IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00086791.html
   My bibliography  Save this paper

General equilibrium analysis in ordered topological vector spaces

Author

Listed:
  • Charalambos Aliprantis

    () (Department of Economics - Purdue University [West Lafayette])

  • Monique Florenzano

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

  • Rabee Tourky

    () (Department of Economics - Purdue University [West Lafayette])

Abstract

The second welfare theorem and the core-equivalence theorem have been proved to be fundamental tools for obtaining equilibrium existence theorems, especially in an infinite dimensional setting. For well-behaved exchange economies that we call proper economies, this paper gives (minimal) conditions for supporting with prices Pareto optimal allocations and decentralizing Edgeworth equilibrium allocations as non-trivial equilibria. As we assume neither transitivity nor monotonicity on the preferences of consumers, most of the existing equilibrium existence results are a consequence of our results. A natural application is in Finance, where our conditions lead to new equilibrium existence results, and also explain why some financial economies fail to have equilibrium.

Suggested Citation

  • Charalambos Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "General equilibrium analysis in ordered topological vector spaces," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086791, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00086791
    DOI: 10.1016/j.mateco.2003.11.004
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00086791
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-00086791/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
    2. 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.
    3. Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-1137, September.
    4. Monteiro, P.K. & Tourky, R., 2000. "Mas-Colell Price Equilibrium Existence Theorem the Case of Smooth Disposal," Papiers d'Economie Mathématique et Applications 2000.82, Université Panthéon-Sorbonne (Paris 1).
    5. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
    6. Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998. "Portfolio dominance and optimality in infinite security markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 347-366, October.
    7. 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.
    8. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
    9. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 353-370, January.
    10. Tourky, Rabee, 1998. "A New Approach to the Limit Theorem on the Core of an Economy in Vector Lattices," Journal of Economic Theory, Elsevier, vol. 78(2), pages 321-328, February.
    11. Aliprantis, Charalambos D. & Brown, Donald J. & Burkinshaw, Owen, 1987. "Edgeworth equilibria in production economies," Journal of Economic Theory, Elsevier, vol. 43(2), pages 252-291, December.
    12. Aliprantis, C. D. & Tourky, R. & Yannelis, N. C., 2000. "The Riesz-Kantorovich formula and general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 55-76, August.
    13. Messaoud Deghdak & Monique Florenzano, 1999. "Decentralizing Edgeworth equilibria in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 297-310.
    14. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
    15. 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.
    16. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
    17. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    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. Achille Basile & Maria Gabriella Graziano, 2012. "Core Equivalences for Equilibria Supported by Non-linear Prices," CSEF Working Papers 309, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    3. Carlos Hervés-Beloso & V. Martins-da-Rocha & Paulo Monteiro, 2009. "Equilibrium theory with asymmetric information and infinitely many states," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 295-320, February.
    4. Roko Aliprantis & Monique Florenzano & Daniella Puzzello & Rabee Tourky, 2006. "The wedge of arbitrage free prices : anything goes," Cahiers de la Maison des Sciences Economiques b06070, Université Panthéon-Sorbonne (Paris 1).
    5. repec:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0133-3 is not listed on IDEAS
    6. Ellen Fukuda & L. Graña Drummond, 2013. "Inexact projected gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 473-493, April.
    7. repec:spr:etbull:v:2:y:2014:i:2:d:10.1007_s40505-014-0044-6 is not listed on IDEAS
    8. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques b04116, Université Panthéon-Sorbonne (Paris 1).
    9. V. Martins-da-Rocha & Frank Riedel, 2006. "Stochastic equilibria for economies under uncertainty with intertemporal substitution," Annals of Finance, Springer, vol. 2(1), pages 101-122, January.
    10. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
    11. Klishchuk, Bogdan, 2015. "New conditions for the existence of Radner equilibrium with infinitely many states," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 67-73.

    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:cesptp:halshs-00086791. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.