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Existence of an Equilibrium in a General Competitive Exchange Economy with Indivisible Goods and Money

Author

Listed:
  • Satoru Fujishige

    () (Division of Systems Science, Graduate School of Engineering Science, Osaka University)

  • Zaifu Yang

    () (Cowles Foundation for Research in Economics, Yale University
    Faculty of Business Administration, Yokohama National University)

Abstract

We introduce a general competitive exchange economy with indivisible goods and money. There are finitely many agents and finitely many indivisible goods. Each agent is initially endowed with several units of each indivisible good and certain amount of money. Money is treated as a perfectly divisible good. The agents¡¯ preferences depend on the bundle of indivisible goods and the quantity of money they consume. Preferences are quite general and are not required to be quasilinear in money. We derive a necessary and sufficient condition for the existence of a competitive equilibrium in the economy. The model and the existence results we provide here unify and extend most models and existence results that have appeared in the literature.

Suggested Citation

  • Satoru Fujishige & Zaifu Yang, 2002. "Existence of an Equilibrium in a General Competitive Exchange Economy with Indivisible Goods and Money," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 135-147, May.
  • Handle: RePEc:cuf:journl:y:2002:v:3:i:1:p:135-147
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    References listed on IDEAS

    as
    1. Bevia, Carmen & Quinzii, Martine & Silva, Jose A., 1999. "Buying several indivisible goods," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 1-23, January.
    2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, October.
    3. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 1997. "Existence of an equilibrium in a competitive economy with indivisibilities and money," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 101-109, August.
    4. Kaneko, Mamoru & Yamamoto, Yoshitsugu, 1986. "The existence and computation of competitive equilibria in markets with an indivisible commodity," Journal of Economic Theory, Elsevier, vol. 38(1), pages 118-136, February.
    5. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.
    6. Scarf, Herbert E, 1986. "Neighborhood Systems for Production Sets with Indivisibilities," Econometrica, Econometric Society, vol. 54(3), pages 507-532, May.
    7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    8. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    9. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    10. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    11. Danilov, V. & Koshevoy, G. & Lang, C., 2013. "Equilibria in Markets with Indivisible Goods," Journal of the New Economic Association, New Economic Association, vol. 18(2), pages 10-34.
    12. Yang, Zaifu, 2000. "Equilibrium in an exchange economy with multiple indivisible commodities and money," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 353-365, April.
    13. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers 644, Cowles Foundation for Research in Economics, Yale University.
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    More about this item

    Keywords

    Indivisibility; Equilibrium; Fixed point; Discrete optimization;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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