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Nonconvex Production Technology and Price Discrimination

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Author Info
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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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 513.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:513

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Related research
Keywords: Price Discrimination; Product Line Design; Nonconvex Production;

Find related papers by JEL classification:
D42 - Microeconomics - - Market Structure and Pricing - - - Monopoly
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

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  1. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January. [Downloadable!] (restricted)
  2. Leonard J. Mirman & David Sibley, 1980. "Optimal Nonlinear Prices for Multiproduct Monopolies," Bell Journal of Economics, The RAND Corporation, vol. 11(2), pages 659-670, Autumn. [Downloadable!] (restricted)
  3. Steven Matthews & John Moore, 1985. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Discussion Papers 661, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  4. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-28, June. [Downloadable!] (restricted)
  5. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August. [Downloadable!] (restricted)
  6. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June. [Downloadable!] (restricted)
  7. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  8. Jovanovic, Boyan & Rob, Rafael, 1987. "Demand-Driven Innovation and Spatial Competition over Time," Review of Economic Studies, Blackwell Publishing, vol. 54(1), pages 63-72, January. [Downloadable!] (restricted)
    Other versions:
  9. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer. [Downloadable!] (restricted)
  10. Richard Schmalensee, 1978. "Entry Deterrence in the Ready-to-Eat Breakfast Cereal Industry," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 305-327, Autumn. [Downloadable!] (restricted)
  11. David S. Sibley & Padmanabhan Srinagesh, 1997. "Multiproduct Nonlinear Pricing with Multiple Taste Characteristics," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 684-707, Winter. [Downloadable!] (restricted)
  12. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December. [Downloadable!] (restricted)
  13. Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Blackwell Publishing, vol. 49(1), pages 3-13, January. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
  15. Shaked, Avner & Sutton, John, 1983. "Natural Oligopolies," Econometrica, Econometric Society, vol. 51(5), pages 1469-83, September. [Downloadable!] (restricted)
  16. Spence, A Michael, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," Review of Economic Studies, Blackwell Publishing, vol. 47(5), pages 821-41, October. [Downloadable!] (restricted)
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