Personalized pricing when consumers can purchase multiple items

We discuss the effect of personalized pricing on profits and welfare in a Hotelling model in which consumers can simultaneously purchase from both firms. We have the following results. If the additional gain from the second purchase (henceforth, the additional gain) is small, personalized pricing improves consumer welfare but harms firms' profits. If the additional gain is intermediate, personalized pricing improves consumer welfare and firms' profits. Finally, if the additional gain is large, personalized pricing improves firms' profits but harms consumer welfare. The latter results contrast with that under the single-unit purchase assumption in the literature: personalized pricing improves consumer welfare but harms firms' profits. We extend the model by assuming that firms can endogenously choose one of the pricing policies: uniform or personalized pricing. We show that both firms choose personalized pricing in any case and uniform pricing under some parameters; multiple equilibria can co-exist in those parameters. Our results imply that when we discuss the impact of personalized pricing on profits and welfare, we need to consider the propensity of consumers' multistore shopping.