The Degree of Distortions under Second-Degree Price Discrimination

We consider second-degree price discrimination for two types of consumers. When the net-of-cost valuation functions cross at least once at some positive quantity, it is always optimal to serve both types of consumers. Moreover, the type with the higher valuation peak always gets the socially efficient quantity. The sufficient and necessary condition for the overall efficiency is the peak of each type's net-of-cost valuation is above the other type's net-of-cost valuation at that peak quantity. For two general linear demands, we quantify the degree of efficiency, upward and downward distortions