انتخاب مکان و تبعیض قیمت در یک انحصار فروش دوگانه
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Regional Science and Urban Economics, Volume 32, Issue 3, May 2002, Pages 339–358
This paper analyses the problem of price discrimination and product design in a duopoly model with both horizontal and vertical differentiation. Discriminatory contracts are first characterised at each customer location. It is then shown that firms’ locations have a big impact on their discriminatory ability and that equilibrium locations are not monotonic with respect to the heterogeneity parameter for the distribution of consumer preferences over quality; however firms never locate too far away from the first and third quartiles.
This paper studies price discrimination and product design in a duopoly where firms offer alternative contracts that discriminate between different groups of consumers. Much is known about the analysis of such contracts under monopoly, following a seminal paper of Mussa and Rosen (1978) that has initiated a family of principal–agent problems illustrating the equivalence between price discrimination using quantity discounts (second-degree discrimination) and monopoly pricing of products of differing quality.1 Discriminatory practices are also very common in oligopolistic industries, but the analysis of this setting is not entirely well understood. If firms offer perfect substitutes, then we can expect efficient Bertrand-type outcomes. Prices will be brought in line with costs, and customers will buy their preferred quality. However, if firms offer imperfect substitutes, then matters are more complex. For instance, it is not obvious whether the mechanism at work is simply a transfer between buyers and sellers, or whether allocations are affected as well. I consider a model of two firms located at some points of a line segment along which consumers are located. Consumers have heterogeneous preferences both over a horizontal parameter (brand) and a vertical one (quality). It is assumed that firms observe the location parameter while vertical preferences are private information. The difference in types gives a rationale for non-linear contracts, while the horizontal dimension is used at first to control for the intensity of price competition. For given firms’ locations, I characterise discriminatory contracts that change according to preferences over brand and quality. In particular, I discuss how there are three different discriminatory mechanisms at work (‘monopoly-type’, ‘intermediate’ and ‘competitive’ price discrimination) that define three corresponding regions according to consumers’ tastes.2 By providing a closed-form solution to contracts, I can proceed one step further and address another question that represents the second theme of this paper. I endogenise firms’ locations, thus contributing to an extensive literature on spatial competition in Hotelling-type models where firms first choose locations and then price schedules. While Lederer and Hurter (1986) consider the case of perfect spatial price discrimination with identical consumers with inelastic demand, Hamilton and Thisse (1992), study perfect spatial price discrimination and quantity-dependent price discrimination when customers have downward-sloping demands. However, Hamilton and Thisse assume perfect observability also on customers’ types, hence they study first-degree discrimination without adverse selection in the pricing game. On the other hand, in this paper I tackle the more interesting case of second-degree price discrimination (still with perfect spatial price discrimination)3 and I introduce a novel aspect in the spatial analysis: the location choice of a firm affects, among other things, also the firm’s discriminatory ability in the last stage of the game. In particular, I show how the symmetric location equilibrium is non-monotonic in the difference between types. When types are relatively similar, firms tend to locate closer to each other as the difference between types increases and ‘monopoly-type’ discriminatory contracts prevail in the last stage of the game. When the difference is high enough, the reverse is true and firms locate further apart as the difference between types increases. Finally, when the difference is very high, efficient discriminatory contracts emerge everywhere and firms also choose socially optimal locations. The basic set up of the model is presented in Section 2. The solutions to the first-best and to the monopoly case are briefly recalled in Section 3. As is common in location models, in the duopoly I restrict the analysis to subgame perfect Nash equilibria with locations chosen first and then contracts. Solving backwards, Section 4 discusses discriminatory contracts, with firms at fixed locations. Section 5 studies the location game and Section 6 concludes.
نتیجه گیری انگلیسی
This paper has analysed price discrimination and location choice in a duopoly game. Optimal contracts have been characterised and it has been shown that contracts change according to taste parameters over brand and quality. When firms, at a given location, offer discriminatory contracts, they behave as if the rival firm was offering the best possible deal to its own customers. Consumers’ participation constraints become type-dependent and, when vertical preferences are not too different, there are three different discriminatory mechanisms at work that define three corresponding regions according to consumers’ tastes. As brand preferences become weaker and/or differences between customers are more marked, quality distortions are reduced gradually until they are eliminated. Once location choices are endogenised, each firm takes into account the effect that its choice has on its discriminatory ability. The symmetric equilibrium in locations is not monotonic in vertical taste parameters. As vertical heterogeneity increases, firms first get closer and then further apart. However, product differentiation is ‘intermediate’ since firms always locate ‘around’ the first and third quartiles. Finally, when vertical taste parameters are sufficiently different, efficiency results both on locations and quality allocations.