Multilateral Vertical Contracting with an Alternative Supply: The Welfare Effects of a Ban on Price Discrimination

Transcription

1 Review of Industrial Organization (2006) 28:63 80 Springer 2006 DOI /s Multilateral Vertical Contracting with an Alternative Supply: The Welfare Effects of a Ban on Price Discrimination STÉPHANE CAPRICE University of Toulouse (INRA), Bât.F, 21 Allée de Brienne, F Toulouse, France caprice@toulouse.inra.fr Abstract. Rey and Tirole [Handbook of Industrial Organization. Amsterdam: Elsevier (2005)] considered a model in which a monopolist sells to downstream firms using nonlinear contracts. They showed that banning price discrimination fully restores the supplier s ability to leverage its monopoly power by enabling it to commit not to offer side discounts. I show that the situation changes when the supplier competes against a fringe of less efficient rivals rather than being a monopolist. Then banning price discrimination may cause per-unit prices to fall and welfare to increase. The dominant supplier can take advantage of a strategic bargaining effect: reducing the per-unit price makes the outside option of buying from the fringe less profitable, allowing the dominant supplier to extract more bargaining surplus through the fixed fee. Key words: bargaining effect, bilateral oligopoly, price discrimination, vertical contracting. JEL Classifications: K21, L13, L42. I. Introduction Antitrust authorities have been significantly concerned with price discrimination in intermediate-good markets. For example, the principal act covering price discrimination in the United States, the Robinson Patman Act, was introduced with the explicit intention of protecting small business from unfair advantages possessed by large buyers in intermediate-good markets. There has been considerable back and forth in the academic literature about whether banning price discrimination on intermediate-good markets is good policy. Bork s (1978) view was that price discrimination in intermediate-good markets is likely to be socially efficient and thus should not be proscribed. He suggested that price discrimination enables an upstream supplier to make selective price cuts to those customers over whom it has the least market power, price cuts that would not be profitable if price

2 64 STÉPHANE CAPRICE discrimination were not allowed (i.e., if all prices had to be lowered). Hence, under price discrimination, an intermediate-good supplier will lower price to some buyers without raising prices to the remaining buyers. As a result, price discrimination leads to lower final-good prices from which the ultimate consumers benefit. A more recent theoretical literature identified welfare gains from forbidding price discrimination on intermediate-good markets (Katz, 1987; De-Graba, 1990; Yoshida, 2000). For example, in DeGraba s (1990) model, if the downstream firms have different marginal costs of production, the price-discriminating input supplier will charge the low-cost downstream firm a higher price than it charges the high-cost downstream firm, partially offsetting the cost advantage. Thus, price discrimination results in a smaller cost differential between downstream firms, which causes the lower-cost downstream firm to produce less and the higher-cost firm to produce more than under uniform pricing. In yet more recent work, Rey and Tirole (2005) showed that banning price discrimination reduces social welfare. Unlike the papers cited in the preceding paragraph, which restrict attention to wholesale contracts with linear prices, Rey and Tirole considered nonlinear prices. Their analysis is relevant to many intermediate-good markets in which nonlinear pricing is part of the contracts between suppliers and retailers. By restricting the contract space to linear prices, the previous analysis artificially ruled out the commitment problem that faces the upstream monopolist in Rey and Tirole and related work (see, e.g., Hart and Tirole, 1990; O Brien and Shaffer, 1992; McAfee and Schwartz, 1994; Marx and Shaffer 2004a, b). A downstream firm cannot observe the quantities negotiated with its rival, so the supplier has an incentive to sell extra quantity at a discount to the other downstream firm. Anticipating these extra sales, each downstream firm is willing to pay less. Thus, the upstream firm may not fully exploit its monopoly power. Uniform pricing prevents such unilateral discounts and restores the supplier s ability to leverage its monopoly power. This paper reverses some of these conclusions regarding the welfare effect of banning price discrimination. As in Rey and Tirole (2005), I allow for nonlinear contracts in the form of two-part tariffs. The new feature of my model is that the upstream firm faces competition rather than being a monopolist. Specifically, my model involves two downstream firms and an upstream firm that faces a fringe of less efficient rivals. In equilibrium, downstream firms do not purchase from this fringe but its presence puts competitive pressure on the low-cost supplier. Upstream competition leads to a new bargaining effect in addition to the commitment effect in Rey and Tirole (2005). A ban on price discrimination allows the low-cost firm to make a credible commitment to charge a low per-unit price. This low per-unit price reduces the profitability of buying from the alternative

