Nonconvex Production Technology and Price Discrimination
(Research Seminar, November 13th, 2003)
Bing Jing
New York University
Abstract
A modern firm often employs multiple production technologies based on distinct engineering principles, causing non-convexities in the firm's unit cost as a function of product quality. Extending the model of Mussa and Rosen (1978), this paper investigates how a monopolist's product line design may crucially depend on features of the unit cost function. When there is no constraint on the number of quality levels it may offer, we show that the firm's optimal product choice consists of those quality levels where the unit cost coincides with its convex envelope. When such a constraint exists (due to possible fixed costs associated with offering each quality), the optimal location of quality levels still lies within those regions of the quality domain where the unit cost function coincides with its convex envelope. We further show that the firm's profit is a supermodular function of its quality levels, and characterize a necessary condition for the optimal quality location.
(Joint paper with Roy Radner, Stern School of Business, Economics & IOMS-Information Systems)
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