Welfare and output in third-degree price discrimination: A note

Abstract

One main result about the welfare effects of third-degree price discrimination by a monopolist is that an increase in total output is a necessary condition for welfare improvement. This note provides two examples showing that this proposition cannot be generalized to an oligopoly with heterogenous firms. In these examples, price discrimination makes competition more favorable to the low cost firm. This fact induces a cost saving that overcome the welfare loss from consumer misallocations associated to price discrimination. JEL classification numbers: D43, D60, L13

On the welfare effects of regulating the number of discriminatory prices

“…For a given partition A k ∈ P k , the optimization problem reduces to the maximization of k continuous functions, i.e., Π A i (P i ) with respect to P i for i = 1, ..., k. It suces now to apply lemma 1 for each i = 1, ..., k to obtain a solution. Since the total number of partitions is nite, an optimal prot policy must exist, i.e., a solution to the optimization problem (12) exists. Let (A * k ; P * k ) denotes this optimal prot policy and let us assume for the moment it is unique.…”

“…11 See for instance theorem 10.3 page 215 in Blume and Simon (1994). 12 To see what the angle formed by two vectors is, consider the case of two vectors of R 2 , u = (x1, y1) and v = (x2, y2). In the special case in which u = (0, 1) and v = (1, 0), it is easy to see that the angle formed by these two vectors is 90 o .…”

Pricing music using personal data: mutually advantageous first-degree price discrimination

“…It is thus not surprising that, in contrast to second and third-degree price discrimination, which have been abundantly discussed (Schmalensee 1981;Bester and Petrakis 1996;Hamilton and Slutsky 2004;Liu and Serfes 2005;Galera and Zaratiegui 2006;Malueg and Snyder 2006), the literature devoted to first-degree price discrimination is comparatively scarce.…”

On international cost-sharing of pharmaceutical R&D

“…This result generated a stream of contributions addressing its generality. Galera and Zaratiegui (2006) show that under asymmetric oligopoly when third-degree price discrimination favors the lower cost firm, the welfare loss may be offset by the cost savings. Felder (2006) proposes to add to the distortion from the Ramsey prices another distortion originated from a subsidy to consumers as a way to offset the welfare reducing effect of price discrimination.…”