Gaussian Demand and Commodity Bundling

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In an important and widely cited essay, Adams and Yellen (1976) examine the use of package selling as a price discrimination device.' They consider a monopolist producing two goods with constant unit costs and facing buyers with diverse tastes. The marginal utility of a second unit of either good is assumed to be zero for all buyers. The two goods are independent in demand for all buyers, so that any buyer's reservation price for the first unit of either good is independent of the market price of the other. Thus the maximum amount any buyer would pay for a bundle consisting of one unit of each good is the sum of the two reservation prices, and buyers are completely described by the values of those two prices.2 Resale markets are assumed away. In order to obtain comparative results for alternative pricing strategies, the distribution of reservation prices in the Adams-Yellen framework is assumed to be bivariate normal. Implications of Gaussian demand are explored. Pure bundling is shown to 'operate by reducing buyer diversity, thus facilitating the capture of consumers' surplus. It generally makes buyers worse off than unbundled sales; it is more profitable if average reservation prices are high enough. Mixed bundling combines advantages of both pure bundling and unbundled sales, and it is generally strictly more profitable than either. Bundling, which treats goods symmetrically, seems most attractive under symmetric reservation price distributions. * I am indebted to Severin Borenstein for superb research assistance, to the Ford Motor Company for research support through a grant to M.I.T., and to the Harvard Economics Department for housing me as a Visiting Scholar while most of this research was performed. Of course, only I can be held responsible for this essay's shortcomings. 1. The first clear recognition of this possibility seems to have been by Stigler (1968), but also see Burstein (1960). 2. Paroush and Peles (1981) relax the assumption that consumers purchase at most one unit of each good, but they consider only two types of buyers, both with linear demand functions. (They retain the assumption that demands are independent for all buyers.) Telser (1979) and Phillips (1981) use different frameworks to analyze bundling policies. Spence (1980) explores the relation between bundling across commodities, as here, and bundling multiple units of the same