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Nonconvex Production Technology and Price Discrimination

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  • Bing Jing
  • Roy Radner

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 the non-convexities in the unit cost function. We show that the firm does not offer those qualities where the unit cost exceeds its convex envelope. Consequently, there are "gaps" in its optimal quality choice. When the firm is only permitted to offer a limited number of quality levels (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
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Suggested Citation

  • Bing Jing & Roy Radner, 2004. "Nonconvex Production Technology and Price Discrimination," Working Papers 04-04, New York University, Leonard N. Stern School of Business, Department of Economics.
    • Handle: RePEc:ste:nystbu:04-04
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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