Weyl and Fabinger (2013) analyze the social incidence of competition and the output and welfare effects of third-degree price discrimination by considering the hypothetical entrance of exogenous quantity into a market. The formulas they use for this purpose, however, are correct only for marginal changes in exogenous quantity starting at zero or if demand functions are linear. We show how using the correct formulas changes Weyl and Fabinger’s analyses and leads to new results on the social incidence of competition and on the output and welfare effects of third-degree price discrimination in monopoly and oligopoly markets.

Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity, and Uniformity: Comment by Leslie M. Marx and Greg Shaffer. Published in volume 94, issue 3, pages 796-801 of American Economic Review, June 2004

Oligopoly models where prior actions by firms affect subsequent marginal costs have been useful in illuminating policy debates in areas such as antitrust regulation, environmental protection, and international competition. We discuss properties of such models when a Cournot equilibrium occurs at the second stage. Aggregate production costs strictly decline with no change in gross revenue or gross consumer surplus if the prior actions strictly increase the variance of marginal costs without changing the marginal-cost sum. Therefore, unless the cost of inducing second-stage asymmetry more than offsets this reduction in production costs, the private and social optima are asymmetric. (JEL D43, L13, L40)