Third-Degree Price Discrimination Versus Uniform Pricing

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