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

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  • Pierre-Andre Chiappori
  • Robert McCann

    (Institute for Fiscal Studies and University of Toronto)

  • Lars Nesheim

    ()
    (Institute for Fiscal Studies)

Abstract

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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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. 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.
  2. 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.
  3. 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.
  4. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer, vol. 2(1), pages 103-27, January.
  5. 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.
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Cited by:
  1. James J. Heckman & Rosa L. Matzkin & Lars Nesheim, 2009. "Nonparametric Identification and Estimation of Nonadditive Hedonic Models," NBER Working Papers 15226, National Bureau of Economic Research, Inc.
  2. Seungjin Han & Shintaro Yamaguchi, 2013. "Compensating Wage Differentials in Stable Job Matching Equilibrium," Global COE Hi-Stat Discussion Paper Series gd12-285, Institute of Economic Research, Hitotsubashi University.
  3. Pierre-André Chiappori & Sonia Oreffice & Climent Quintana-Domeque, 2012. "Matching with a Handicap: The Case of Smoking in the Marriage Market," CHILD Working Papers Series 8, Centre for Household, Income, Labour and Demographic Economics (CHILD) - CCA.
  4. André De Palma & Soumyanetra Munshi, 2012. "Multi-player, Multi-prize, Imperfectly Discriminating Contests," Working Papers hal-00683688, HAL.
  5. Pierre-Andre Chiappori & Costas Meghir, 2014. "Intrahousehold Inequality," Cowles Foundation Discussion Papers 1948, Cowles Foundation for Research in Economics, Yale University.
  6. Blanchet, Adrien & Carlier, Guillaume, 2012. "Optimal Transport and Cournot-Nash Equilibria," TSE Working Papers 12-321, Toulouse School of Economics (TSE).
  7. G. Carlier & I. Ekeland, 2010. "Matching for teams," Economic Theory, Springer, vol. 42(2), pages 397-418, February.
  8. Rachel Griffith & Lars Nesheim, 2010. "Estimating households' willingness to pay," CeMMAP working papers CWP24/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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