Multi-Dimensional Product Differentiation

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 firms’ locations. Our analysis concerns both measures. First, fixing firms’ locations, we show that equilibrium prices can increase or decrease with unit transport costs. 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 an equilibrium where firms choose intermediate locations, contrary to common findings in existing studies which assume uniform distribution.