IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00265684.html
   My bibliography  Save this paper

Continuity and Uniqueness of Equilibria for Linear Exchange Economies

Author

Listed:
  • Jean-Marc Bonnisseau

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Michael Florig

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Alejandro Jofré

    (CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago] - UCHILE - Universidad de Chile = University of Chile [Santiago] - CNRS - Centre National de la Recherche Scientifique)

Abstract

The purpose of this paper is to study the continuity and uniqueness properties of equilibria for linear exchange economies. We characterize the sets of utility vectors and initial endowments for which the equilibrium price is unique and respectively the set for which the equilibrium allocation is unique. We show that the equilibrium allocation correspondence is continuous with respect to the initial endowments and we characterize the set of full measure where the equilibrium allocation correspondence with respect to the initial endowments and utility vectors is continuous.

Suggested Citation

  • Jean-Marc Bonnisseau & Michael Florig & Alejandro Jofré, 2001. "Continuity and Uniqueness of Equilibria for Linear Exchange Economies," Post-Print halshs-00265684, HAL.
    • Handle: RePEc:hal:journl:halshs-00265684
    DOI: 10.1023/A:1017517020329
    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. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Differentiability of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 265-288, May.
    2. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    3. Bottazzi, Jean-Marc, 1994. "Accessibility of Pareto optima by Walrasian exchange processes," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 585-603, November.
    4. Jouini, Elyes, 1993. "The graph of the Walras correspondence : The production economies case," Journal of Mathematical Economics, Elsevier, vol. 22(2), pages 139-147.
    5. repec:dau:papers:123456789/5639 is not listed on IDEAS
    6. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    7. Cheng, Hsueh-Cheng, 1979. "Linear economies are "gross substitute" systems," Journal of Economic Theory, Elsevier, vol. 20(1), pages 110-117, February.
    8. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
    9. Eaves, B. Curtis, 1976. "A finite algorithm for the linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 197-203, July.
    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. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Differentiability of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 265-288, May.
    2. Yoav Kolumbus & Menahem Levy & Noam Nisan, 2023. "Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling," Papers 2307.04108, arXiv.org, revised Jan 2024.
    3. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 727-741, November.
    4. Shikhman, V. & Nesterov, Yu. & Ginsburgh, V., 2018. "Power method tâtonnements for Cobb–Douglas economies," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 84-92.
    5. Antonio Miralles, 2017. "Ex-ante efficiency in assignments with seniority rights," Review of Economic Design, Springer;Society for Economic Design, vol. 21(1), pages 33-48, March.
    6. M. Florig, 2004. "Equilibrium Correspondence of Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 97-109, January.

    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. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Differentiability of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 265-288, May.
    2. M. Florig, 2004. "Equilibrium Correspondence of Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 97-109, January.
    3. Gaël Giraud & Dimitrios Tsomocos, 2010. "Nominal uniqueness and money non-neutrality in the limit-price exchange process," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 303-348, October.
    4. Gaël Giraud & Céline Rochon, 2007. "Natural rate of unemployment and efficiency: a dynamic analysis with flexible prices and increasing returns," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00155739, HAL.
    5. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 727-741, November.
    6. Gaël Giraud & Dimitrios Tsomocos, 2004. "Global uniqueness and money non-neutrality in a Walrasian dynamics without rational expectations," Cahiers de la Maison des Sciences Economiques b04121, Université Panthéon-Sorbonne (Paris 1).
    7. Jean-Marc Bonnisseau & Orntangar Nguenamadji, 2013. "Discrete Walrasian exchange process," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1091-1100, April.
    8. Devanur, Nikhil R. & Garg, Jugal & Végh, László A., 2016. "A rational convex program for linear Arrow-Debreu markets," LSE Research Online Documents on Economics 69224, London School of Economics and Political Science, LSE Library.
    9. Monique Florenzano & Emma Moreno-García, 2001. "Linear exchange economies with a continuum of agents," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(4), pages 253-272.
    10. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    11. Bottazzi, Jean-Marc & De Meyer, Bernard, 2003. "A market game for assets and taxed investors," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 657-675, July.
    12. Bonnisseau, Jean-Marc & Nguenamadji, Orntangar, 2010. "On the uniqueness of local equilibria," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 623-632, September.
    13. Daniele Cassese & Paolo Pin, 2018. "Decentralized Pure Exchange Processes on Networks," Papers 1803.08836, arXiv.org, revised Mar 2022.
    14. Gaël Giraud & Céline Rochon, 2010. "Transition to Equilibrium in International Trades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00657038, HAL.
    15. KOUTSOUGERAS, Leonidas C., 1998. "On a three way equivalence," LIDAM Discussion Papers CORE 1998009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Gaël Giraud, 2007. "Walrasian non-tatonnement with incomplete and imperfectly competitive markets," Documents de travail du Centre d'Economie de la Sorbonne b07021, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    17. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    18. Konovalov, Alexander & Marakulin, Valeri, 2006. "Equilibria without the survival assumption," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 198-215, April.
    19. Simina Br^anzei & Nikhil R. Devanur & Yuval Rabani, 2019. "Proportional Dynamics in Exchange Economies," Papers 1907.05037, arXiv.org, revised Sep 2023.
    20. Konovalov, A. & Marakulin, V., 2001. "Equilibria Without the Survival Assumption : A Non-Standard Analysis Approach," Discussion Paper 2001-34, Tilburg University, Center for Economic Research.

    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:hal:journl:halshs-00265684. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.