On the degree of distortions under second-degree price discrimination

This paper highlights the limitations and applicability of results developed by Chao & Nahata (2015) for nonlinear pricing. Although Chao and Nahata appear to provide necessary and sufficient conditions for general utility functions, we show that one of their results leads only to a restatement of two constraints, and another result may not be valid when consumers can freely dispose of the good. Their model allows for the possibility that higher quantities will have a lower price than smaller quantities. We provide conditions under free disposal that preclude this anomaly. Our analysis suggests that further research on violations of the single-crossing condition should be encouraged.