Price cycles in markets with customer recognition

Given that having bought earlier front a firm. reveals something about the customers, the firms can try to use this piece of information by better fitting their market practices with respect to their previous customers. I consider an infinitely lived monopolist selling to a market where demand is composed of overlapping generations of forward-looking consumers. The monopolist can price differently to its previous customers than to its new customers. The new customers can either have chosen not to buy the product in the previous period or be new in the market. The main result is that, without full market coverage, the equilibrium involves cycles in the price being offered to the new customers. The monopolist is worse off than if it could not recognize its previous customers. The impact of durable goods, long-term contracts, and age recognition is also considered.