IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v74y2018icp62-67.html
   My bibliography  Save this article

Curvature and uniqueness of equilibrium

Author

Listed:
  • Loi, Andrea
  • Matta, Stefano

Abstract

Let E(r) be the equilibrium manifold associated to a smooth pure exchange economy with fixed total resources r. Balasko (1980) has shown that if the equilibrium price is unique for every economy, then the price is constant, hence the curvature of E(r) is zero. By endowing E(r) with the metric induced from its ambient space, we show that, in the case of two commodities and an arbitrary number of agents, if the curvature of E(r) is zero then there is a unique equilibrium for every economy. Hence the zero curvature condition is sufficient to guarantee the uniqueness of equilibrium.

Suggested Citation

  • Loi, Andrea & Matta, Stefano, 2018. "Curvature and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 62-67.
    • Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:62-67
    DOI: 10.1016/j.jmateco.2017.11.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406817301325
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2017.11.002?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. Shapley, Lloyd S & Shubik, Martin, 1977. "An Example of a Trading Economy with Three Competitive Equilibria," Journal of Political Economy, University of Chicago Press, vol. 85(4), pages 873-875, August.
    2. Balasko, Yves, 1980. "Number and definiteness of economic equilibria," Journal of Mathematical Economics, Elsevier, vol. 7(3), pages 215-225, December.
    3. Loi, Andrea & Matta, Stefano, 2011. "Catastrophes minimization on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 47(4), pages 617-620.
    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. Loi, Andrea & Matta, Stefano & Uccheddu, Daria, 2023. "Equilibrium selection under changes in endowments: A geometric approach," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    2. Andrea Loi & Stefano Matta & Daria Uccheddu, 2023. "Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency," Papers 2308.03706, arXiv.org.
    3. Loi, Andrea & Matta, Stefano, 2021. "Minimal entropy and uniqueness of price equilibria in a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    5. Andrea Loi & Stefano Matta & Daria Uccheddu, 2022. "Equilibrium selection: a geometric approach," Papers 2208.10860, arXiv.org.
    6. Andrea Loi & Stefano Matta, 2021. "Risk aversion and uniqueness of equilibrium: a polynomial approach," Papers 2107.01947, arXiv.org, revised Oct 2021.
    7. Loi, Andrea & Matta, Stefano, 2019. "Minimality and uniqueness of equilibrium," MPRA Paper 98055, University Library of Munich, Germany.
    8. Giménez, Eduardo L., 2022. "Offer curves and uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 98(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. Loi, Andrea & Matta, Stefano & Uccheddu, Daria, 2023. "Equilibrium selection under changes in endowments: A geometric approach," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    2. Juergen Huber & Martin Shubik & Shyam Sunder, 2009. "Default Penalty as a Disciplinary and Selection Mechanism in Presence of Multiple Equilibria," Cowles Foundation Discussion Papers 1730, Cowles Foundation for Research in Economics, Yale University.
    3. Martin Shubik & Alok Kumar, 2001. "A Computational Analysis of the Core of a Trading Economy with Three Competitive Equilibria and a Finite Number of Traders," Cowles Foundation Discussion Papers 1290, Cowles Foundation for Research in Economics, Yale University.
    4. Cheng-Zhong Qin & Martin Shubik, 2005. "A Credit Mechanism for Selecting a Unique Competitive Equilibrium," Cowles Foundation Discussion Papers 1539, Cowles Foundation for Research in Economics, Yale University, revised Nov 2006.
    5. Sean Crockett & Daniel Friedman & Ryan Oprea, 2021. "Naturally Occurring Preferences And General Equilibrium: A Laboratory Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 831-859, May.
    6. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, August.
    7. Loi, Andrea & Matta, Stefano, 2019. "Minimality and uniqueness of equilibrium," MPRA Paper 98055, University Library of Munich, Germany.
    8. Timothy J. Kehoe & David K. Levine, 1990. "Indeterminacy in Applied Intertemporal General Equilibrium Models," Levine's Working Paper Archive 2042, David K. Levine.
    9. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    10. Minwook KANG, 2015. "A Concrete Example of the Transfer Problem with Multiple Equilibria," Economic Growth Centre Working Paper Series 1504, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    11. Chen-Zhong Qin & Lloyd S. Shapley & Martin Shubik, 2009. "Marshallian Money, Welfare, and Side-Payments," Cowles Foundation Discussion Papers 1729, Cowles Foundation for Research in Economics, Yale University.
    12. Junichi Minagawa, 2012. "On the instability of competitive equilibrium: a further example," Economics Bulletin, AccessEcon, vol. 32(1), pages 80-85.
    13. Cheng-Zhong Qin & Thomas Quint & Martin Shubik, 2017. "Default, Efficiency and Uniqueness," Cowles Foundation Discussion Papers 2095, Cowles Foundation for Research in Economics, Yale University.
    14. Felix Kubler & Herakles Polemarchakis, 2004. "Stationary Markov equilibria for overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 623-643, October.
    15. Crockett, Sean & Friedman, Daniel & Oprea, Ryan, 2017. "Aggregation and convergence in experimental general equilibrium economies constructed from naturally occurring preferences," Discussion Papers, Research Professorship Market Design: Theory and Pragmatics SP II 2017-501, WZB Berlin Social Science Center.
    16. Andrea Loi & Stefano Matta, 2012. "Structural stability and catastrophes," Economics Bulletin, AccessEcon, vol. 32(4), pages 3378-3385.
    17. Alok Kumar & Martin Shubik, 2004. "Variations on the Theme of Scarf's Counter-Example," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 1-19, August.
    18. Andrea Loi & Stefano Matta & Daria Uccheddu, 2022. "Equilibrium selection: a geometric approach," Papers 2208.10860, arXiv.org.
    19. Andrea Loi & Stefano Matta & Daria Uccheddu, 2023. "Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency," Papers 2308.03706, arXiv.org.
    20. 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.

    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:74:y:2018:i:c:p:62-67. 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.