Nonconvex Production Technology and Price Discrimination

Abstract

We revisit the issue of product line design by a monopolist andextend the model of Mussa and Rosen (1978) in two ways. First, weconsider the case in which the unit cost is a nonconvex function ofproduct quality. We show that the firm does not offer those qualitieswhere 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 ofthese finitely many quality levels. This characterization again has theproperty that none of these qualities will lie within an interval wherethe unit cost is linear or exceeds its lower convex envelope. Severalimplications of the above results are discussed.

Keywords: Product Line Design, Price Discrimination, Product