3 EFFECTS OF BAN ON PRICE DISCRIMINATION 65 supplier. Reducing the profitability of downstream firms outside option in this way allows the low-cost supplier to extract more surplus from the downstream firms through the fixed fee. Surprisingly, this bargaining effect may swamp the commitment effect from Rey and Tirole (2005), so that a ban on price discrimination may actually cause prices to fall. Indeed, the bargaining effect may be so strong that the low-cost supplier prices below marginal cost if price discrimination is banned. A ban on price discrimination tends to cause price to fall when the cost difference between the suppliers is sufficiently narrow. The exact mechanism through which this bargaining effect works is somewhat subtle and requires formal analysis. As noted, credibly committing to a low per-unit price for both downstream firms reduces the value of the outside option of turning to the alternative, high-cost supplier. However, reducing the per-unit price also reduces the industry profit to be shared between the downstream firms and the low-cost supplier since the low per-unit price causes the downstream firms to be too competitive. The low-cost supplier must balance desire to capture a larger share of the surplus pie with a low per-unit price against the reduction in the size of the pie to be divided. It should be emphasized that a ban on price discrimination is required for the bargaining effect to operate. In the absence of such a ban, the possibility of unilateral price discounts always drives the equilibrium per-unit price to the marginal cost of production. This paper is related to the literature cited above on the welfare benefits of banning price discrimination in intermediate-good markets (Katz, 1987; DeGraba, 1990; Yoshida, 2000). The underlying mechanism is different. For example, Katz (1987) considered a supplier and an asymmetric downstream duopoly, in which only the large firm can credibly threaten to integrate backward. The lower retail price is caused by an alignment of all input prices on the lower input price: the small firm benefits from the large firm s bargaining power. By contrast, a ban on price discrimination does not require downstream asymmetries for prices to fall in my model. The bargaining effect arises because the low-cost supplier tries to offset the reduction in its profits caused by the presence of an alternative supply. In addition, note the underlying mechanisms are completely different in the two papers since the upstream firm benefits from the ban on price discrimination in my model but not in Katz s. A similar bargaining effect to the one in this paper can be found in several other recent papers. The bargaining effect arises, for example, in Avenel and Caprice s (2006) model of contracting with downstream product differentiation, in Marx and Shaffer s (1999) model of sequential bargaining between two suppliers and a single retailer, and in Chen and Riordan s (2004) model of the strategic interplay between

4 66 STÉPHANE CAPRICE vertical integration and exclusive dealing. None of these papers consider the question of a ban on price discrimination that is the focus of my paper. The remainder of this paper is organized as follows. The formal analytical framework and the discriminatory pricing are presented in Section II. Section III contains the analysis of banning price discrimination. Some illustrative welfare results are provided in Section IV. Section V discusses results robustness and concludes. II. Model An upstream firm U produces an input at marginal cost c. It competes against a fringe of less efficient rivals, whose marginal cost is c c. The input is used by two downstream firms, D 1 and D 2, which transform the input into the final product on a one-for-one basis at zero marginal cost. The upstream firm U makes take-it-or-leave-it contract offers (w i,f i ) to each downstream firm D i, where w i is the wholesale price of the input and F i is the fixed fee. Competition among the high-cost fringe suppliers ensures that a downstream firm would pay c if it turned to the fringe for its supply. 1 The timing of the game is as follows. Stage 1: The upstream firm U makes offers simultaneously and secretly, one for each firm. Neither downstream firm can observe what happened in the other negotiation. Stage 2: Downstream firms either accept or reject offers simultaneously. Stage 3: At the beginning of this stage, each downstream firm observes which supplier is supplying its rival: the low-cost supplier U or a less efficient rival from the fringe. After observing this, downstream firms compete in a noncooperative quantity game. At the start of the stage 3, acceptance or rejection decisions are public, but supply conditions are always secret. 2 This assumption reflects the fact that, while it can be hard to observe supply conditions, it is somewhat easier to observe the input used by the rival to produce and, thus, to learn its accep- 1 Another approach would be to assume that instead of a competitive fringe of highcost suppliers, there is a single high-cost supplier that also offered two-part tariffs in competition with the low-cost supplier. Restricting attention to weakly undominated strategies for the high-cost supplier, in equilibrium the high-cost supplier offers contracts involving a wholesale price of c and no fixed fee, the same outcome as with a fringe of high-cost suppliers. 2 With secret discounts, a firm does not know the true wholesale price charged to its rival (inferring prices ex post from a rival s market behaviour can also be problematic if there are exogenous firm-specific shocks). By contrast, acceptance or rejection decisions may be observable.

