Publication Date: December 2019
Revision Date: February 2020
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 a weakening of 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 Codes: C72, D82, D83CFDP 2213