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Buying several indivisible goods

Author

Listed:
  • Carmen Beviá Baeza

    (Universidad Autónoma de Barcelona)

  • José Angel Silva Reus

    (Universidad de Alicante)

Abstract

This paper studies economies where agents exchange indivisible goods and money. Agents havepotencial use for all indivisible goods and the indivisible goods are differentiated. We assume thatagents have quasilinear utilities in money, have sufficiently money endowments to afford anygroup of objects priced below their reservation values, have reservation values which aresubmodular and satisfy the Cardinality Condition. This Cardinality Condition requires that for eachagent the marginal utility of an object only depends on the number of objects to which it is added,not an their characteristics. Under these assumptions, we show that the set of competitiveequilibrium prices is a non empty lattice and that, in any equilibrium, the price of an object isbetween the social value of the object and its second best use.

Suggested Citation

  • 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).
  • Handle: RePEc:ivi:wpasad:1997-27
    as

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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1997-27.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    3. Henry, Claude, 1970. "Indivisibilites dans une Economie d'Echanges. (With English summary.)," Econometrica, Econometric Society, vol. 38(3), pages 542-558, May.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Ning Sun & Zaifu Yang, 2008. "A Double-Track Auction for Substitutes and Complements," KIER Working Papers 656, Kyoto University, Institute of Economic Research.
    3. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 209-222, March.
    4. Alessandra Casella & Aniol Llorente-Saguer & Thomas R. Palfrey, 2012. "Competitive Equilibrium in Markets for Votes," Journal of Political Economy, University of Chicago Press, vol. 120(4), pages 593-658.
    5. Talman, Dolf & Yang, Zaifu, 2009. "A discrete multivariate mean value theorem with applications," European Journal of Operational Research, Elsevier, vol. 192(2), pages 374-381, January.
    6. Yang, Yi-You, 2013. "Competitive equilibrium with indivisible objects," MPRA Paper 74662, University Library of Munich, Germany, revised 19 Oct 2016.
    7. 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.
    8. Ning Sun & Zaifu Yang, 2014. "An Efficient and Incentive Compatible Dynamic Auction for Multiple Complements," Discussion Papers 14/06, Department of Economics, University of York.
    9. 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.
    10. Echenique, Federico, 2007. "Counting combinatorial choice rules," Games and Economic Behavior, Elsevier, vol. 58(2), pages 231-245, February.
    11. Goossens D.R. & Müller R. & Spieksma F.C.R., 2007. "Matrix bids in combinatorial auctions: expressiveness and micro-economic properties," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. 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.
    13. Hatfield, John William & Plott, Charles R. & Tanaka, Tomomi, 2016. "Price controls, non-price quality competition, and the nonexistence of competitive equilibrium," Games and Economic Behavior, Elsevier, vol. 99(C), pages 134-163.
    14. Sanchez-Soriano, Joaquin & Lopez, Marco A. & Garcia-Jurado, Ignacio, 2001. "On the core of transportation games," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 215-225, March.
    15. Yang, Yi-You, 2015. "On the Maximal Domain Theorem," MPRA Paper 67265, University Library of Munich, Germany.
    16. 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.
    17. Meertens, M.A., 2005. "On balancedness of superadditive games and price equilibria in exchange economies," Economics Letters, Elsevier, vol. 86(1), pages 43-49, January.
    18. Ning Sun & Zaifu Yang, 2014. "An Efficient and Incentive Compatible Dynamic Auction for Multiple Complements," Journal of Political Economy, University of Chicago Press, vol. 122(2), pages 422-466.
    19. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September.
    20. Carmen Bevié, 2009. "Manipulation Games in Economics with Indivisible Goods," Working Papers 371, Barcelona Graduate School of Economics.
    21. 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," Discussion Paper 1999-76, Tilburg University, Center for Economic Research.
    22. Yang, Zaifu, 2003. "A competitive market model for indivisible commodities," Economics Letters, Elsevier, vol. 78(1), pages 41-47, January.
    23. 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.
    24. Talman, A.J.J. & Yang, Z.F., 2009. "A discrete multivariate mean value theorem with applications," Other publications TiSEM d48f2a19-dcc2-40e4-9085-5, Tilburg University, School of Economics and Management.
    25. Danilov, V. & Koshevoy, G. & Lang, C., 2013. "Equilibria in Markets with Indivisible Goods," Journal of the New Economic Association, New Economic Association, vol. 18(2), pages 10-34.

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