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 Alberta, Canada
pass@ualberta.ca.

Received: 2 February 2012
Revised: 13 July 2012

Abstract

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.