Random Price Discrimination

When a monopolist randomly sorts customers, price discrimination “concavifies” the revenue function of the firm, so that it may be optimal for a monopolist to divide customers into groups that have the same demand function and charge them different prices. It is impossible to rule out this type of result whenever the revenue function is somewhere convex in the “economically relevant” set of quantities, because there always exists a non-decreasing cost function that leads to that conclusion. It is also impossible to rule out the case where, with respect to monopoly, the firm raises or lowers price to all classes and, accordingly, the case where the social welfare decreases or increases. Received December 13, 2001; revised version received June 3, 2002 Published online: February 17, 2003 I am indebted to Carlo Beretta, Giuseppe Colangelo, Umberto Galmarini, Guido Merzoni, Gerd Weinrich and especially to Carla Peri for helpful discussions and comments. I have also benefited from insightful suggestions of three anonymous referees. Finally, I wish to thank participants to seminars at the Catholic University of Milan and University of Bologna. The usual disclaimer applies. Funds from MIUR are gratefully acknowledged.