Regularity properties of optimal transportation problems arising in hedonic pricing models
Department of Mathematical and Statistical Sciences, 632 CAB,
University of Alberta, Edmonton, T6G 2G1
Revised: 13 July 2012
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.
Mathematics Subject Classification: 35J15 / 49N60 / 58E17 / 91B68
Key words: Optimal transportation / hedonic pricing / Ma–Trudinger–Wang curvature / matching / Monge–Kantorovich / regularity of solutions
© EDP Sciences, SMAI, 2013