IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v9y1997i3p385-426.html
   My bibliography  Save this article

Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)

Author

Listed:
  • Konard Podczeck

    (Institut fØr Wirtschaftswissenschaften, UniversitÄt Wien, Hohenstaufengasse 9, A-1010 Wien, AUSTRIA)

Abstract

Contrary to the finite dimensional set-up, the hypothesis of an atomless measure space of traders does not entail convexity of aggregate demand sets if there are infinitely many commodities. In this paper an assumption is introduced which sharpens the non-atomicity hypothesis by requiring that there are "many agents of every type." When this condition holds, aggregate demand in an infinite dimensional setting becomes convex even if individual preferences are non-convex. This result is applied to prove the existence of competitive equilibria in such a context.

Suggested Citation

  • Konard Podczeck, 1997. "Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 385-426.
  • Handle: RePEc:spr:joecth:v:9:y:1997:i:3:p:385-426
    Note: Received: December 10; revised version 199 5 March 8, 1996
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bernard Cornet & V. F. Martins-Da-Rocha, 2005. "Fatou¡¯S Lemma For Unbounded Gelfand Integrable Mappings," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200503, University of Kansas, Department of Economics, revised Feb 2005.
    2. Noguchi, Mitsunori, 2000. "Economies with a measure space of agents and a separable commodity space," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 157-173, September.
    3. Bernard Cornet, 2020. "The Gale–Nikaido–Debreu lemma with discontinuous excess demand," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 169-180, October.
    4. Tourky, Rabee & Yannelis, Nicholas C., 2001. "Markets with Many More Agents than Commodities: Aumann's "Hidden" Assumption," Journal of Economic Theory, Elsevier, vol. 101(1), pages 189-221, November.
    5. Bernard Cornet & V. Filipe Martins-Da-Rocha, 2021. "Fatou's Lemma for Unbounded Gelfand Integrable Mappings," Post-Print hal-03506933, HAL.
    6. Khan, M. Ali & Sagara, Nobusumi, 2016. "Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 95-107.
    7. repec:dau:papers:123456789/6273 is not listed on IDEAS
    8. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    9. Achille Basile & Maria Gabriella Graziano & Ciro Tarantino, 2018. "Coalitional fairness with participation rates," Journal of Economics, Springer, vol. 123(2), pages 97-139, March.
    10. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    11. Konrad Podczeck, 2001. "On Core-Walras (Non-)Equivalence for Economies with a Large Commodity Space," Vienna Economics Papers vie0107, University of Vienna, Department of Economics.
    12. Niccolò Urbinati, 2020. "Walrasian objection mechanism and Mas Colell's bargaining set in economies with many commodities," Working Papers 07, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    13. Kim, Taesung & Yannelis, Nicholas C., 1997. "Existence of Equilibrium in Bayesian Games with Infinitely Many Players," Journal of Economic Theory, Elsevier, vol. 77(2), pages 330-353, December.
    14. Filipe Martins-da-Rocha, V., 2003. "Equilibria in large economies with a separable Banach commodity space and non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 863-889, November.
    15. Niccolò Urbinati, 2023. "The Walrasian objection mechanism and Mas-Colell’s bargaining set in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 45-68, July.
    16. Suzuki, Takashi, 2013. "Core and competitive equilibria of a coalitional exchange economy with infinite time horizon," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 234-244.
    17. Jang, Hyo Seok & Lee, Sangjik, 2020. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 57-64.
    18. Cea-Echenique, Sebastián & Fuentes, Matías, 2024. "On the continuity of the Walras correspondence in distributional economies with an infinite-dimensional commodity space," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 61-69.
    19. Konrad Podczeck, 2001. "On Core-Walras (Non-) Equivalence for Economies with a Large Commodity Space," Vienna Economics Papers 0107, University of Vienna, Department of Economics.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

    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:spr:joecth:v:9:y:1997:i:3:p:385-426. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.