Economic Theory

, Volume 42, Issue 2, pp 275–315 | Cite as

Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types



We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplier types and qualities can be either discrete of continuous, in which case they are allowed to be multidimensional. Prices play a double role: they keep some agents out of the market, and they match the remaining ones pairwise. We define equilibrium prices and equilibrium distributions, and we prove that equilibria exist, we investigate to what extend equilibrium prices and distributions are unique, and we prove that equilibria are efficient. In the particular case when there is a continuum of types, and a generalized Spence–Mirrlees condition is satisfied, we prove the existence of a pure equilibrium, where demand distributions are in fact demand functions, and we show to what extent it is unique. The proofs rely on convex analysis, and care has been given to illustrate the theory with examples.


Hedonic goods Competitive markets Equilibrium Optimal transportation 

JEL Classification

C62 C78 D41 D50 


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  1. Becker G.: A study of the allocation of time. Econ J 75, 493–517 (1965)CrossRefGoogle Scholar
  2. Carlier G.: Duality and existence for a class of mass transportation problems and economic applications. Adv Math Econ 5, 1–21 (2003)Google Scholar
  3. Court, L.: Entrepreneurial and consumer demand theories for commodity spectra. Econometrica 9, pp. 135–62 and 241–97 (1941)Google Scholar
  4. Ekeland I., Heckman J., Nesheim L.: Identification and estimation of hedonic models. J Polit Econ 112(S1), 60–109 (2004)CrossRefGoogle Scholar
  5. Ekeland I.: An optimal matching problem. ESAIM Control Optim Calculus Var 11(1), 57–71 (2005)CrossRefGoogle Scholar
  6. Gretzki N., Ostroy J., Zame W.: The nonatomic assignment model. Econ Theory 2, 103–127 (1992)CrossRefGoogle Scholar
  7. Gretzki N., Ostroy J., Zame W.: Perfect competition in the continuous assignment model. J Econ Theory 88, 60–118 (1999)CrossRefGoogle Scholar
  8. Griliches, Z. ed.: Price indexes and quality change. London: Harvard University Press (1971)Google Scholar
  9. Houthakker H.: Compensated changes in quantities and qualities consumed. Rev Econ Stud 19(3), 155–164 (1952)CrossRefGoogle Scholar
  10. Koopmans T., Beckmann M.: Assignment problems and the location of economic activities. Econometrica 25, 53–76 (1957)CrossRefGoogle Scholar
  11. Lancaster K.: A new approach to consumer theory. J Polit Econ 74(2), 132–157 (1966)CrossRefGoogle Scholar
  12. Muth R.: Household production and consumer demand function. Econometrica 39, 699–708 (1966)CrossRefGoogle Scholar
  13. Ramachandran, R., Ruschendorf, L.: Assignment models for constrained marginals and restricted markets. In: Distributions with given marginals and statistical modelling, pp. 195–209. Dordrecht: Kluwer (2002)Google Scholar
  14. Mussa M., Rosen S.: Monopoly and product quality. J Econ Theory 18, 301–317 (1978)CrossRefGoogle Scholar
  15. Rochet J.C., Choné P.: Ironing, sweeping and multidimensional screening. Econometrica 66(4), 783–826 (1998)CrossRefGoogle Scholar
  16. Rosen, S.: Hedonic prices and implicit markets: product differentiation in pure competition. J Polit Econ (82), pp. 34–55 (1974)Google Scholar
  17. Shapley L.S., Shubik M.: The assignment game I: the core. Int J Game Theory 1, 111–130 (1972)CrossRefGoogle Scholar
  18. Villani, C.: Topics in mass transportation. Graduate Studies in Mathematics, AMS (2003)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Canada Research Chair in Mathematical EconomicsUniversity of British ColumbiaVancouverCanada

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