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Verifying gross substitutability


  • Jos A.M. Potters

    () (Department of Mathematics, Nijmegen University, P.O. Box 9010,6500 GL Nijmegen,THE NETHERLANDS)

  • Anita van Gellekom

    () (Department of Mathematics, Nijmegen University, P.O. Box 9010,6500 GL Nijmegen,THE NETHERLANDS)

  • Hans Reijnierse

    () (Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, THE NETHERLANDS .)


In labor market models as well as in exchange economies with indivisible goods gross substitutability is used as a property to guarantee the existence of competitive equilibria. This paper develops an easy way to check gross substitutability for utility functions concerning a finite set of indivisible goods (or employees) and money. Concavity is one of the conditions that has to be satisfied. Only one other, but similar, type of relation must be checked to guarantee gross substitutability.

Suggested Citation

  • Jos A.M. Potters & Anita van Gellekom & Hans Reijnierse, 2002. "Verifying gross substitutability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 767-776.
  • Handle: RePEc:spr:joecth:v:20:y:2002:i:4:p:767-776
    Note: Received: 21 August 2000; revised version: 28 November 2001

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    Cited by:

    1. Ostrovsky, Michael & Paes Leme, Renato, 2015. "Gross substitutes and endowed assignment valuations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    2. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    3. Yang, Yi-You, 2013. "Competitive equilibrium with indivisible objects," MPRA Paper 74662, University Library of Munich, Germany, revised 19 Oct 2016.
    4. Yang, Yi-You, 2013. "A classification approach to Walrasian equilibrium with substitutability," MPRA Paper 47945, University Library of Munich, Germany.
    5. 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).
    6. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
    7. repec:eee:gamebe:v:106:y:2017:i:c:p:294-316 is not listed on IDEAS
    8. repec:jmi:articl:jmi-v1i1a5 is not listed on IDEAS
    9. repec:eee:gamebe:v:104:y:2017:i:c:p:456-467 is not listed on IDEAS
    10. Kazuo Murota & Yu Yokoi, 2015. "On the Lattice Structure of Stable Allocations in a Two-Sided Discrete-Concave Market," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 460-473, February.
    11. Yang, Yi-You, 2013. "Competitive equilibrium for indivisible objects," MPRA Paper 57637, University Library of Munich, Germany, revised 28 Jul 2014.

    More about this item


    Gross substitutability; Competitive equilibrium; Labor market; Exchange economies with indivisible goods.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • J40 - Labor and Demographic Economics - - Particular Labor Markets - - - General


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