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Equilibria with indivisible goods and package-utilities

Author

Listed:
  • Danilov, Vladimir I.

    (Sonderforschungsbereich 504)

  • Koshevoy, Gleb A.

    (Sonderforschungsbereich 504)

  • Lang, Christine

    (Sonderforschungsbereich 504)

Abstract

We revisit the issue of existence of equilibrium in economies with indivisible goods and money, in which agents may trade many units of items. In [5] it was shown that the existence issue is related to discrete convexity. Classes of discrete convexity are characterized by the unimodularity of the allowable directions of one-dimensional demand sets. The class of graphical unimodular system can be put in relation with a nicely interpretable economic property of utility functions, the Gross Substitutability property. The question is still open as to what could be the possible, challenging economic interpretations and relevant examples of demand structures that correspond to other classes of discrete convexity. We consider here an economy populated with agents having a taste for complementarity; their utilities are generated by compounds of specific items grouped in 'packages'. Simple package-utilities translate in a straightforward fashion the fact that the items forming a package are complements. General package-utilities are obtained as the convolution (or aggregation) of simple packageutilities. We prove that if the collection of packages of items, that generates the utilities of agents in the economy, is unimodular then there exists a competitive equilibrium. Since any unimodular set of vectors can be implemented as a collection of 0-1 vectors ([3]), we get examples of demands for each class of discrete convexity.

Suggested Citation

  • Danilov, Vladimir I. & Koshevoy, Gleb A. & Lang, Christine, 2008. "Equilibria with indivisible goods and package-utilities," Sonderforschungsbereich 504 Publications 08-30, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    • Handle: RePEc:xrs:sfbmaa:08-30
    Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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    Cited by:

    1. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.

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