Durable Goods Monopoly with Limited Choice of Commitment Strategy: When Should the Monopolist Precommit?

Abstract

Consider a firm (a monopolist) offering a unique product to a fixed number of potential customers. Suppose that no consumer desires more than one unit of the good, within a given period or across periods; that is, there is no value to repeat purchases. In addition, suppose that customers vary with respect to their initial reservation prices, which decline over time. A natural interpretation is that the monopolist is selling a good that is durable. Alternatively, the firm is providing an entertainment or fashion good. Consumers may place a premium on obtaining the product quickly, before it becomes less useful, less stylish, or less novel. Coase [7] conjectured that this firm's ability to extract surplus is limited because the firm has to compete with itself across time periods. High-valuation customers would be unwilling to pay a high initial price because they would anticipate that over time, the firm will be reducing the price in order to sell to lower-valuation customers. Subsequent literature formalizes this as a time inconsistency problem faced by a monopolist unable to make intertemporal commitments.' A separate strand of the literature proceeds from the polar assumption that the monopolist can precommit to any multiperiod pricing strategy. Comparison to Coase's monopolist is simple: higher profits are obtainable under precommitment because more surplus is extracted from high valuation customers. An important proposition due to Stokey [22] is that it will be optimal for the monopolist to precommit to a declining intertemporal price schedule if consumers with higher initial valuations have a higher rate of time preference.2 Otherwise, the optimal strategy is to hold price constant at the static monopoly level and to sell no more than the static monopoly quantity.3