The degree of distortions under second-degree price discrimination

•We consider second-degree price discrimination for two types of consumers.•No consumer will be excluded when valuation functions cross at a positive quantity.•The type with the higher valuation peak is always served at the efficient quantity.•The sufficient and necessary condition for overall efficiency is provided.•For two general linear demands, we quantify the degree of distortions.

Under second-degree price discrimination, both types of consumers get efficient quantities when the net-of-cost valuation functions intersect at least once at some positive quantity and the point of intersection lies between the two peaks. Distortions can be upward or downward.