Vertically Differentiated Durable Goods Monopoly: Coexistence of Contrasting Markov-Perfect Equilibria

A monopolist sells over an infinite number of periods a durable good (available at different quality levels) to customers who differ in their preference for quality. The firm is able in each period to exercise second-degree price discrimination to new customers, i.e., to offer a menu of choices. We study the case where it cannot commit to future menus. We show that the static Mussa-Rosen equilibrium, where all trade takes place in the initial period and the monopolist obtains its full-commitment profits, is always a Markov-Perfect equilibrium of this game. However we also show that there exists another MPE with strongly Coasian features in which market coverage is progressive and profits are below their full commitment level, vanishing in the limit when the minimum time between two different offers becomes infinitesimal.