The welfare effects of third-degree price discrimination

The welfare effects of third-degree price discrimination are known to be negative when demand functions are linear, marginal cost is constant and all markets are served. This paper shows that discrimination lowers welfare for a more general class of demand functions. Demand varies across markets with additive and multiplicative shift factors. Total welfare (defined as consumer surplus plus profits) with discrimination is lower than with uniform pricing when the density function of consumer valuations satisfies a weak version of concavity that encompasses logconcavity. Most standard demand functions including linear, quadratic, probit, logit, exponential and iso-elastic ones, satisfy this assumption, which is also a weak sufficient condition for existence.