Comments on "Gaussian Demand and Commodity Bundling"

Abstract

Different commodities are often sold together as a (e.g., complete dinners in a restaurant, stereo systems). In mixed strategies, the individual components of the bundle are also offered for sale separately. In block booking or pure strategies, they are not. Via simple hypothetical examples of two-product firms, Stigler (1963) and Adams and Yellen (1976) have demonstrated that these selling practices can increase profit even if there is no cost advantage to bundling and the component products are independent in demand. It is obvious from these examples that heterogeneity in consumer tastes (especially in relative valuations of the firm's two products) is a necessary condition for profitable bundling. Unfortunately, more specific principles to describe concisely the necessary and/or sufficient conditions for profitable bundling are not so obvious. Since consumer demand in the examples is represented by a complete enumeration of consumer reservation prices, optimal prices and pricing strategies must be determined by trial and error. Marginal analysis is inappropriate or uninformative. More important, these numerical examples do not yield characterizations of profit for each strategy as functions of a small number of parameters that summarize the relevant features of the distribution of reservation prices in the consumer population. By assuming that reservation prices (for the firm's two products) are distributed in the consumer population according to the bivariate normal probability law, Schmalensee (in this issue) has constructed a class of examples within which the profitability of bundling can be analyzed as a function of production costs, the mean and variance of the reservation price for each commodity, and the correlation between the two commodities' reservation prices. Although this analysis is sometimes mathematically complex, Schmalensee is quite thorough. Subject to the normality assumption, many of the questions suggested by the