Geodesic
Regularity properties of optimal transportation problems arising in hedonic pricing models
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 668-678

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We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma-Trudinger-Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form b(x,y) = H(x + y) where H is a convex function on ℝn. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely continuous with respect to Lebesgue measure, implying that buyers are fully separated by the contracts they sign, a result of potential economic interest.

DOI : 10.1051/cocv/2012027
Classification : 35J15, 49N60, 58E17, 91B68
Keywords: optimal transportation, hedonic pricing, Ma-Trudinger-Wang curvature, matching, Monge-Kantorovich, regularity of solutions 
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     author = {Pass, Brendan},
     title = {Regularity properties of optimal transportation problems arising in hedonic pricing models},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {668--678},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {3},
     year = {2013},
     doi = {10.1051/cocv/2012027},
     mrnumber = {3092356},
     zbl = {1271.91053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012027/}
}
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Pass, Brendan. Regularity properties of optimal transportation problems arising in hedonic pricing models. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 668-678. doi: 10.1051/cocv/2012027

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