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Competitive Equilibria in Economies with Multiple Divisible and Multiple Divisible Commodities

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  • Koshevoy, G.A.
  • Talman, A.J.J.

    (Tilburg University, Center for Economic Research)

Abstract

In this paper we consider a general equilibrium model with a finite number of divisible and indivisible commodities.In models with indivisibilities it is typically assumed that there is only one perfectly divisible good, which serves as money.The presence of money in the model is used to transfer the value of certain amounts of indivisible goods.For such economies with one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity.For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model.In the models to be presented in this paper we allow for multiple divisible commodities and a finite number of producers with non-increasing returns to scale technologies.Convexity is replaced by pseudoconvexity, while the indivisible parts of individual demands and supply should belong to some class of discrete convexity.In the first model money is present.Money is strictly desired by the consumers like in the other models, is indispensable for production and enough money should be present in the economy.To guarantee existence of a general equilibrium individual demands and supplies should be products of divisible and indivisible parts.In the second model there is no money, but at least one linear production technology is present in order to produce the divisible goods.Individual endowments being sufficienly large for production guarantee 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 2002-71.

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Date of creation: 2002
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Handle: RePEc:dgr:kubcen:200271

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Keywords: commodities; money; general equilibrium;

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References

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  1. Garratt, Rod, 1995. "Decentralizing Lottery Allocations in Markets with Indivisible Commodities," Economic Theory, Springer, vol. 5(2), pages 295-313, March.
  2. Karl Shell & Randall Wright, 2010. "Indivisibilities, Lotteries and Sunspot Equilibria," Levine's Working Paper Archive 2061, David K. Levine.
  3. 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.
  4. 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.
  5. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers 644, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. Martine Quinzii & Carmen Bevia & JosÅ A. Silva, 2003. "Buying Several Indivisible Goods," Working Papers 9720, University of California, Davis, Department of Economics.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  13. Jinpeng Ma, 1998. "Competitive Equilibrium with Indivisibilities," Departmental Working Papers 199809, Rutgers University, Department of Economics.
  14. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
  15. 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.
  16. 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.
  17. Herbert E. Scarf, 1984. "Neighborhood Systems for Production Sets with Indivisibilities," Cowles Foundation Discussion Papers 728, Cowles Foundation for Research in Economics, Yale University.
  18. Tjalling C. Koopmans & Martin J. Beckmann, 1955. "Assignment Problems and the Location of Economic Activities," Cowles Foundation Discussion Papers 4, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Koshevoy, G.A. & Talman, A.J.J., 2006. "Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money," Discussion Paper 2006-51, Tilburg University, Center for Economic Research.

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