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Third-degree Price Discrimination Versus Uniform Pricing

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Abstract

We compare the revenue of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave revenue functions and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This revenue bound obtains for any arbitrary number of segments and prices that the seller would use in case he would engage in third-degree price discrimination. We further establish that these conditions are tight, and that a weakening of common support or concavity leads to arbitrarily poor revenue comparisons.

Suggested Citation

  • Dirk Bergemann & Francisco Castro & Gabriel Weintraub, 2019. "Third-degree Price Discrimination Versus Uniform Pricing," Cowles Foundation Discussion Papers 2213, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2213
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d22/d2213.pdf
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    References listed on IDEAS

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    1. Iñaki Aguirre & Simon Cowan & John Vickers, 2010. "Monopoly Price Discrimination and Demand Curvature," American Economic Review, American Economic Association, vol. 100(4), pages 1601-1615, September.
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    More about this item

    Keywords

    First Degree Price Discrimination; Third Degree Price Discrimination; Uniform Price; Approximation; Concave Demand Function; Market Segmentation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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