Welfare‐increasing third‐degree price discrimination

• DOI: http://doi.org/10.1111/1756-2171.12128
• Published date: 01 May 2016
• Author: Simon Cowan
• Date: 01 May 2016

RAND Journal of Economics

Vol.47, No. 2, Summer 2016

pp. 326–340

Welfare-increasing third-degree price

discrimination

Simon Cowan∗

When demand functions in different markets are derived from distributions of reservation prices

that differ only in their means, conditions exist such that third-degree price discrimination leads

to greater total output and greater total welfare. Welfare is higher with discrimination than with

a uniform price when demand functions are derived from logistic distributions with different

means. Welfare and consumer surplus are higher with discrimination for demands derived from

a distribution related to the Pareto. In general, whether discrimination increases total output

depends on demand being more convex in markets in which prices fall with discrimination than

in those in which prices rise.

1. Introduction

Under what conditions does third-degree price discrimination lead to greater social welfare

than uniform (nondiscriminatory) pricing? This is a long-standing question in economics that

has only been answered partially. This article provides broader answers. In particular, it shows

that social welfare is raised if demand functions are derived from logistic distributions that differ

only in their means, and that total output is higher with discrimination for many similar demand

functions with differing means.

A monopolist using third-degree price discrimination divides customers into separate mar-

kets on the basis of observable characteristics and sets prices that vary across the markets.

Alternatively, the firm may be unable to discriminate, because of regulation or arbitrage, and

thus must set a common price across markets. Pigou (1920) showed that if demand functions are

linear and all markets are served with positive quantities at the uniform price, then a move to

discriminatory prices keeps total output constant. In this case, discrimination reduces social wel-

fare (the sum of consumer surplus and profits), because the welfare-maximizing way to allocate

output across markets requires equating marginal utilities, which only a common price ensures.

If welfare is to rise with discrimination, there must be an increase in output sufficient to offset

the misallocation effect. Much of the literature since Pigou has been somewhat negative about

the welfare effects of third-degree price discrimination. Aguirre, Cowan, and Vickers (2010)

∗University of Oxford; simon.cowan@economics.ox.ac.uk.

I am grateful to two referees, Ben Hermalin, I˜

naki Aguirre, Achim Czerny, Peter Neary, Markus Reisinger, Marius

Schwartz, Glen Weyl,and participants at the 2013 SAET conference in Paris and of seminars at UC Dublin and WHU in

Vallendarin 2014 for helpful comments and suggestions.

326 C2016, The RAND Corporation.