Output and welfare effects in the classic monopoly price discrimination problem

This paper uses convexity arguments to determine the effects of monopolistic third-degree price discrimination on total output and welfare. We focus on benchmark cases, including constant demand elasticities, with constant curvature of inverse demand ?. We show how the effects of price discrimination depend on (a) the degree of curvature ? relative to zero (for output) and one (for welfare), and (b) whether low-price markets have greater curvature than high-price markets