IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v98y2022ics0304406821001385.html
   My bibliography  Save this article

Offer curves and uniqueness of competitive equilibrium

Author

Listed:
  • Giménez, Eduardo L.

Abstract

We establish sufficient conditions to guarantee the uniqueness of competitive equilibrium by properly restricting the distribution of endowments and preference profiles in a two-commodity, two-agent exchange economy. If agents’ offer curves share a common directional monotonicity property –i.e., at least one commodity is always normal for all agents–, then competitive equilibrium is unique. If not, we can provide testable geometric conditions for uniqueness by restricting the support of the distributions of individuals’ preferences and endowments that characterize the agents’ offer curves. The conditions are checked in well-known utility representations of preferences commonly used in the literature to illustrate the failure of uniqueness of equilibrium.

Suggested Citation

  • Giménez, Eduardo L., 2022. "Offer curves and uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    • Handle: RePEc:eee:mateco:v:98:y:2022:i:c:s0304406821001385
    DOI: 10.1016/j.jmateco.2021.102575
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406821001385
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2021.102575?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jerison, Michael, 1999. "Dispersed excess demands, the weak axiom and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 31(1), pages 15-48, February.
    2. John Chipman, 2010. "Multiple equilibrium under CES preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 129-145, October.
    3. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    4. E. Eisenberg, 1961. "Aggregation of Utility Functions," Management Science, INFORMS, vol. 7(4), pages 337-350, July.
    5. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    6. Kehoe, Timothy J., 1991. "Computation and multiplicity of equilibria," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 38, pages 2049-2144, Elsevier.
    7. Marhuenda, F, 1995. "Distribution of Income and Aggregation of Demand," Econometrica, Econometric Society, vol. 63(3), pages 647-666, May.
    8. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    9. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    10. Loi, Andrea & Matta, Stefano, 2019. "Minimality and uniqueness of equilibrium," MPRA Paper 98055, University Library of Munich, Germany.
    11. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550, November.
    12. Anjan Mukherji, 1997. "On the uniqueness of competitive equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 509-520.
    13. Rose-Anne Dana, 2001. "original papers : Uniqueness of Arrow-Debreu and Arrow-Radner equilibrium when utilities are additively separable," Review of Economic Design, Springer;Society for Economic Design, vol. 6(2), pages 155-173.
    14. Cheng-Zhong Qin & Martin Shubik, 2012. "Selecting a unique competitive equilibrium with default penalties," Journal of Economics, Springer, vol. 106(2), pages 119-132, June.
    15. Bergstrom Theodore C & Shimomura Ken-Ichi & Yamato Takehiko, 2009. "Simple Economies with Multiple Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-31, December.
    16. Kamiya, Kazuya, 1984. "On the Existence and Uniqueness of General Equilibrium Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 79-83, February.
    17. 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.
    18. Balasko Yves, 1995. "Economies with a Unique Equilibrium: A Simple Proof of Arc-connectedness in the Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 67(2), pages 556-565, December.
    19. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    20. Balasko, Yves, 1975. "Some results on uniqueness and on stability of equilibrium in general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 95-118.
    21. Hens, Thorsten & Loeffler, Andras, 1995. "Gross substitution in financial markets," Economics Letters, Elsevier, vol. 49(1), pages 39-43, July.
    22. Yves Balasko, 2011. "General Equilibrium Theory of Value," Economics Books, Princeton University Press, edition 1, number 9482.
    23. 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.
    24. Marshall, Alfred, 1879. "The Pure Theory of Foreign Trade," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number marshall1879.
    25. John K.-H. Quah, 1997. "The Law of Demand when Income Is Price Dependent," Econometrica, Econometric Society, vol. 65(6), pages 1421-1442, November.
    26. repec:bla:econom:v:37:y:1970:i:146:p:178-84 is not listed on IDEAS
    27. Pearce, I F & Wise, J, 1973. "On the Uniqueness of Competitive Equilibrium: Part I, Unbounded Demand," Econometrica, Econometric Society, vol. 41(5), pages 817-828, September.
    28. Gjerstad, S., 1996. "Multiple Equilibria in Exchange Economies with Homothetic, Nearly Identical Preferences," Papers 288, Minnesota - Center for Economic Research.
    29. Cass, David & Okuno, Masahiro & Zilcha, Itzhak, 1979. "The role of money in supporting the pareto optimality of competitive equilibrium in consumption-loan type models," Journal of Economic Theory, Elsevier, vol. 20(1), pages 41-80, February.
    30. Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(1), pages 119-147.
    31. Pearce, Ivor F & Wise, J, 1974. "On the Uniqueness of Competitive Equilibrium: Part II, Bounded Demand," Econometrica, Econometric Society, vol. 42(5), pages 921-932, September.
    32. A. P. Kirman & K. J. Koch, 1986. "Market Excess Demand in Exchange Economies with Identical Preferences and Collinear Endowments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 457-463.
    33. 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.
    34. repec:dau:papers:123456789/6560 is not listed on IDEAS
    35. Loi, Andrea & Matta, Stefano, 2018. "Curvature and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 62-67.
    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. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    2. Andrea Loi & Stefano Matta, 2024. "Endowments, patience types, and uniqueness in two-good HARA utility economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 157-165, December.
    3. Won, Dong Chul, 2023. "A new approach to the uniqueness of equilibrium with CRRA preferences," Journal of Economic Theory, Elsevier, vol. 208(C).

