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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
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    Citations

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    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. 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.
    3. 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.
    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. Achille Basile & Maria Gabriella Graziano & Ciro Tarantino, 2018. "Coalitional fairness with participation rates," Journal of Economics, Springer, vol. 123(2), pages 97-139, March.
    6. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    7. 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.
    8. 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.
    9. 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.
    10. 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

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