Behavior-Based Price Discrimination by a Patient Seller

We investigate a model in which one seller and one buyer trade in each of two periods. The buyer has demand for one unit of a non-durable object per period. The buyer's reservation value for the good is private information and is the same in both periods. The seller commits to prices in each of two periods. Prices in the second period may depend on the buyer's first-period behavior. Unlike the equal discount factor case studied in earlier papers, we show that when the seller is more patient than the buyer, second-period prices increase after a purchase. In particular, the optimal dynamic pricing scheme is not a repetition of the optimal static pricing scheme.