Durable-Goods Monopoly with Varying Demand

Abstract

This paper solves for the profit maximising strategy of a durable-goods monopolist when incoming demand varies over time. Each period, additional consumers enter the market; these consumers can then choose whether and when to purchase. We first characterise the consumer's utility maximisation problem and, under a monotonicity condition, show the profit maximising allocation can be solved 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 declines. This asymmetry pushes the price level above that charged by a firm facing the average level of demand. Applications of this framework include deterministic demand cycles, one-off shocks and IID demand draws. The optimal policy outperforms renting and can be implemented by a time consistent best-price provision.

Keywords: durable goods, pricing, mechanism design, optimal stopping

JEL Classification: C73, D82, E32, L12