The welfare effects of third-degree price discrimination with non-linear demand functions

The welfare effects of third-degree price discrimination are analyzed when demand in one market is an additively shifted version of demand in the other market and both markets are served with uniform pricing. Social welfare is lower with discrimination if the slope of demand is log-concave or the convexity of demand is non-decreasing in the price. The demand functions commonly used in models of imperfect competition satisfy at least one of these sufficient conditions.