Durable Goods Monopoly with Quality Improvements over Time

We examine a dynamic, durable goods model. A monopolist faces two types of consumers who value the monopolist’s goods differently. The quality of the good improves over time and an improvement is only valuable to consumers if they have previous improvements. In each period, the monopolist can sell any possible bundle of previous improvements along with the current improvement. The firm cannot condition its prices or bundles that it offers an individual consumer. Thus, we are in the anonymous purchasing framework as defined by Fudenberg and Tirole (1998). Furthermore, the firm cannot commit to either future prices or bundles. Our main application is the software market, but the model also addresses issues important in other markets such as those for video games. We characterize the subgame perfect Markov equilibrium. Our results include the following. The equilibrium will exhibit cycles in the sense that the distance between the qualities of goods held by high and low types will grow from an initial level and then the low types will “catch-up” to the quality distance at the beginning of a cycle. This generates an underlying stationarity of the equilibrium. We interpret this catching up phase as an introduction of a new generation of software as opposed to an upgrade. We also show that the equilibrium can be “non-Coasian” in the following sense: there can be periods where there are no sales of an improvement to the low value consumers in a period, even though all high value consumers already possess the improvement. The reason that the firm may engage in such a strategy is that not selling to low value consumers today makes it more costly for high value consumers to mimic low value consumer’s behavior and obtain information rents. This allows the firm to charge a higher price for the current improvement to the high value consumers. In other words, the intertemporal incentive compatibility constraint for the high value consumers is relaxed by not selling to low value consumers. We relate our work to the bundling literature where consumers can have many different preference parameters.