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Existence of an Equilibrium in a Competitive Economy with Indivisibilities and Money

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  • van der Laan, G.
  • Talman, A.J.J.

    (Tilburg University, Center For Economic Research)

  • Yang, Z.F.

Abstract

In this paper we introduce a model of an exchange economy with indivisible goods and money.There are nitely many agents each of whom owns one unit of each of nitely many di erent types of indivisible goods and certain amount of money. Each type of indivisible good is subject to quality di erentiation.We demonstrate that under fairly mild conditions on demand the economy has a price equilibrium.The proof is based on a generalization of the well-known lemma of Knaster, Kuratowski and Mazurkiewicz (KKM) in combinatorial topology.The results in the paper generalize those of Gale in case of just one indivisible good present in the economy.
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Suggested Citation

  • van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 1996. "Existence of an Equilibrium in a Competitive Economy with Indivisibilities and Money," Discussion Paper 1996-35, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:d6a39049-ea90-4a33-97c9-b01aea574df8
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    References listed on IDEAS

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    1. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    2. 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.
    3. 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.
    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. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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    Citations

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    Cited by:

    1. Koshevoy, Gleb A. & Talman, Dolf, 2006. "Competitive equilibria in economies with multiple indivisible and multiple divisible commodities," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 216-226, April.
    2. Z. Yang, 2001. "An Intersection Theorem on an Unbounded Set and Its Application to the Fair Allocation Problem," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 429-443, August.
    3. Saitoh, Hiroki, 2004. "Existence of positive equilibrium price vectors in indivisible goods markets: a note," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 109-112, July.
    4. 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.
    5. Klemperer, Paul & Baldwin, Elizabeth & Edhan, Omer & Jagadeesan, Ravi & Teytelboym, Alexander, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," CEPR Discussion Papers 14926, C.E.P.R. Discussion Papers.
    6. Koshevoy, G.A. & Talman, A.J.J., 2006. "Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money," Other publications TiSEM 130306fe-6e3c-499c-b776-c, Tilburg University, School of Economics and Management.
    7. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 1999. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible, Indivisible Commodities and Linear Production Technologies," Other publications TiSEM e7e05539-3fab-4998-818d-0, Tilburg University, School of Economics and Management.
    8. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2002. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies," Journal of Economic Theory, Elsevier, vol. 103(2), pages 411-428, April.
    9. Ning Sun & Zaifu Yang, 2008. "A Double-Track Auction for Substitutes and Complements," KIER Working Papers 656, Kyoto University, Institute of Economic Research.
    10. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Market allocation of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 457-466, December.
    11. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    12. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2002. "Existence and welfare properties of equilibrium in an exchange economy with multiple divisible and indivisible commodities and linear production," Other publications TiSEM 5a5610bf-4f85-4a25-963c-c, Tilburg University, School of Economics and Management.
    13. Danilov, Vladimir & Koshevoy, Gleb & Murota, Kazuo, 2001. "Discrete convexity and equilibria in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 251-273, May.
    14. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September.
    15. Yang, Zaifu, 2003. "A competitive market model for indivisible commodities," Economics Letters, Elsevier, vol. 78(1), pages 41-47, January.
    16. 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.
    17. Z. F. Yang, 2000. "Multipermutation-Based Intersection Theorem and Its Applications," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 477-487, February.
    18. Satoru Fujishige & Zaifu Yang, 2020. "A Universal Dynamic Auction for Unimodular Demand Types: An Efficient Auction Design for Various Kinds of Indivisible Commodities," Discussion Papers 20/08, Department of Economics, University of York.

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