5 EFFECTS OF BAN ON PRICE DISCRIMINATION 67 tance decision. Furthermore, even if the products of the upstream firms are homogeneous, they could have different names and be easy to identify. It is worth noting that a breakdown in negotiations between the lowcost supplier and a customer is assumed to be observable but not verifiable (in court), and therefore cannot be contracted upon. 3 Let π i (w i,y i,y i ) be downstream firm i s flow payoff, function in its wholesale price, its quantity and the quantity of its rival. Since retailers products are substitutes for final-good consumers, π i / y i < 0. Then, let y BR i (w i,y i ) denote firm i s best response to y i : yi BR (w i,y i ) = arg max π i (w i,y i,y i ), (1) y i and πi BR (w i,y i ) denote the related flow payoff: πi BR (w i,y i ) = max π i (w i,y i,y i ). (2) y i Assume the product market equilibrium is unique for any (w 1,w 2 ) in which both firms are active, with firm i s equilibrium flow payoff given by π i (w i,w i ). For w i sufficiently large; firm i s flow payoff is zero. Otherwise, if both firms are active, equilibrium flow payoffs display the following properties: firm i s gross profit decreases in w i, its own input price, and increases in w i, its rival input price: i.e., π i / w i < 0 and π i / w i > 0. Assume in addition that 2 π i / w i w i < 0, implying that a decrease in the firm s marginal cost is less valuable to it the lower the rival s marginal cost. Roughly speaking, the lower marginal cost to the rival makes the rival more aggressive in any equilibrium. Hence, the value to the initial firm of a given reduction in its marginal cost can be expected to be lower. Let y i (w i,w i ) be firm i s equilibrium quantity as a function of the wholesale prices. Then, if both downstream firms accept U s contracts and are active, U s flow payoff is 2 i=1 (w i c)y i (w i,w i ) and the overall joint payoff of U and downstream firms is (w 1,w 2 ) = 2 (w i c)y i (w i,w i ) + i=1 2 π i (w i,w i ). (3) Let u (w 1,w 2 ) be U s payoff if it could publicly commit to the two contracts (w 1,F 1 ) and (w 2,F 2 ). The dependence of u on the fixed fees can be suppressed because contracts must satisfy the constraint that each retailer earns non-negative profits. In equilibrium these constraints obviously hold with equality i.e., F 1 = π 1 (w 1,w 2 ) π 1 (c,w 2 ) and F 2 = π 2 (w 2,w 1 ) i=1 3 Section V discusses the sensitivity of the results to this assumption and considers how the results would change under alternative assumptions concerning contractibility.

