilibrium price will move in a direction opposite to that of the perturbation. A distinguishing feature of this paper's approach is the heavy use of the indirect utility function, though we also provide results that allow for the translation of conditions imposed on indirect utility functions to conditions imposed on direct utility functions. Indeed we apply this to the special case of exchange economies where all agents have directly additive utilities - essentially a complete markets finance model with agents having von Neumann-Morgenstern utility functions. We show that the structural properties of demand near an equilibrium price depend on variations in the coefficient of relative risk aversion.

Suggested Citation

  • John K.-H. Quah, 2000. "The Weak Axiom and Comparative Statics," Econometric Society World Congress 2000 Contributed Papers 0437, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0437
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/RePEc/es2000/0437.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    2. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, Enero-Abr.
    3. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
    4. Shafer, Wayne & Sonnenschein, Hugo, 1993. "Market demand and excess demand functions," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 14, pages 671-693, Elsevier.
    5. Grandmont, Jean-Michel, 1992. "Transformations of the commodity space, behavioral heterogeneity, and the aggregation problem," Journal of Economic Theory, Elsevier, vol. 57(1), pages 1-35.
    6. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
    7. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
    8. Polterovich, Victor & Mityushin, Leonid, 1978. "Criteria for Monotonicity of Demand Functions," MPRA Paper 20097, University Library of Munich, Germany.
    9. John Muellbauer, 1975. "Aggregation, Income Distribution and Consumer Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 525-543.
    10. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    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. Quah, John K.-H., 2008. "The existence of equilibrium when excess demand obeys the weak axiom," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 337-343, February.
    2. John Quah, 2001. "Comparative Statics of the Weak Axiom," Economics Papers 2001-W3, Economics Group, Nuffield College, University of Oxford.
    3. Quah, John K. -H., 2003. "Market demand and comparative statics when goods are normal," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 317-333, June.
    4. Nachbar, John H., 2004. "General equilibrium comparative statics: discrete shocks in production economies," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 153-163, February.
    5. Michael Jerison, 2001. "Demand Dispersion, Metonymy and Ideal Panel Data," Discussion Papers 01-11, University at Albany, SUNY, Department of Economics.
    6. John K.H. Quah, 2003. "The Law of Demand and Risk Aversion," Econometrica, Econometric Society, vol. 71(2), pages 713-721, March.

    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. John Quah, 2001. "Comparative Statics of the Weak Axiom," Economics Papers 2001-W3, Economics Group, Nuffield College, University of Oxford.
    2. Werner Hildenbrand & Alois Kneip, 2005. "On behavioral heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(1), pages 155-169, January.
    3. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
    4. CHIAPPORI, Pierre-André & EKELAND, Ivar & KUBLER, Félix & POLEMARCHAKIS, Heracles, 2000. "The identification of preferences from equilibrium prices," LIDAM Discussion Papers CORE 2000024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers 06-07, University at Albany, SUNY, Department of Economics.
    6. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, September.
    7. Jean-Michel Grandmont, 2017. "Behavioral Heterogeneity: Pareto Distributions of Homothetic Preference Scales and Aggregate Expenditures Income Elasticities," Discussion Paper Series DP2017-31, Research Institute for Economics & Business Administration, Kobe University.
    8. Herings, P.J.J. & Kubler, F., 1999. "The Robustness of the CAPM - A Computational Approach," Other publications TiSEM 06a4e5b2-f380-4d5b-a96f-8, Tilburg University, School of Economics and Management.
    9. Sabiou M. Inoua & Vernon L. Smith, 2020. "The Classical Theory of Supply and Demand," Working Papers 20-11, Chapman University, Economic Science Institute.
    10. E. B. de Villemeur, 1999. "Aggregation of demand and distribution of characteristics : A difficulty in modelling behavioural heterogeneity," Thema Working Papers 99-38, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    11. Gaël GIRAUD & Isabelle MARET, 2005. "The Exact Insensitivity of Market Budget Shares and the 'Balancing Effect'," Working Papers of BETA 2005-02, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    12. Lehmann-Waffenschmidt, Marco, 1995. "On the equilibrium price set of a continuous perturbation of exchange economies," Journal of Mathematical Economics, Elsevier, vol. 24(5), pages 497-519.
    13. Hayashi, Takashi, 2008. "A note on small income effects," Journal of Economic Theory, Elsevier, vol. 139(1), pages 360-379, March.
    14. repec:dau:papers:123456789/6360 is not listed on IDEAS
    15. Xinyang Wang, 2026. "Equilibrium Stability and Uniqueness with a Large Number of Commodities and Patient Consumers," Papers 2605.02817, arXiv.org.
    16. Gael Giraud & Isabelle Maret, 2001. "Behavioral Heterogeneity in Large Economies," Working Papers of BETA 2001-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    17. Gaël Giraud & Isabelle Maret, 2007. "The Exact Insensitivity of Market Budget Shares and the "Balancing Effect"," Working Papers halshs-00155753, HAL.
    18. Grandmont, Jean-Michel, 1992. "Transformations of the commodity space, behavioral heterogeneity, and the aggregation problem," Journal of Economic Theory, Elsevier, vol. 57(1), pages 1-35.
    19. Alan Kirman, 2006. "Heterogeneity in Economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(1), pages 89-117, May.
    20. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.

    More about this item

    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:wc2000:0437. 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: Christopher F. Baum (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.