Multi-dimensional Product Differentiation

Abstract

We analyze product differentiation in a multi-dimensional model with non-uniform consumer distribution. The level of product differentiation is measured by both unit transport costs and firm locations. Our analysis concerns both measures. First, fixing firms' locations, we show that equilibrium prices can increase or decrease with unit transport cost. The overall result depends on the interplay of a shifting effect and a rotating effect -- the latter exists only in multi-dimensional models. Second, fixing unit transport costs, we find that under non-uniform distribution, there may exist no equilibrium where firms maximize differentiation on one dimension but minimize differentiation on other dimensions. Instead, there may exist equilibrium where firms choose intermediate locations, contrary to the common findings in existing studies which assume uniform distribution.

Keywords: Multi-dimensional product differentiation, Unit transport cost, Location choice

JEL Classification: D43, L13