Welfare effects of price discrimination when demand curves are constant elasticity

Welfare Effects of Third-Degree Price Discrimination: Ippolito Meets Schmalensee and Varian

“…See Aguirre, Cowan and Vickers (2010) for sufficient conditions based on the shape of the demand and inverse demand functions to determine the sign of the welfare effect. 8 Ippolito (1980) and more recently Cowan (2011) analyze the effect of third-degree price discrimination on consumer surplus and find reasonable settings where the effect is positive. In a related paper Leeson and Sobel (2008) consider costly price discrimination.…”

“…Schmalensee (1981)'s direct approach to the welfare effect and Varian's celebrated bounds on social welfare (1985,1989,1992) have dominated both the research and the teaching of the welfare effects of third-degree price discrimination for the last twenty-five years. Our analysis, inspired by the pioneering work by Ippolito (1980) and its generalization to n markets by Aguirre (2008), offers some advantages over Schmalensee's and Varian's. Firstly, it focuses directly on the change in welfare (instead of on indirect Lagrangian techniques or on exogenous bounds) and allows the output effect (that is, the social valuation of the change in total output) to be distinguished neatly from the misallocation effect.…”

Monopoly price discrimination with constant elasticity demand

“…Greenhut and Ohta (1976) show through a numerical example that price discrimination may increase output with constant elasticity demands. Ippolito (1980) obtains the result via numerical simulations that total output increases under third-degree price discrimination in the two-market case. Formby, Layson and Smith (1983) using Lagrangean techniques show that monopolistic price discrimination increases total output over a wide range of constant elasticities.…”

“…Since third-degree price discrimination is viewed as an ine¢ cient way of distributing a given quantity of output between di¤erent consumers or submarkets, an increase in total output is a necessary condition for price discrimination to increase social welfare (Robinson, 1933, Ippolito, 1980, Schmalensee, 1981, Varian, 1985, Schwartz, 1990, and Bertoletti, 2004. So a focal point in the literature has been the analysis of the e¤ects of price discrimination on output: in the case of linear demand price discrimination does not change output when all markets are served (Pigou, 1920, andRobinson, 1933), but in the general non-linear case the e¤ect of price discrimination on output and, therefore, on welfare may be either positive or negative.…”

“…Formby, Layson and Smith (1983) using Lagrangean techniques show that monopolistic price discrimination increases total output over a wide range of constant elasticities. 4 Using numerical simulations Ippolito (1980) shows that the e¤ect of third-degree price discrimination is undetermined and more likely to be positive when both the di¤erence between elasticities and the share of the strong market are high enough. state whether the e¤ect on welfare of full discrimination is positive or negative.…”