On the welfare effects of regulating the number of discriminatory prices

We consider a profit-maximizing monopolist that faces N≥2 different markets while the number k of discriminatory prices is chosen by the regulator. Unlike the classical approach in which only the polar cases are considered, we explicitly analyze the case in which k is an integer between 1 and N. As a consequence, the monopolist׳s profit maximization program is a mixed-integer programming problem, the solution of which is called the optimal profit policy. Assuming that demands are linear, we show that the socially optimal number of discriminatory prices is never higher than a threshold k¯, defined as the smallest integer such that all the markets are served. This result allows us to disentangle the good aspect of price discrimination from the bad one and this shows that regulating the number of discriminatory prices is welfare enhancing, compared to the classical approach. Further welfare results are derived when demands are parallel, and a discussion of the conditions under which regulating the market segmentation itself is socially worthwhile is also provided. Finally, we consider the case of three markets and derive sufficient conditions under which the socially optimal number of discriminatory prices is equal to two.