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Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money

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  • Koshevoy, G.A.
  • Talman, A.J.J.

    (Tilburg University, Center for Economic Research)

Abstract

A general equilibrium model is considered with multiple divisible and multiple indivisible commodities.In models with indivisibles it is always assumed that an indivisible commodity, called money, is present that is used to transfer the value of certain amounts of indivisible goods.For these economies with a finite number of divisible and indivisible goods and money and without producers it is well understood that a general equilibrium exists if the individual demands and supplies for the indivisibele goods belong to a same class of discrete convexity.In this paper we a model with multiple divisible and multiple undivisible commodities, in which none of the divisible goods may serve as money.Moreover, there are a finite number of producers owning a non-increasing returns to scale technology.One of the producesrs is assumed to have a linear production technology in order to produce divisible goods. Individual endowments being sufficienly large for production and discrete convexity guarantees the existence of a competitive equilibrium.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-51.

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Date of creation: 2006
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Handle: RePEc:dgr:kubcen:200651

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Keywords: indivisible commodities; divisible commodities; discrete convexity; competitive equilibrium;

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References

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  1. Laan, G. van der & 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.
  2. Koshevoy, G.A. & Talman, A.J.J., 2002. "Competitive Equilibria in Economies with Multiple Divisible and Multiple Divisible Commodities," Discussion Paper 2002-71, Tilburg University, Center for Economic Research.
  3. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers 644, Cowles Foundation for Research in Economics, Yale University.
  4. Garratt, Rod & Qin, Cheng-Zhong, 1996. "Cores and Competitive Equilibria with Indivisibilities and Lotteries," Journal of Economic Theory, Elsevier, vol. 68(2), pages 531-543, February.
  5. 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.
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  7. 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.
  8. 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 urn:nbn:nl:ui:12-89376, Tilburg University.
  9. Carmen Beviá Baeza & José Angel Silva Reus, 1997. "Buying several indivisible goods," Working Papers. Serie AD 1997-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
  11. Garratt, Rod, 1995. "Decentralizing Lottery Allocations in Markets with Indivisible Commodities," Economic Theory, Springer, vol. 5(2), pages 295-313, March.
  12. 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.
  13. 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.
  14. Herbert E. Scarf, 1984. "Neighborhood Systems for Production Sets with Indivisibilities," Cowles Foundation Discussion Papers 728, Cowles Foundation for Research in Economics, Yale University.
  15. 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.
  16. 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.
  17. 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.
  18. 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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