Partial price discrimination by an upstream monopolist

Bru, Lluís; Faulí-Oller, Ramon; Sandonís, Joel Article Partial price discrimination by an upstream monopolist SERIEs - Journal of the Spanish Economic Association Provided in Cooperation with: Spanish Economic Association Suggested Citation: Bru, Lluís; Faulí-Oller, Ramon; Sandonís, Joel (2011) : Partial price discrimination by an upstream monopolist, SERIEs - Journal of the Spanish Economic Association, ISSN 1869-4195, Springer, Heidelberg, Vol. 2, Iss. 2, pp. 217-231, https://doi.org/10.1007/s13209-010-0030-7 This Version is available at: https://hdl.handle.net/10419/77802 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/2.0/ SERIEs (2011) 2:217–231 DOI 10.1007/s13209-010-0030-7 ORIGINAL ARTICLE Partial price discrimination by an upstream monopolist Lluís Bru ·Ramon Faulí-Oller ·Joel Sandonís Received: 25 September 2008 / Accepted: 20 April 2010 / Published online: 21 August 2010 © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract We analyze third degree price discrimination by an upstream monopolist to a continuum of heterogeneous downstream firms. The novelty of our approach is to recognize that customizing prices may be costly. As a consequence, partial price discriminationarisesinequilibrium;inparticular, we showthatinefficientdownstream firms receive personalized prices whereas efficient firms are charged a uniform price. The extreme cases of complete price discrimination and uniform price arise in our setting as particular cases, depending on the cost of customizing prices. Keywords Price discrimination ·Input markets JEL Classification D4 ·L11 ·L12 We thank the editor, Pedro Mira and two anonymous referees for very helpful advice. We also thank Aleix Calveras, Daniel Cardona-Coll, María Paz Espinosa, Angel Hernando, Inés Macho-Stadler, David Pérez-Castrillo and Juana Santamaría for their comments. Financial support from SEJ 2004-02172, SEJ 2007-67895, SEJ 2007-62656, FEDER funds and the IVIE is gratefully acknowledged. L. Bru Departament d’Economia del’Empresa, Universitat de les Illes Balears, Campus de la carretera de Valldemossa km. 7.5, 07122 Palma de Mallorca, Spain e-mail: [email protected] R. Faulí-Oller ·J. Sandonís (B ) Departament de Fonaments del’Anàlisi Econòmica, Universitat d’Alacant, Campus de Sant Vicent, 03071 Alacant, Spain e-mail: [email protected] R. Faulí-Oller e-mail: [email protected] 123 218 SERIEs (2011) 2:217–231 1 Introduction In this paper, we analyze third degree price discrimination by an upstream monopolist. Third degree price discrimination can be defined as the possibility to charge different linear prices to different (groups of) customers. In order for price discrimination to be feasible, it must be possible to separate different (groups of) customers, which is called market segmentation. The seller must also be able to keep resales from occurring. There has been a long debate on the competitive effects of price discrimination. The Robinson-Patman Act, for example, makes it unlawful to discriminate in price betweendifferentpurchasersiftheeffectofthediscriminationmaysubstantially lessen competition or create a monopoly. Many papers have studied the welfare effects of price discrimination. For the case of final good markets we can mention, among others, Robinson (1933), Schmalensee (1981), Varian (1980) and Schwartz (1990). However, as Yoshida (2000) recognizes “the vast majority of legal and other policy disputes over price discrimination concern input markets, not final good markets”. Then, it seems important to analyze cases where the discriminating monopolist is an input supplier and the buyers are downstream firms producing a final good. In this setting, Katz (1987) and DeGraba (1990) show that price discrimination lowers welfare, because low cost downstream firms are charged higher prices. Total output, however, does not change as a consequence of price discrimination. Yoshida (2000) constructs a model where total output does change and obtains the counterintuitive result that an increase in total output is a sufficient condition for a welfare decrease. New information technologies facilitate implementing price discrimination, because they allow firms to obtain personalized information about customers. These technologies are used in intermediate markets in the relationship between suppliers and retailers and also in final markets in the relationship between retailers and consumers. Concerning the first case, tags attached to products allows an accurate tracking of each particular good allowing to know how it goes along the value chain from the production plant to the warehouse, an from the warehouse to the supermarket. Accurate tracking allows to improve distribution reducing for instance inventory costs. Concerning final markets an example of the introduction of new technologies would be the new uses of loyalty cards by supermarkets. Each time the card is swiped at the point of sale the content of the purchase can be incorporated into the information record about the customers. This allows retailers to target customers with personalized prices. Another example would be an internet store that uses consumer tracking technologies such as clickstream tracking, on-line registration, and cookies. Selling on the Internet with such technologies enables a firm to better understand each individual customer’s tastes and to offer individualized prices (see Chen 2006). In fact, there is an entire industry known as “yield management” that charges firms for specialized consulting and software to help them implement price discrimination.1 The introduction of these new technologies can be useful for the business strategy of firms, improving productivity, allowing price discrimination, but must be 1The example on tags is extracted from The Economist, “The future is still smart”, June 24th 2004. Examples of loyalty cards and tracking technologies are further discussed in Shapiro and Varian (1999). 