    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. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, August.
    2. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    3. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    4. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    5. Yves Balasko & Octavio Tourinho, 2014. "Factor proportionality in multiple households closed CGE models: theory and illustrations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 119-136, October.
    6. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    7. Won, Dong Chul, 2023. "A new approach to the uniqueness of equilibrium with CRRA preferences," Journal of Economic Theory, Elsevier, vol. 208(C).
    8. 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.
    9. Pascal Gauthier & Timothy J. Kehoe & Erwan Quintin, 2022. "Constructing pure-exchange economies with many equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 541-564, April.
    10. John Quah, 2001. "Comparative Statics of the Weak Axiom," Economics Papers 2001-W3, Economics Group, Nuffield College, University of Oxford.
    11. Yves Balasko, 2013. "Heckscher-Ohlin explained by Walras," Textos para discussão 610, Department of Economics PUC-Rio (Brazil).
    12. Andrea Loi & Stefano Matta, 2024. "Endowments, patience types, and uniqueness in two-good HARA utility economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 157-165, December.
    13. Bodenstein, Martin, 2011. "Closing large open economy models," Journal of International Economics, Elsevier, vol. 84(2), pages 160-177, July.
    14. 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.
    15. Gaël Giraud & Isabelle Maret, 2007. "The Exact Insensitivity of Market Budget Shares and the "Balancing Effect"," Working Papers halshs-00155753, HAL.
    16. Andrea Loi & Stefano Matta, 2021. "Risk aversion and uniqueness of equilibrium: a polynomial approach," Papers 2107.01947, arXiv.org, revised Oct 2021.
    17. Gael Giraud & John Quah, 2002. "Heterotic Models of Aggregate Demand," Economics Papers 2002-W18, Economics Group, Nuffield College, University of Oxford.
    18. Denizalp Goktas & Jiayi Zhao & Amy Greenwald, 2023. "T\^atonnement in Homothetic Fisher Markets," Papers 2306.04890, arXiv.org.
    19. Donald C. Keenan & Taewon Kim, 2022. "Closing the invisible hand: a rehabilitation of tâtonnement dynamics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(3), pages 681-711, July.
    20. Covarrubias, Enrique, 2013. "Global invertibility of excess demand functions," MPRA Paper 47300, University Library of Munich, Germany.

    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:eee:mateco:v:98:y:2022:i:c:s0304406821001385. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.