Regularity properties of optimal transportation problems arising in hedonic pricing models

TL;DR

This paper analyzes the regularity properties of optimal transportation surplus functions in hedonic pricing models, deriving conditions for their curvature and providing explicit examples satisfying these conditions.

Contribution

It introduces a formula for the Ma-Trudinger-Wang curvature of surplus functions and provides explicit examples satisfying the (A3w) condition in hedonic pricing.

Findings

Derived a formula for the Ma-Trudinger-Wang curvature.

Provided explicit examples of surplus functions satisfying (A3w).

Showed the space of equilibrium contracts has maximal dimension.

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 \textbf{(A3w)}. We use this to give explicit new examples of surplus functions satisfying \textbf{(A3w)}, of the form $b(x,y)=H(x+y)$ where $H$ is a convex function on $\mathbb{R}^n$. We also show that the space of equilibrium contracts in the hedonic pricing model has the maximal possible dimension, a result of potential economic interest.