Bounding the Relative Profitability of Price Discrimination

Abstract:     
We derive bounds on the ratio of a monopolist's profit from third-degree price discrimination to that from uniform pricing. If a monopolist serves N independent markets, demand is continuous, and the cost function is superadditive, then the profit ratio is bounded by N. This bound is tight unless under price discrimination some markets are sold no output or are charged equal prices. The profit ratio can be bounded under more general conditions if the monopolist can ration demand under uniform pricing. We provide examples showing the profit ratio cannot generally be bounded when marginal cost is decreasing, fixed cost is positive, or demand is discontinuous. We extend the analysis to situations in which the monopolist sells several products or sells to distinct markets for which there are heterogeneous transportation costs.

Keywords: third-degree price discrimination, uniform pricing, profit bounds

JEL Classifications: D42, L12, L41

Working Paper Series