123 SERIEs (2011) 2:217–231 219 accompanied by investments that can be extremely costly.2Therefore, firms must decide whether to introduce these technologies in their marketing strategies and the intensity of their use. In the present paper, we study firms’ incentives to price discriminate when customizing prices is costly. This introduces an interesting trade-off in the analysis: the gains of price discrimination have to be compared with its costs, which allows us to endogenously determine the extent of price discrimination. Our paper is close in spirit to Liu and Serfes (2004) in the sense that, in both papers, price discrimination involves a costly investment that imposes a trade-off on the decision to price discriminate. However, whereas Liu and Serfes (2004) focus on final good markets we investigate intermediate markets. Moreover, the nature of the investment is very different in the two papers. Whereas in Liu and Serfes (2004) it improves market segmentation, in our paper it is used to customize prices. To the best of our knowledge, this possibility has been neglected so far by the literature. We consider an upstream monopolist selling an input to a continuum of downstream firms producing a homogeneous good. We assume that downstream firms are heterogeneous in their production cost. Transactions between the upstream supplier and downstream firms can occur either at a common posted price or at a personalized price. The latter option requires a costly specific investment in the form of a link that allows the upstream firm to adjust the supply contract to the individual characteristics of the firms.3In other words, the creation of links allows the upstream firm to price discriminate among its linked customers. Price discrimination is profitable because firms’ differences in costs translate into different elasticity of input demands. In particular, it is the case that the higher the cost of a downstream firm the higher its input demand elasticity. Therefore, the upstream firm would like to adjust upwards the wholesale price for low cost firms and downwards for high cost firms, knowing that the personalized contract will only be accepted if it offers a discount with respect to the posted price. Regarding the creation of links, we will analyze two possible cases: on the one hand, the links are created by the upstream firm in a centralized way; on the other hand, each downstream firm decides whether to establish a link with the upstream firm. In the first case, the upstream firm prefers to connect high cost firms, because low cost firms would reject the personalized contract whenever the posted price market exists. In the second case, we have that the gains of creating a link for downstream firms are increasing in their costs, because the higher their costs the higher the discount they will receive in the personalized contract. This explains that, again, market is segmented such that high cost firms create links and are treated personally and low cost firms attend the posted price market. 2For example, according to Lieberman (1991,1993) a yield management firm charges upwards of $10 million for the software required to implement price discrimination for a single large firm. 3This cost can represent an investment in a technology that allows for personal communication. It can also include the direct costs associated with tailoring and enforcing a large number of contracts (Lafontaine and Oxley 2004). Or it could also arise as a fee that an intermediary firm charges to connect buyers and sellers. 123 220 SERIEs (2011) 2:217–231 In both cases, in equilibrium, some firms receive a personalized price while others are supplied at a common price. This is what we call partial price discrimination. The extreme cases of complete price discrimination and uniform pricing, studied in the earlier literature, arise in our setting as particular cases when the cost of the link vanishes and when it is large enough respectively. Regarding the effect of (partial) price discrimination on social welfare, things are simplified because we get the result that total output does not depend on the distribution of links. Then, (partial) price discrimination only affects total production costs. Given that the upstream firm subsidizes inefficient firms through price discrimination, total cost increases, which reduces social welfare. Therefore, in our context, we could prescribe not to allow for price discrimination. Lafontaine and Oxley (2004) illustrates the existence of partial price discrimination