We analyze a dynamic game between consumers and the sole seller of a durable good. Unlike previous analyses, we assume that there exists a finite collection of buyers rather than a continuum. None of the main conclusions of the literature on durable-goods monopoly survives this change in assumption. Coase's conjecture that a durable-goods monopolist cannot earn supracompetitive profits in the continuous-time limit, Bulow's proposition that renting a durable is always more profitable than selling it, and Stokey's proposition that precommitting to a time path of prices is always optimal are all false when the set of buyers is finite. Thus the assumption of a continuum of consumers--so innocuous and useful a simplification in other contexts--has proved misleading in the context of durable-goods monopoly.

We analyze a dynamic game between consumers and the sole seller of a durable good. Unlike previous analyses, we assume that there exists a finite collection of buyers rather than a continuum. None of the main conclusions of the literature on durable-goods monopoly survives this change in assumption. Coase's conjecture that a durable-goods monopolist cannot earn supracompetitive profits in the continuous-time limit, Bulow's proposition that renting a durable is always more profitable than selling it, and Stokey's proposition that precommitting to a time path of prices is always optimal are all false when the set of buyers is finite. Thus the assumption of a continuum of consumers--so innocuous and useful a simplification in other contexts--has proved misleading in the context of durable-goods monopoly.