Nonconvex Production Technology and Price Discrimination

Abstract

We revisit the issue of product line design by a monopolist and extend the model of Mussa and Rosen (1978) in two ways. First, we consider the case in which the unit cost is a nonconvex function of product quality. We show that the firm does not offer those qualities where the unit cost is linear or exceeds its lower convex envelope. Consequently, there are "gaps" in its optimal quality choice. Second, when the firm can offer only a limited number of quality levels (due to possible fixed costs), we characterize the optimal location of these finitely many quality levels. This characterization again has the property that none of these qualities will lie within an interval where the unit cost is linear or exceeds its lower convex envelope. Several implications of the above results are discussed.