Price Competition for Exclusive Customers : A Discrete-Continuous Choice Model

This paper examines the tension between competition for the customer and competition in the market in a differentiated-product oligopoly. Consumers make purchases through an exclusive supply relationship that is modeled as a discrete-continuous choice problem. We characterize Bertrand-Nash equilibrium when firms set one-part or two-part price schedules. When firms commit to a two-part price schedule in advance of customers' selection of a supplier, equilibrium unit prices equal marginal costs and fixed fees obey an inverse elasticity rule. When firms cannot commit, bargain-then-ripoff pricing arises where unit prices are above marginal cost and fixed fees are possibly below customer-specific fixed costs. Two-part pricing with commitment yields higher profits - even compared to one-part pricing - provided access demand is log-concave in the fixed fee. One-part pricing, however, provides greater consumer and social welfare than two-part pricing without commitment. If usage demand is sufficiently price elastic, one-part pricing also results in greater consumer and social welfare, though less profit, than two-part pricing of either kind. Finally, when consumers differ in their usage demand, unit prices may be below marginal cost. Firms earn smaller margins on high-usage customers, in contrast to the usual monopoly result