Monopoly Price Discrimination and Demand Curvature

Abstract

This paper presents a general analysis of the effects of monopolistic third-degree price discrimination on welfare and output when all markets are served. Sufficient conditions — involving straightforward comparisons of the curvatures of the direct and inverse demand functions in the different markets — are presented for discrimination to have negative or positive effects on social welfare and output. (JEL D42)

Optimal low-price guarantees with anchoring

“…For a more thorough understanding of the theoretical conditions under which welfare can be expected to rise or fall under direct price discrimination by a monopolist, we refer the interested reader to Aguirre et al (2010). In the abstract, however, and for the reasons just discussed, we see no reason for policy makers to condemn the use of low-price guarantees per se, and even less reason for policy makers to ban price-beating while allowing price-matching.…”

“…It was first shown by Robinson (1933), then by Schmalensee (1981), and most recently by Aguirre et al (2010) that the curvature of demands is critical in determining the sign of the output effect. With linear demands, for example, it is known that if both markets are served at the uniform price, output will be unchanged under discrimination, and thus discrimination will be unambiguously bad.…”

Horizontal Mergers in the Presence of Vertical Relationships

“…1 Mankiw and Whinston (1986) and Suzumura and Kiyono (1987) show that, under a Cournot oligopoly model with fixed set-up costs, the level of entry in the free-entry equilibrium is socially excessive. Ghosh and Morita (2007) find that free entry can lead to a socially insufficient number of firms in a successive oligopoly model, but it can still be socially excessive under a range of parameterizations.…”

“…We show that the positive welfare effect of the downstream merger dominates its negative effect due to concentration under a range of parameterizations. 1 A key element of our results is the effect of horizontal mergers on input price. A necessary condition for downstream mergers to increase welfare is that they reduce the equilibrium input price.…”

Monopoly price discrimination with constant elasticity demand

“…2 1 A great many papers have addressed this issue, including Leontief (1940), Edwards (1950), Silberberg (1970), Greenhut and Ohta (1976), Smith and Formby (1981), Schmalensee (1981), Varian (1985), Shih, Mai and Liu (1988), Cheung and Wang (1994) and, more recently, Cowan (2007), Aguirre, Cowan and Vickers (2010) (ACV) and Cowan (2012). 2 Neither the "adjusted concavity" criterion (Robinson, 1933, Cheung andWang, 1994), nor the "slope ratio" criterion (Edwards, 1950), nor the "mean-value theorem" criterion (Shih, Mai and Liu, 1988), can be applied to illustrate that price discrimination increases total output with constant elasticity demand.…”