Integrating Models of Price Discrimination

The marketing, economics, and operations management literatures have recognized many ways in which a firm can price discriminate. The question of how to price discriminate (e.g. how to price a product line) has received considerable attention but most of this work has assumed that price discrimination is optimal. However, the question of whether to price discriminate is also important as firms often forgo this option. For example, a firm may offer only a single product or version, not engage in intertemporal pricing, offer a single customer service queue, not offer advance purchase discounts, or not offer coupons. In this paper, we develop a very general model of monopoly price discrimination that yields two important contributions. First, we derive a single intuitive condition that determines whether price discrimination is profitable. The condition relates to changes in the social surplus, which is the difference between consumer benefits and firm costs, when a consumer upgrades from a low quality product to a high quality product. We show that price discrimination is profitable if and only if the percentage change in social surplus from product upgrades is increasing in consumers’ willingness to pay. We refer to this as an increasing percentage differences condition. Second, while applications of second-degree price discrimination have much in common, few papers attempt to unify them in a single model. Using our framework, we both recover and generalize many results from applications of price discrimination in the marketing, economics, and operations management literatures. Our paper unifies these seemingly disparate applications of price discrimination by explicitly recognizing their common elements. † We would like to acknowledge Justin Johnson, Preston McAfee, Marco Ottoviani, Kathryn Spier, Duncan Simester, Birger Wernerfelt, and especially Lars Stole and Guofu Tan for their helpful comments. An earlier version of this paper was titled “When is Price Discrimination Profitable?”