Multi-dimensional price discrimination

We examine the profitability and welfare implications of price discrimination in a multi-dimensional model. First, when firms price discriminate on one and the same dimension, uniform price lies in between discriminatory prices and price discrimination raises profits relative to uniform pricing. This is in contrast to common findings in existing one-dimensional models featuring best-response asymmetry, suggesting that price discrimination can have qualitatively different implications in one- and multi-dimensional models. Second, price discrimination on one and the same dimension is the likely outcome when price discrimination decisions are endogenized using a two-stage discrimination-then-pricing game. Correspondingly, an observation of one-dimensional price discrimination in practice does not necessarily indicate that the underlying model should be one-dimensional.