IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v49y2013i6p435-440.html
   My bibliography  Save this article

The equilibrium set of infinite dimensional Walrasian economies and the natural projection

Author

Listed:
  • Accinelli, Elvio

Abstract

The natural projection plays a fundamental role to understand the behavior of the Walrasian economies. In this paper, we extend this method to analyze the behavior of infinite dimensional economies. We introduce the definition of the social equilibrium set, and we show that there exists a bijection between this set and the Walrasian equilibrium set of an infinite dimensional economy. In order to describe the main topological characteristics of both sets, we analyze the main differential characteristics of the excess utility function and then, we extend the method of the natural projection as suggested by Y. Balasko.

Suggested Citation

  • Accinelli, Elvio, 2013. "The equilibrium set of infinite dimensional Walrasian economies and the natural projection," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 435-440.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:6:p:435-440
    DOI: 10.1016/j.jmateco.2013.08.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406813000736
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2013.08.005?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. 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.
    2. Elvio ACCINELLI & Puchet MARTIN, 2010. "A Classification Of Infinity Dimensional Walrasian Economies," EcoMod2005 280900000, EcoMod.
    3. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
    4. Araujo A. & Monteiro P. K., 1994. "The General Existence of Extended Price Equilibria with Infinitely Many Commodities," Journal of Economic Theory, Elsevier, vol. 63(2), pages 408-416, August.
    5. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
    6. Edward C. Prescott & Rajnish Mehra, 2005. "Recursive Competitive Equilibrium: The Case Of Homogeneous Households," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 11, pages 357-371, World Scientific Publishing Co. Pte. Ltd..
    7. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    8. Araujo, Aloisio, 1985. "Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience," Econometrica, Econometric Society, vol. 53(2), pages 455-461, March.
    9. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
    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. 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.
    2. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.

    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. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    2. Gorokhovsky, Alexander & Rubinchik, Anna, 2022. "Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. 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.
    4. Accinelli, Elvio & Covarrubias, Enrique, 2014. "Smooth economic analysis for general spaces of commodities," MPRA Paper 53222, University Library of Munich, Germany.
    5. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, April.
    6. 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.
    7. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    8. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    9. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    10. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    11. John Geanakoplos, 2008. "Overlapping Generations Models of General Equilibrium," Cowles Foundation Discussion Papers 1663, Cowles Foundation for Research in Economics, Yale University.
    12. Basile, Achille & Graziano, Maria Gabriella & Papadaki, Maria & Polyrakis, Ioannis A., 2017. "Cones with semi-interior points and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 36-48.
    13. Manjira Datta & Kevin Reffett & Łukasz Woźny, 2018. "Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 593-626, October.
    14. Riedel, Frank, 2005. "Generic determinacy of equilibria with local substitution," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 603-616, August.
    15. Charalambos Aliprantis & Rabee Tourky, 2009. "Equilibria in incomplete assets economies with infinite dimensional spot markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 221-262, February.
    16. Burke, Jonathan L., 2000. "General Equilibrium When Economic Growth Exceeds Discounting," Journal of Economic Theory, Elsevier, vol. 94(2), pages 141-162, October.
    17. 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.
    18. Araujo, Aloisio & Gama, Juan Pablo & Novinski, Rodrigo & Pascoa, Mario R., 2019. "Endogenous discounting, wariness, and efficient capital taxation," Journal of Economic Theory, Elsevier, vol. 183(C), pages 520-545.
    19. 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.
    20. Abramovich, Y A & Aliprantis, C D & Zame, W R, 1995. "A Representation Theorem for Riesz Spaces and Its Applications to Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 527-535, May.

    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:49:y:2013:i:6:p:435-440. 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.