in the franchising industry. They compare the contracting practices of North American franchisors at home and in Mexico and they are able to analyze the extent of contract customization in the foreign market. They find a low use of contract customization and that firms do not adjust their foreign contracts as they accumulate experience in the Mexican market. They conclude that benefits of using different contracts in the two markets must be insufficient to warrant the costs of customization. In the last section of the paper, we apply the model to a case where the links are provided by an intermediary firm. We can interpret the intermediary as a Business-to- Business (B2B) firm that allows for online communications and transactions between buyers and sellers in exchange for a per-transaction fee. We consider the case of a nonindustry participant.4Observe that e-commerce is a good illustration of our model, given that price discrimination is a common practice in the Internet. For example, one implication that has already been noticed in the business press is that the extent of the information obtained in Internet opens new possibilities for firms to price discriminate. One very important information that sellers can obtain comes from the past purchase record of their customers (“it [Safeway] uses its website for (...) collecting and mining data on consumer’s preferences both from the site and from loyalty cards, so it can personalize promotions” (The Economist, June 24th 1999). Another advantage of Internet is that as communication is personal, price cuts are only observed by targeted sellers. The following quotation of the FTC Report on “Competition Policy in the world of B2B Electronic Marketplaces” clarifies the situation “(...) sellers can customize price lists to reflect agreements reached with specific buyers but ensure that those prices can be viewed only by the intended buyers”. In the paper, we consider that a link between the upstream firm and a particular downstream firm is created only when both of them pay a subscription fee charged by the intermediary firm. We obtain partial price discrimination as the equilibrium outcome of an extended game where the cost of creating a link is endogenously chosen by an intermediary firm. We get, as before, that high cost firms are the ones treated 4In practice, the fast growth of the e-commerce has induced also large firms to organize their own B2B to manage their relationships with customers and suppliers (Milliou and Petrakis 2004). For example, in 1999, Ford and General Motors announced that their huge purchasing operations would be transferred to the web. 123 SERIEs (2011) 2:217–231 221 personally. Moreover, the burden of the (endogenous) cost of price discrimination mainly falls over the downstream side of the market. The rest of the paper is organized as follows. In the following section, we present the general model and solve it for the cases where the upstream firm and downstream firms choose the links respectively. In Sect. 3, we apply the model to the case where the links are provided by an intermediary firm. Finally, the last section discusses the results and opens new avenues for future research. 2 The model We assume that there is an upstream monopolist producing an intermediate good at no cost. There also exists a continuum of downstream firms that transform this input on a one-for-one basis into a final homogeneous good. The cost of this transformation for downstream firm iis given by: Ci(qi)=ciqi+q2 i. There is a continuum of downstream firms, heterogeneous in parameter ci, which is uniformly distributed in the interval [0,1]. Market demand is given by P(Q)=A−Q. The timing of the game is as follows: In the first stage, the links are created. We will consider two different possibilities, namely, either they are chosen in a centralized way by the upstream firm or they are decided individually by downstream firms. In any case, the cost of creating a link is f. In the second stage, the upstream firm decides a linear wholesale price wto supply the input to the firms attending the posted price market and an individual linear wholesale price wito be offered to each linked downstream firm i. Inthethirdstage,downstreamfirmsdecidehowmanyunitstobuyfromtheupstream firm and how many units to sell to final consumers. We allow linked firms to attend the posted price market and, therefore, they will make use of the personalized prices only when w≥wi. We look for the Subgame Perfect Nash Equilibrium of the game solving it by backward induction. Solving explicitly this game is complex. Moreover, as we show below, in order to obtain the equilibrium distribution of links, which is our main interest, it is enough to solve a simplified version of the game (called Game I) where linked firms do not have the option to be supplied in the posted price market. Very nicely, we will show that there is a strong relationship between the equilibria of Game I and the equilibria of our original game. In the third stage, as we have a continuum of firms, they behave as price taking firms. On the one hand, linked firm ichooses output qito maximize its profits: πi=Pqi−ciqi−q2 i−wiqi. 123 222 SERIEs (2011) 2:217–231 This leads to the following individual