A Theory of Monopoly of Complementary Goods

Abstract

Tie-in sales of complementary commodities are a pervasive business practice often subject to different interpretations. It is sometimes easy to explain the presence of tie-ins because the cost of the combination is lower than the sum of the costs of the components sold separately. No doubt this explains why new automobiles come equipped with four wheels instead of having wheels sold separately from the car. There is a theoretical possibility that tie-ins are used by monopolists in order to increase their monopoly return even though the cost of the combination is the same as the sum of the costs of the components. The purpose of this work is to furnish a formal analysis of tie-in sales by a monopolist in order to see if this is so. In addition we shall study under what conditions if any a monopolist who sells the component commodities separately might sell one or more of them at prices below their marginal costs. Thus suppose a vendor of peanuts and beer has an exclusive concession in a sports arena. Would profit maximization lead him to sell the peanuts at a price below their marginal cost and the beer at a price above their marginal cost? Allen (1949, sec. 14.4) studies this The theory of monopoly of complementary goods raises two important issues. First, when can a monopolist increase his net return by selling at least one of a set of complementary commodities at a price below its marginal cost? This paper shows that this practice is consistent with a maximum monopoly net return and rational customers who calculate correctly the cost of the combination of complementary commodities. Second, it is shown that a monopolist can increase his net return by forming groups of complementary commodities and selling these groups to different types of customers. It is a maintained hypothesis that the total cost of a set of complements is a linear function of the quantities. Hence, the theory relies on the nature of the demand conditions to explain these practices. The theory applies to tie-in sales, block booking, and resale price maintenance. * I am grateful to Joel Gibbons, Sheldon Kimmel, Yoram Peles, Sherwin Rosen and William W. Sharkey for their helpful comments and criticisms. The responsibility for all errors is mine.