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Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness

  • Pierre-Andre Chiappori
  • Robert McCann

    (Institute for Fiscal Studies and University of Toronto)

  • Lars Nesheim

    ()

    (Institute for Fiscal Studies)

Hedonic pricing with quasilinear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness of the stable match. An appendix resolves an old problem (# 111) of Birkhoff in probability and statistics [5], by giving a necessary and sufficient condition on the support of a joint probability to guarantee extremality among all joint measures with the same marginals.

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File URL: http://cemmap.ifs.org.uk/wps/cwp2307.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP23/07.

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Date of creation: Sep 2007
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Handle: RePEc:ifs:cemmap:23/07
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  1. Neil E. Gretsky & Joseph M. Ostroy & William R. Zame, 1990. "The Nonatomic Assignment Model," UCLA Economics Working Papers 605, UCLA Department of Economics.
  2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  3. James Heckman & Rosa Matzkin & Lars Nesheim, 2005. "Nonparametric estimation of nonadditive hedonic models," CeMMAP working papers CWP03/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Gretsky, Neil E. & Ostroy, Joseph M. & Zame, William R., 1999. "Perfect Competition in the Continuous Assignment Model," Journal of Economic Theory, Elsevier, vol. 88(1), pages 60-118, September.
  5. Carlier, Guillaume, 2003. "Duality and existence for a class of mass transportation problems and economic applications," Economics Papers from University Paris Dauphine 123456789/6443, Paris Dauphine University.
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