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Competitive equilibria in economies with multiple indivisible and multiple divisible commodities

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  • Koshevoy, Gleb A.
  • Talman, Dolf

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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  • 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.
  • Handle: RePEc:eee:mateco:v:42:y:2006:i:2:p:216-226
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    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. 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.
    3. 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.
    4. 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.
    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. Garratt, Rod, 1995. "Decentralizing Lottery Allocations in Markets with Indivisible Commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 295-313, March.
    7. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    8. Scarf, Herbert E, 1986. "Neighborhood Systems for Production Sets with Indivisibilities," Econometrica, Econometric Society, vol. 54(3), pages 507-532, May.
    9. 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.
    10. 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.
    11. 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.
    12. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
    13. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    14. 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.
    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. Shell, Karl & Wright, Randall, 1993. "Indivisibilities, Lotteries, and Sunspot Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-17, January.
    17. 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.
    18. 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.
    19. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part II: The Case of Two Activities," Econometrica, Econometric Society, vol. 49(2), pages 395-423, March.
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    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. 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.

    More about this item

    JEL classification:

    • D2 - Microeconomics - - Production and Organizations
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D6 - Microeconomics - - Welfare Economics
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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