Dynamic Price Discrimination and Quality Provision Based on Purchase History

This paper develops a general two-period model of product line pricing with customer recognition. Specifically, we consider a monopolist who can sell vertically differentiated products over two periods to heterogeneous consumers. Each consumer demands one unit of the product in each period. In the second period, the monopolist can condition the price-quality offers on the observed purchasing behavior in the first period. In this setup, the monopolist can price discriminate consumers not only by quality, but also by purchase history. Several interesting results are derived. First, we fully characterize the monopolist's optimal pricing strategy when there are two types of consumers, and a simple condition is given to determine whether the monopolist will price discriminate by quality in the first period. We compare it to the case when there is no customer recognition or the firm is able to commit to its future actions. When the type space is a continuum, we show that there is no fully separating equilibrium, and some properties of the optimal contracts (price-quality pairs) are characterized within the class of partitional PBE.