Durable-Goods Monopoly with Varying Demand

This paper solves for the profit-maximizing strategy of a durable-goods monopolist when incoming demand varies over time. We first characterize the consumers' optimal purchasing decision by a cut-off rule. We then show that, under a monotonicity condition, the profit-maximizing cut-offs can be derived through a myopic algorithm, which has an intuitive marginal revenue interpretation. Consumers' ability to delay creates an asymmetry in the optimal price path, which exhibits fast increases and slow decreases. This asymmetry creates an upward bias in the level of prices, pushing them above the price charged by a firm facing the average level of demand. The optimal policy outperforms renting and can be implemented by a time-consistent best-price provision.