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.
Mots-clés : optimal transportation, hedonic pricing, Ma-Trudinger-Wang curvature, matching, Monge-Kantorovich, regularity of solutions
@article{COCV_2013__19_3_668_0,
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://www.numdam.org/articles/10.1051/cocv/2012027/}
}
TY - JOUR AU - Pass, Brendan TI - Regularity properties of optimal transportation problems arising in hedonic pricing models JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 668 EP - 678 VL - 19 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012027/ DO - 10.1051/cocv/2012027 LA - en ID - COCV_2013__19_3_668_0 ER -
%0 Journal Article %A Pass, Brendan %T Regularity properties of optimal transportation problems arising in hedonic pricing models %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 668-678 %V 19 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012027/ %R 10.1051/cocv/2012027 %G en %F COCV_2013__19_3_668_0
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. http://www.numdam.org/articles/10.1051/cocv/2012027/
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