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Existence of an equilibrium in a competitive economy with indivisibilities and money

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

    (Tilburg University)

  • Yang, Z.F.

    (Tilburg University)

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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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-73837.

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Date of creation: 1997
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Publication status: Published in Journal of Mathematical Economics (1997) v.28, p.101-109
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-73837

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Web page: http://www.tilburguniversity.edu/

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References

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  1. Mamoru Kaneko, 1980. "The Central Assignment Game and the Assignment Markets," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 563, Cowles Foundation for Research in Economics, Yale University.
  2. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 644, Cowles Foundation for Research in Economics, Yale University.
  3. Kaneko, Mamoru & Yamamoto, Yoshitsugu, 1986. "The existence and computation of competitive equilibria in markets with an indivisible commodity," Journal of Economic Theory, Elsevier, Elsevier, vol. 38(1), pages 118-136, February.
  4. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 8(4), pages 111-128, Fall.
  5. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
  6. 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. Laan, G. van der & 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," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-89376, Tilburg University.
  2. Danilov, Vladimir & Koshevoy, Gleb & Murota, Kazuo, 2001. "Discrete convexity and equilibria in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, Elsevier, vol. 41(3), pages 251-273, May.
  3. Koshevoy, G.A. & Talman, A.J.J., 2006. "Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money," Discussion Paper, Tilburg University, Center for Economic Research 2006-51, Tilburg University, Center for Economic Research.
  4. Koshevoy, G.A. & Talman, A.J.J., 2002. "Competitive Equilibria in Economies with Multiple Divisible and Multiple Divisible Commodities," Discussion Paper, Tilburg University, Center for Economic Research 2002-71, Tilburg University, Center for Economic Research.
  5. 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.
  6. 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.
  7. Ning Sun & Zaifu Yang, 2008. "A Double-Track Auction for Substitutes and Complements," KIER Working Papers, Kyoto University, Institute of Economic Research 656, Kyoto University, Institute of Economic Research.
  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, Elsevier, vol. 103(2), pages 411-428, April.
  9. Laan, G. van der & 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," Discussion Paper, Tilburg University, Center for Economic Research 1999-76, Tilburg University, Center for Economic Research.
  10. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September.
  11. Yang, Zaifu, 2003. "A competitive market model for indivisible commodities," Economics Letters, Elsevier, Elsevier, vol. 78(1), pages 41-47, January.
  12. Saitoh, Hiroki, 2004. "Existence of positive equilibrium price vectors in indivisible goods markets: a note," Mathematical Social Sciences, Elsevier, Elsevier, vol. 48(1), pages 109-112, July.

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