6 68 STÉPHANE CAPRICE π 2 (c,w 1 ) and these equalities can be used to substitute for the fixed fees. U s payoff can thus be written u(w 1,w 2 ) = (w 1,w 2 ) 2 π i (c,w i ). (4) i=1 Assume that the firms flow payoffs are symmetric, i.e., given (w 1,w 2 ) and (w 1,w 2 ), where w 1 = w 2 and w 2 = w 1, then π 1(w 1,w 2 ) = π 2(w 1,w 2 ). Assume in addition that (w,w) is twice differentiable and is concave in w and that arg max w 0 (w,w) is unique. The same properties will naturally extend to the function u(w, w). Let w m the input price that maximizes the overall joint payoff (3): w m = arg max (w,w). (5) w 0 Thus (w m,w m ) is the maximum overall joint payoff. Supposing that c = and that upstream firm U could commit to a single contract for both downstream firms, U would offer each one the efficient contract (w m,f m ), where F m = π i (w m,w m ). Each downstream firm i would accept its offer, would supply y i (w m,w m ), and U would earn (w m,w m ). This is the monopolist s commitment solution (i.e., without an alternative supply). However, absent a ban on price discrimination, U cannot commit to a single contract and furthermore it is not a monopolist but faces the threat of a second source. To derive the equilibrium in the absence of commitment to a single contract, I adopt the refinement of out-of-equilibrium beliefs that is standard in the literature of passive conjectures. This means that, at stage 2, when downstream firms receive (unexpected) offers, they do not revise their beliefs about the offers made to their rival. Such conjectures are also called market-by-market-bargaining conjectures. 4 Let (w1,w 2 ) denote the unique candidate equilibrium in wholesale prices and (y1,y 2 ) the corresponding equilibrium in quantities, i.e., y 1 = y 1 (w1,w 2 ) and y 2 = y 2(w2,w 1 ). Under passive beliefs, for any contract (w i,f i ) offered, if D i accepts the contract, it expects D j to play the candidate equilibrium quantity yj since by assumption firm j cannot observe changes in w i ; hence D i plays 4 The commitment problem arises under other belief structures as well. For instance, under wary beliefs introduced by McAfee and Schwartz (1994), following an out-of-equilibrium contract offer, a downstream firm would believe that its rival received the best response to its contract offer from the point of view of the upstream firm. See Segal and Whinston (2003) for a general analysis of equilibria under various belief structures.

7 EFFECTS OF BAN ON PRICE DISCRIMINATION 69 yi BR (w i,yj ). If, on the other hand, D i rejects the contract offer, its rejection is observed by D j and it expects to play an asymmetric Cournot Nash equilibrium in which its marginal cost is c and D j s marginal cost is wj. D i thus chooses quantity yi BR (c,y j (wj,c )) such that yi BR (c,y j (wj,c )) = y i (c,wj ). Retailer i s incentive compatibility constraint (the constraint that the retailer not resort to the alternative supply) is πi BR (w i,yj ) F i π i (c,wj ). The optimal contract (w i,f i ) maximizes subject to (w i c)y BR i (w i,y j ) + F i + (w j c)y j (6) πi BR (w i,yj ) F i π i (c,wj ). (7) Upon substituting (7), which holds as an equality, into (6), the optimal wholesale price is the value of w i maximizing (w i c)yi BR (w i,yj ) + π i BR (w i,yj ) π i(c,wj ) + (w j c)y j. (8) PROPOSITION 1. In equilibrium with passive beliefs, U charges the two downstream firms a wholesale price that equals its equals its marginal cost: w i = c, i = 1, 2. Equilibrium quantities Cournot Nash quantities, y i = y i (c, c). The firms profits are π U = (c,c) 2π i (c,c) π i = π i (c, c), i = 1, 2. The proofs of this all subsequent propositions can be found in the Appendix. The intuition for Proposition 1 is as follows. Since the downstream firm s output choice is unaffected by the unobserved changes in wholesale price paid by its rival, the upstream firm U, in its dealings with any firm, acts as if the two were integrated and faced a given residual downstream demand. This result, due to Hart and Tirole (1990) and further analysed by O Brien and Shaffer (1992) and McAfee and Schwartz (1994), highlights the commitment problem faced by a supplier. The existence of an alternative source does not affect quantities and industry profits. It only affects the division of profits between U and the downstream firms. U always supplies the two downstream firms at a wholesale price equal to marginal cost. The wholesale price is the same as in the absence of the second source. But in the presence of the second source, the fixed fee paid by each downstream equals 1 2 (c,c) π i(c,c). U s profit is u(c, c) = (c,c) 2π i (c,c). Because each downstream firm now can alternatively buy from the fringe at the constant marginal cost

