Intertemporal allocation with unknown discounting

Abstract

We consider the problem faced by a durable-good monopolist who can allocate a single good at any time, but is uncertain of a buyer's values and temporal preferences for receiving the good. We derive conditions under which it is optimal for the monopolist to ignore the uncertainty about the buyer's discount factor and allocate immediately via a single first-period price. Under one condition, the seller optimally offers a single first-period price if she would weakly raise this price upon learning that the buyer cannot be too impatient (Corollary 2). A related condition states that the single first-period price is optimal if buyer types with higher discount factors have stochastically higher values (Corollary 3). These conditions also apply when sellers face ambiguity regarding the buyer's discount factor. Our results provide a novel justification for ignoring heterogeneous discount factors when the seller is incompletely informed about buyer's temporal preferences.