استراتژی قیمت گذاری بهینه برای کالاهای انحصاری بادوام

In this paper, we reconsider the profitability of a durable-good monopoly when the seller's discount rate may be different from the buyers’. In an infinite-horizon continuous-time full-commitment model, the monopoly can achieve more than the static monopoly profit if and only if the seller is more patient than the buyers. Under this condition, the price function is strictly decreasing over time. These results remain valid in models with buyers arriving sequentially, where the seller may have only one unit to sell or can produce more at constant marginal cost.

The issue of durable-goods monopoly has been studied extensively in the literature. The focus has been on whether and how the monopoly earns its static monopoly profit in a dynamic model.1 There is a presumption that the static monopoly profit is the maximal profit a (static or dynamic) monopoly can obtain. This paper shows that this speculation is true only in some cases. The condition for its validity closely associates with the relative discount rates of the monopoly and the buyers. In most of the literature, it is assumed that the discount rates for the buyers and the seller are exactly the same. Evidence indicates otherwise. One can argue that a firm has better access to low-interest-rate loans than the consumer, and therefore the firm's discount rate is often lower than the consumer's.2 While it is not the focus of this paper to examine how to measure the discount rates and who have the higher numbers, the effects of different discount rates still need to be investigated. The issue then becomes how much more the monopoly can earn in a dynamic model when its discount rate is different than its buyers? In this paper, we answer this question in an infinite horizon model with a continuum of buyers where the monopoly has full commitment power. It is easy to see that the monopolist can earn at least the static monopoly profit by offering the monopoly price at all times. Is that the maximum profit the monopolist can earn? The answer is no. We find that when the monopolist is more patient than the buyers, which is usually the case, the monopolist can extract more profit from the buyers by offering a strictly declining pricing path. Even though delay is costly to the seller, it is even more costly to the buyers. A monopolist can exploit this property to discriminate among buyers with different willingnesses to pay. This result justifies the conventional wisdom: a dynamic monopoly ought to do ‘better’ than a static monopoly. If we consider the extreme case where the buyers are infinitely impatient, the seller can discriminate perfectly between each buyer and earn all the surplus. The property that a dynamic monopoly can earn more than a static monopoly is first exhibited in Sobel and Takahashi (1983) in a discrete-time model for the class of demand functions: q=1−F(p), where View the MathML source. When the seller and the buyers’ discount rates are equal, Gul (1987) and Ausubel and Deneckere (1987) show that the static monopoly profit is the maximum a dynamic monopoly can get. This paper generalizes these results to a general demand function and different discount rates in a continuous-time model. A simple necessary and sufficient condition for higher profits is provided. This condition is proved to be quite robust. It remains valid in models with sequential stochastic arrival of new buyers, such as the one considered by Sobel (1991). It is also valid in a related bargaining model.3 The rest of the paper is organized as follows. In Section 2, the basic model is established and the major result regarding the seller's profit is proved. In 3 and 4, random arrivals of new buyers are considered, in a monopoly setting and in a bargaining setting respectively. In Section 5, we conclude.

In this paper, we obtain an important result in a very general setting. When a durable-goods monopoly has full commitment power, it can earn more than the static monopoly profit by decreasing its price over time if it is more patient than the buyers. This justifies the common observation that the prices for most durable goods are indeed declining over time. Of course, there could be other explanations for this phenomenon, such as decreasing marginal cost of production because of learning by doing or technological advances. This paper assesses that even if the cost of production is constant, the prices are expected to decline, as long as the monopoly is more patient than the buyers. This result seems to be very robust, as it remains valid in a variety of models studied in the paper.