Customer-class pricing, parallel trade and the optimal number of market segments☆

a r t i c l e i n f o JEL classifications: D42 L11 L50 Keywords: Monopoly Third-degree price discrimination Endogenous market segmentation Parallel trade We consider the optimal market segmentation problem of a monopolist that faces a continuum of customers when it is costly to prevent resale (or parallel trade) among groups. In our framework, the monopolist chooses the number k ≥ 1 of market segments, but also their design and the discriminatory prices. All these quantities are chosen to maximize the total profit. We solve the profit maximization problem when demands are linear and parallel as a function of the cost of separating markets. We show that market segmentation and prices cannot be chosen independently, and we also show that it is optimal to create only a few market segments. We then turn to the welfare analysis and show that the socially optimal number of market segment is equal to three. Price discrimination is a common practice both in the private sector and the public sector (e.g., McAfee, 2008; Steinberg and Weisbrod, 2005). It is well-known that hotels, car manufacturers, airline companies, but also national museums and galleries charge a different price for the same good or service to different subsets of customers. For a private firm, price discrimination is seen as a natural way to increase its profit; the set of customers is segmented on the basis of some observable characteristics (e.g., age, geography, gender) related to their price sensitivity, and customers of different market segments are charged a different price. For example, the price of a train ticket can differ according to whether the purchaser is a senior citizen or not while the price of medications or cars can depend on the country where the purchase is made (McAfee, 2008; Goldberg and Verboven, 2001). This customer-class pricing is generally called third-degree price discrimination from the pioneered work of Arthur Pigou (1932). In the monopoly literature on the subject, it is generally assumed that the underlying set of customers has already been divided in a given number of perfectly sealed market segments (i.e., classes, groups or sub-markets), so that the monopolist problem reduces to a pure pricing one. We argue that this rather simplistic picture of the monopolist problem is surprising not only because both the design and the number of market segments are critical variables of the overall marketing strategy, but also because this simplistic …