Equilibrium existence in the linear model: Concave versus convex transportation costs

Abstract

We focus on the general linear-quadratic transportation costs in the linear model. Earlier results have shown that no pure-strategy price equilibrium exists for whatever firm locations in this context. Since there is no price equilibrium for the whole market, our first objective is to calculate the feasible equilibrium region with concave costs. A crucial change of variables allows us to explicitly calculate the necessary conditions to obtain the feasible equilibrium regions. Finally, we compare the equilibrium regions with both the concave and the convex cases and find that the feasible region with convex costs is bigger than that with concave costs.