Third-Degree Price Discrimination Versus Uniform Pricing

21 Pages Posted: 19 Feb 2020 Last revised: 22 Jul 2020

See all articles by Dirk Bergemann

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Francisco Castro

University of California, Los Angeles (UCLA) - Anderson School of Management

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University

Date Written: June 30, 2020

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 holds 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 weakening either common support or concavity leads to arbitrarily poor revenue comparisons.

Keywords: First Degree Price Discrimination, Third Degree Price Discrimination, Uniform Price, Approximation, Concave Demand Function, Market Segmentation

JEL Classification: C72, D82, D83

Suggested Citation

Bergemann, Dirk and Castro, Francisco and Weintraub, Gabriel Y., Third-Degree Price Discrimination Versus Uniform Pricing (June 30, 2020). Cowles Foundation Discussion Paper No. 2213R, Available at SSRN: https://ssrn.com/abstract=3540156 or http://dx.doi.org/10.2139/ssrn.3540156

Dirk Bergemann (Contact Author)

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
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203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Francisco Castro

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States
6465528479 (Phone)
90095 (Fax)

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

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