IDEAS home Printed from https://ideas.repec.org/p/ude/wpaper/0798.html
   My bibliography  Save this paper

A Characterization of the Singular Economies of the Infinite Dimensional Models in General Equilibrium Theory

Author

Listed:
  • Elvio Accinelli

    (IMERL, Facultad de Ingeniería, Udelar)

  • Martín Puchet

    (UNAM)

Abstract

The aim of this paper is to characterize the set of singular economies, when there are a finite set of consumers with infinitely many goods in the sense that goods differ in the time which they are consumed or in the state of the world in which they become available. There exist l available goods in each time or in each state of the world. Employing well know results of the “ Singularity Theory” on differentiable maps, we characterize the structure of the equilibrium set from the so called singular economies. In the last section we introduce a continuous time economy and -although in a limited waywe study the dynamics along the equilibrium path. We show that if there exist singularities then the equilibrium set isn’t a finite set, moreover it may be a continuous set of equilibria. It is important to notice that we will not describe our models in terms of the tˆatonnement. The process of endowments move the price system, we don’t need the demand law to characterize the equilibrium manifold.

Suggested Citation

  • Elvio Accinelli & Martín Puchet, 1998. "A Characterization of the Singular Economies of the Infinite Dimensional Models in General Equilibrium Theory," Documentos de Trabajo (working papers) 0798, Department of Economics - dECON.
    • Handle: RePEc:ude:wpaper:0798
    as

    Download full text from publisher

    File URL: https://hdl.handle.net/20.500.12008/2318
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Balasko, Yves, 1997. "Equilibrium analysis of the infinite horizon model with smooth discounted utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 783-829, May.
    2. Elvio Accinelli, 1996. "Some remarks about uniquenes of equilibrium for infinite dimensional economies," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 11(1), pages 3-32.
    3. Balasko, Yves, 1997. "The natural projection approach to the infinite-horizon model," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 251-263, April.
    Full references (including those not matched with items on IDEAS)

    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. van der Laan, Gerard & Withagen, Cees, 2003. "Quasi-equilibrium in economies with infinite dimensional commodity spaces: a truncation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 423-444, January.
    2. Elvio Accinelli & Martín Puchet, 2001. "A characterization of Walrasian economies of infinity dimension," Documentos de Trabajo (working papers) 0701, Department of Economics - dECON.
    3. Covarrubias, Enrique, 2011. "The equilibrium set of economies with a continuous consumption space," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 137-142, March.
    4. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    5. Accinelli, E. & Covarrubias, E., 2014. "An extension of the Sard–Smale Theorem to convex domains with an empty interior," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 123-128.
    6. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    7. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.
    8. Elvio Accinelli, 1999. "Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry?," Documentos de Trabajo (working papers) 0999, Department of Economics - dECON.
    9. Manjira Datta & Leonard Mirman & Olivier F. Morand & Kevin Reffett, 2001. "Monotone Methods for Distorted Economies," Working papers 2001-03, University of Connecticut, Department of Economics.
    10. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
    11. Licari, Juan Manuel, 2006. "On the regularity of equilibria in dynamic economies," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 618-625, August.
    12. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    13. Elvio Accinelli Gamba & Leobardo Plata Pérez, 2008. "Crisis sociales y singularidades. Los fundamentos microeconómicos de las crisis sociales," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 49-88, November.
    14. Stefano Matta, 2021. "A note on local uniqueness of equilibria: How isolated is a local equilibrium?," Papers 2103.04968, arXiv.org.
    15. Balasko, Yves, 2003. "Economies with price-dependent preferences," Journal of Economic Theory, Elsevier, vol. 109(2), pages 333-359, April.

    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:ude:wpaper:0798. 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: Andrea Doneschi or the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/derauuy.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.