قیمت گذاری در سطح مشتری، تجارت موازی و تعداد بهینه بخش های بازار

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 and 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 and 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 picture provides no clues to explain the observed customer-class pricing. Since the aim of the monopolist is obviously to charge as many prices as there are customers, why do most firms choose to create few market segments compared to the large number of customers? For a discriminating monopolist, a realistic explanation may be the cost associated to the prevention and detection of parallel trade (i.e., arbitrage or gray market). It is well-known that when there are large price differences, this may give a strong incentive for some agents to engage in arbitrage (e.g., McAfee, 2008 and Anderson and Ginsburgh, 1999). This phenomenon occurs if customers of a high-priced market segment can easily buy the good from customers of low-priced market segments, but, and more critically, if there exist parallel traders (or gray marketers) that do business by selling the goods from the low-priced market segment to the high-priced market segment without the authorization of the monopolist, the intellectual property rights (IPR) owner. It turns out that via these unauthorized channels distribution may be legal. Consider the case of a manufacturer (of a new patented good) that wishes to charge a different price in each country of the European Union (EU). Since the EU is considered as a single market, parallel imports are consistent with the principle of free movement of goods so that the European Court of Justice has established a policy of "community exhaustion" of rights.1 This means that once the good has been sold by the monopolist (the IPR owner) within the EU, its rights are exhausted. The buyer can thus freely resell the patented good without the authorization of the rights owner. On the contrary, re-importation from a country outside the EU is not allowed. For the particular case of medications, report that 20% of the (branded) pharmaceuticals in the U.K was sold via parallel trade while Arfwedson (2004) reports that within the European Union, parallel import of drugs were estimated to represent 3.3 billion dollars in 2001. A wide variety of industries such as personal computers, perfumes, watches etc. are actually subject to parallel trade. Antia et al. (2006) report that estimates of gray market activity range from 10 billion to 20 billion dollars in economy-wide annual gray market sales. In response to parallel trade, a manufacturer's strategy may simply be to charge a uniform price (Danzon, 1997). However, as noted by Cavusgil and Sikora (1988) in their early paper, and more recently among others by Ahmadi and Yang (2000), Antia et al. (2004) and Myers and Griffith (1999), this parallel trade problem should be anticipated by the discriminating monopolist, and the nonpricing responses to combat it should be part of the marketing strategy. It is only when these proactive strategies are too costly that it may perhaps be optimal for the monopolist to charge a uniform price. In Gerstner and Holthausen (1986), Ahmadi and Yang (2000) and more recently in Zhang and Bell (2010), they also consider a model in which isolating each market segment is costly but they assume that the design and the number of market segments are exogenous. It is thus the aim of the present paper to provide a model in which the monopolist chooses the design, the prices, and the number of market segments when it is costly to prevent parallel trade. We analyze the simplest framework in which there is a continuum of customers, each endowed with a linear demand function. Since it does not make sense in practice to charge a continuum of prices, the monopolist must segment the set of potential customers into classes, but the number of these classes may be very large. Our results reveal several interesting properties. We show that when the monopolist decides to create k + 1 market segments rather than k, this changes both the existing market segments and the prices. This shows that market segmentation and prices cannot be chosen separately. When the cost associated to the prevention of parallel trade is low, we show that it is never optimal to create more than a small number of market segments. This result may explain why in practice the number of market segments is low compared to the high number of customers. We then turn to the welfare analysis assuming that the regulator can costlessly eradicate parallel trade by making it illegal. We show that the socially optimal number of market segments is equal to three (the normative benchmark), which means that the monopolist should be allowed to charge three discriminatory prices. This result then allows us to compare this socially optimal number with the actual one chosen by the monopolist as a function of the isolation cost. When this cost is high, so that it is optimal for the monopolist to choose a single price, we show that everything is as if a fraction of customers were subsidized by another one; approximately 40% of customers with intermediate willingness-to-pay (henceforth WTP) subsidize 30% of those with the highest WTP. On the other hand, when the cost is low so that it is optimal for the monopolist to create more than three market segments, customers with lower WTP are now served and everything is as if they were subsidized by those with the highest WTP. This shows that deviations from the normative benchmark are not symmetric; there is a greater regulatory concern when one market segment is created rather than more than three. The second section is devoted to the presentation of the model while the third one is devoted to the presentation of the results. All the proofs are relegated to Appendix A.

In this paper, we considered a monopolist that faces a continuum of customers when the number of market segments but their design and the discriminatory prices are also endogenous. In our framework, it is the cost associated to the prevention and detection of parallel trade that constraints the monopolist to segment the set of customers. In a costless environment, the monopolist would charge a different price to different individual customers. One result of this paper has been to show that the number of market segments is a relevant quantity from the monopolist's point of view when it is costly to combat parallel trade, but also from a regulatory point of view, even when parallel trade is not a threat. Contrary to what is sometimes believed, a small amount of discrimination alleviates the distributive distortions generated by uniform pricing. While more research on the subject is necessary, it seems important to point out that we adopted throughout the paper an "industrial organization" approach since we only considered the case of a profit-maximizer monopolist. However, one may also consider market segmentation and price discrimination from a "public economics" point of view. One may, for example, analyze the case in which the regulator maximizes a (possibly weighted) social welfare function under some budget constraints (Hartwick, 1978, Le Grand, 1975 and Steinberg and Weisbrod, 2005) or maximizes the social welfare instead of the total profit (Malueg and Schwartz, 1994). Market segmentation and price discrimination are thus interesting topics at the frontier between industrial organization and public economics.