Bounds on the Profitability of a Durable Good Monopolist

A durable good is a long-lasting good that can be consumed repeatedly over time, and a duropolist is a monopolist in the market of a durable good. Theoretically, less is known about durable goods than their more well-studied counterparts, consumable and perishable goods. It was quite startling, therefore, when Ronald Coase (1972) conjectured that a duropolist has no monopoly power at all! Specifically, a duropolist who lacks commitment power cannot sell the good above the competitive price if the time between periods approaches zero. The Coase conjecture was first proved by Gul et al. (1986) under an infinite time horizon model with non-atomic consumers. Remarkably, the situation changes dramatically for atomic consumers and an infinite time horizon. Bagnoli et al. (1989) showed the existence of a subgame perfect Nash equilibrium where the duropolist extracts all the consumer surplus, provided the discount factor is large enough. Thus, for atomic consumers, the duropolist may have perfect price discriminatory power! Observe that, in these cases, duropoly profits are either arbitrarily smaller or arbitrarily larger than the corresponding static monopoly profits – the profit a monopolist for an equivalent consumable good could generate. Neither situation accords in practice with the profitability of durable good producers. Indeed we show that the results of Gul et al. (1986) and Bagnoli et al. (1989) are driven by the infinite time horizons. For finite time horizons, duropoly profits for any equilibrium satisfying the standard skimming property closely relate to static monopoly profits. In particular, for atomic agents, we prove that duropoly profits are always at least as large as static monopoly profits, but never exceed double the static monopoly profits.