Price Discrimination with Correlated Demands

Abstract

In this paper we analyze customer-class price discrimination in the face of uncertain demands.' More precisely, we explore the pricing decision of a multiproduct monopoly facing random, correlated demands. We consider only a uniform price for each customer class; multi-part pricing is not investigated. We are interested in the extent to which uniform customer-class prices can exploit variations in demand characteristics. If cost is a convex function of aggregate demand, then the expected cost of production is greater than the cost of the expectation of the rate of production.2 Since the deviation of expected cost from the cost of the expectation is (to a second order approximation) proportional to the variance of demand, the monopolist can exploit the functional dependence of variance on prices to reduce expected costs.3 This leads to optimal prices that discriminate on the basis of covariances among classes. In other words, prices are set to manipulate the variance of aggregate demand, much in the same way that investors can adjust the portfolio weights attached to individual securities in order to reduce the variance of their portfolio. We observe correlation among consumers or consumer groups in many markets. Many situations in which price discrimination is practiced can be reinterpreted as covariance-based pricing. Think of demand for a facility by a church and a child-care center. The church has positive demand on weekends and the child care center has positive demand during the week. Observed demands are negatively correlated. Costs of providing services can be reduced by sharing the facility and pricing it on the basis of covariances. A different example with a more explicit stochastic element, and so more directly related