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Nonconvex Production Technology and Price Discrimination

Author

Listed:
  • 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

Suggested Citation

  • Bing Jing & Roy Radner, 2004. "Nonconvex Production Technology and Price Discrimination," Econometric Society 2004 North American Summer Meetings 513, Econometric Society.
  • Handle: RePEc:ecm:nasm04:513
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    References listed on IDEAS

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    1. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    2. Matthews, Steven & Moore, John, 1987. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Econometrica, Econometric Society, vol. 55(2), pages 441-467, March.
    3. Boyan Jovanovic & Rafael Rob, 1987. "Demand-Driven Innovation and Spatial Competition Over Time," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 63-72.
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    5. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    6. Jaskold Gabszewicz, Jean & Shaked, Avner & Sutton, John & Thisse, Jacques-Francois, 1986. "Segmenting the market: The monopolist's optimal product mix," Journal of Economic Theory, Elsevier, vol. 39(2), pages 273-289, August.
    7. A. Michael Spence, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," Review of Economic Studies, Oxford University Press, vol. 47(5), pages 821-841.
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    12. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826.
    13. Shaked, Avner & Sutton, John, 1983. "Natural Oligopolies," Econometrica, Econometric Society, vol. 51(5), pages 1469-1483, September.
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    More about this item

    Keywords

    Price Discrimination; Product Line Design; Nonconvex Production;

    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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