Third-Degree Price Discrimination Versus Uniform Pricing

TL;DR

This paper compares the profits of third-degree price discrimination with uniform pricing, showing that under certain conditions, uniform pricing guarantees at least half of the optimal discrimination profits.

Contribution

The paper proves a universal profit bound for uniform pricing relative to third-degree price discrimination under broad conditions.

Findings

Uniform pricing guarantees at least 50% of third-degree discrimination profits.

The profit bound holds regardless of the number of segments or prices used.

Relaxing conditions can lead to arbitrarily worse profit performance.

Abstract

We compare the profit 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 profit functions (in the price space) and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This profit bound holds for any number of segments and prices that the seller might use under third-degree price discrimination. We establish that these conditions are tight and that weakening either common support or concavity can lead to arbitrarily poor profit comparisons even for regular or monotone hazard rate distributions.