8 70 STÉPHANE CAPRICE c, its disagreement payoff is non-zero. Its outside option, i.e., π i (c,c) is a decreasing function of the price c at which it can buy from the alternative supply. III. Banning Price Discrimination I next turn to an analysis of the effect of a ban on wholesale price discrimination. In a model without an alternative upstream supplier, Rey and Tirole (2005) found that banning price discrimination has the perverse effect of restoring the upstream firm s monopoly power. With secret contracts and passive beliefs, the upstream monopolist could not commit to high wholesale prices. Banning price discrimination restores this commitment by assuring each downstream firm that its rival got the same contract as itself. The addition of an alternative supply in my model introduces a bargaining effect. Banning discrimination still benefits the low-cost supplier by restoring its commitment power. However, due to the bargaining effect, a ban on price discrimination may lead to an increase in the quantity sold on the final market and thus increase social welfare. To see this, consider the same framework presented above, and assume that U is restricted to offer the same contract to the two downstream firms, i.e., (w, F ). Observe the game is now played under complete information at each stage. Therefore, there is no scope for opportunistic behaviour from U. Unlike Rey and Tirole s framework, each downstream firm can now alternatively buy from the fringe at price c. Its payoff in the rejection case is not zero but depends now on c. The retailer s disagreement payoff is a decreasing function of the price at which it can buy from the fringe, but, more importantly, it is an increasing function of the price at which its downstream rival buys from the upstream firm. Its disagreement payoff increases as the input price of its rival increases ( π i / w i > 0). The retailer s nonnegative profit constraint is π i (w, w) F π i (c,w). The upstream firm U sets F = π i (w, w) π i (c,w) and w such that its payoff u(w, w) = (w,w) 2π i (c,w) is maximized. PROPOSITION 2. A ban on price discrimination benefits the low-cost supplier U. In equilibrium under a ban on price discrimination, U charges the downstream firms a lower wholesale price than that which would maximize industry profit; i.e., w i = w nd w m, i= 1, 2. Quantities are such that y i (w nd,w nd ) y i (w m,w m ). The firms profits are π U = (w nd,w nd ) 2π i (c,w nd ) π i = π i (c,w nd ), i = 1, 2.

9 EFFECTS OF BAN ON PRICE DISCRIMINATION 71 We investigate how the upstream firm s profit varies with w. Decompose the derivative of the function u(w, w) with respect to w into two terms: [ ] [ d (w, w) 2 π i(c ],w). (9) dw w The first term in (9) shows the effect of an increase in w on industry profit. This derivative is zero at the wholesale price maximizing industry profit w m = arg max w (w,w). A small reduction in w below w m has only a second-order effect on industry profit. However, in light of the second term, this reduction in w leads to a first-order decrease in the downstream firms outside options, and thus a first-order increase in the low-cost supplier s share of industry profit. Hence it is optimal for the low-cost supplier to shade the wholesale price below that maximizing industry profit. It is easy to see that the extra commitment power afforded the ban on price discrimination benefits U. By definition of w nd = arg max w u(w, w), it follows that u(w nd,w nd ) = (w nd,w nd ) 2π i (c,w nd ) u(c, c) = (c,c) 2π i (c,c), which is the supplier s profit under price discrimination. To sum up, U does not get the entire monopoly profit (w m,w m ) because of upstream competition. U supplies y i (w nd,w nd )>y i (w m,w m ) to the two downstream firms for a wholesale price that is equal to w nd and for a payment equals (w nd,w nd ) π i (c,w nd ). Since w nd <w m, the overall joint payoff is smaller than without an alternative supply. 5 PROPOSITION 3. The lower the second source s marginal cost c, the lower are industry profits. The importance of the bargaining effect increases the more efficient is the second source. The lower is c, the better are downstream firms outside options. The low-cost supplier reduces w in order to impair these outside options and increase its share of industry profit. 6 5 The imposition of a ban on price discrimination has the same effect in my model as would a change from passive to symmetric beliefs, whereby following any out-of-equilibrium contract offer, a downstream firm believes that its rival receives the same deviation contract. 6 As the appendix shows, this result hinges on the assumption on the cross-partial derivative 2 π i / w i w i < 0.