supply function for linked firm i: Si(P)=P−ci−wi 2. On the other hand, the individual supply of a non-linked firm jis similarly obtained and amounts to: Sj(P)=P−cj−w 2. The market clearing condition is given by: NP−ci−w 2di +LP−ci−wi 2di =A−P,(1) where N={i∈[0,1]/firm iis not linked}and L={i∈[0,1]/firm iis linked}. We focus on an interior equilibrium in which all downstream firms produce. With some abuse of notation, (1) leads to the following equilibrium price: P(t,w)=2A+n+l+t+wz 3,(2) where zis the mass of set N(hence, the mass of set Lamounts to 1 −z), nand l are defined as n=Ncidi and l=Lcidi respectively, and tis the aggregate of personalized wholesale prices, t=Lwidi. Hence, for a given mass of connected and unconnected firms, the equilibrium price depends on the posted price wand on t. In the second stage, and given the set of linked firms, the monopolist chooses the schedule of personalized wholesale prices {wi}Land the posted price wto maximize its profits: I({wi}L,w)=N wP(t,w)−ci−w 2di +L wiP(t,w)−ci−wi 2di, (3) where superscript Idenotes Game I. These profits can be rewritten as: I({wi}L,w)=wP(t,w)−w 2z−w 2n+P(t,w) 2t−L wici+wi 2di, (4) The first order condition with respect to the posted price is: ∂I({wi}L,w) ∂w =P(t,w)−2w 2z+w 6z2−n 2+z 6t=0,(5) 123 SERIEs (2011) 2:217–231 223 whereas pointwise maximization with respect to personalized wholesale prices lead to first order conditions: ∂I({wi}L,w) ∂wi=w 6z+1 6t+P(t,w) 2−ci+2wi 2=0(6) for all wi∈L. Aggregating over the first order conditions for the personalized prices we have: L ∂I({wi}L,w) ∂widi =wz+t+3P(t,w) 6(1−z)−l+2t 2=0.(7) . From (4) and (6), we obtain that the optimal posted price is equal to w∗=1 2(A−n z) and the aggregate of optimal personalized wholesale prices is equal to t∗=1 2((1−z) A−l). Plugging w∗and t∗into (5) we obtain that the monopolist chooses a personalized wholesale price w∗ i=1 2(A−ci)for a connected downstream firm ci. Notice that, due to the linearity of the model, the personalized contract does not depend on the distribution of links. Plugging w∗and t∗into (1) we get the equilibrium price: P(t∗,w ∗)=1+10A 12 . Observe that the equilibrium price does not depend on the distribution of links either.5 To guarantee that for any distribution of links all firms produce in equilibrium, we must have A>11 4. This guarantees that the most inefficient downstream firm always produces for any level of connected firms. The equilibrium profits of the upstream firm amounts to: I({w∗ i}L,w ∗)=3n2+(2A(A−1)+3 l−1 4)z 24z,(8) where l=Lc2 idi. In the first stage, we have to derive the equilibrium distribution of links depending on whether the links are created by the upstream firm or by downstream firms. We analyze each case in turn. 5Yoshida (2000) considers a more general transformation technology for the inputs. For the particular case of one-to-one relationship between input and output, however, the equilibrium price is the same with and without price discrimination. Hence we obtain that his results extends to any possible level of partial price discrimination. 123 224 SERIEs (2011) 2:217–231 2.1 The upstream firm chooses the links We proceed to characterize the first stage equilibrium of Game I. The decisions of the upstream firm are (1) to choose the number of unconnected firms (that amounts to decide the mass z of set N) and (2) to decide the distribution of connected and unconnected firms (that amounts to the choice of terms nand lin the profit expression). In the following lemma, we find the distribution of connected firms that maximizes (8), for a given measure 1 −zof linked firms. Lemma 1 In Game I, fix the measure z of non-linked firms, then the optimal distribution of links for the upstream firm is such that the set of nonlinked firms is a single interval. Proof For the sake of simplicity we restrict the set of Lsets available to the upstream firm to be countable unions of disjoint sets.6For the distributions not considered in the lemma, there exist numbers 0 ≤a<b<d≤1 and 0 <c<d−b, such that firms in [a,b]∪[b+c,d]are not connected and the ones in [b,b+c]are connected. If z is the measure of unconnected firms and H is the expected cost of unconnected firms other than the ones in [a,b]∪[b+c,d], the payoff of the upstream firm can be written as: I=⎛ ⎝H+ b a cidi + d  b+c cidi⎞ ⎠ 2 +z b+c b c2 idi +constant. Weshow thatthese distributionsare not optimal because the payoff canbe increased changing b. The first derivative of Iwith respect to byields: ∂I ∂b=⎛ ⎝H+ b a cidi + d  b+c cidi⎞ ⎠(b−(b+c)+z((b+c)2−b2), which can be rewritten as: ∂I ∂b=−2c⎛ ⎝H+ b a cidi + d  b+c cidi⎞ ⎠+(2b+c)cz, whereas the second derivative is given by: ∂2I ∂b2=2c2+2cz >0. The convexity of the payoff function implies that these distributions do not maximize the profits of the upstream firm. If we allow the upstream to choose parameter 6The Lemma is true more generally but the general proof involves measure-theoretic arguments. 123 SERIEs (2011) 2:217–231 231 Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. References Chen Y (2006) Marketing innovation. J Econ Manage Strategy 15(1):101–123 DeGraba P (1990) Input market price discrimination and the choice of technology. 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