10 72 STÉPHANE CAPRICE PROPOSITION 4. Under a ban on price discrimination, the equilibrium wholesale price may be less than the marginal cost of production. This implies that quantities on final market may be greater than in a competitive equilibrium and industry profits smaller: and y i (w nd,w nd )>y i (c, c) (w nd,w nd ) < (c, c). There exists a threshold value c such that w nd c if c c. The only motive of such an equilibrium contract is to extract more rents from retailers. Because of the negative relation between the efficiency of the second source and the equilibrium wholesale price in the intermediate market, when the second source is sufficiently competitive, the wholesale price will be driven below the marginal cost of production. Even if the wholesale price ends up being below cost, industry surplus is still positive and the low-cost supplier s payoff is also positive since franchise fees are always higher than the flow losses. By restoring the commitment of the supplier, a ban on price discrimination may increase social welfare. This result depends on the alternative suppliers efficiency, requiring the gap between alternative suppliers cost and that of the low-cost supplier to be sufficiently narrow. IV. Further Welfare Results in Linear Demand Examples To further illustrate the effects of a ban on price discrimination, focusing in particular on the conditions under which a ban increases social welfare, I consider two linear-demand examples. In the first example, the inverse demand function facing downstream firm i given its rival s output is y j is P i (y i,y j ) = 1 y i γy j, i j = 1, 2, (10) where γ (0, 1) measures the degree of downstream rivalry, that is how similar the retailers services are perceived by consumers to be when selling the same product, which, for example, may have to do with differences in the retailers locations, store layouts, sales services, etc. When γ = 0, the retailers services are viewed as independent, but as γ = 1 their services become closer substitutes, in the limit being perfect substitutes. The second example involves n downstream firms producing perfect substitutes. Inverse demand is given by n P(Y)= 1 y i. (11) i=1

11 EFFECTS OF BAN ON PRICE DISCRIMINATION 73 Proposition 4 suggests that a ban on price discrimination may increase or decrease social welfare in my model with upstream competition. In the two linear-demand examples, I can derive explicit conditions on the competitiveness of the downstream market (the degree of downstream substitution, γ, in the first example and the number of downstream firms, n, in the second) under which a ban on price discrimination is welfare enhancing. Taken together, the results in this section paint a complex picture of the conditions under which antitrust authorities should view a ban on price discrimination favorably or not. PROPOSITION 5. In the first example with inverse demand given by Equation (10), a ban on price discrimination increases social welfare if c < c and lowers social welfare if c > c, where c = 2γ(1 c) γ2 (1 c)+ 4c. 4 Further, c / γ > 0. PROPOSITION 6. In the second example with inverse demand given by Equation (11), a ban on price discrimination increases social welfare if c < c and lowers social welfare if c > c, where c = 1 c + 2cn. 2n Further, c / n < 0. Propositions 5 and 6 show that, depending on how increasing competitiveness of the downstream market is indexed, an increase in downstream competitiveness may increase or decrease the set of parameters for which a ban on discrimination would raise social welfare. In the first example, covered by Proposition 5, an increase in competitiveness as indexed by the substitution parameter γ enlarges the set of parameters for which a ban on price discrimination equilibrium increases social welfare. In the second example, covered by Proposition 6, an increase in competitiveness as indexed by the number of firms, n, has the opposite effect. The reason for the ambiguous results is that there are offsetting level effects and marginal effects corresponding to an increase in downstream competitiveness. On the one hand, an increase in downstream competitiveness reduces the level of the downstream firms outside options, reducing the importance of the bargaining effect in level terms. On the other hand, an increase in downstream competitiveness may increase the marginal benefit of impairing their outside option relative to the marginal loss of reducing industry profit. How

12 74 STÉPHANE CAPRICE the two effects counterbalance is a subtle function of both upstream and downstream competitiveness. Although the comparative statics associated with the linear demand examples are subtle, they still provide concrete cases in which a ban on price discrimination is socially beneficial. This result contrasts Rey and Tirole s (2005) finding in a model with an upstream monopolist that a ban on price discrimination always reduced welfare. Also, they showed that the more competitive the downstream segment, whether measured by substitutability in retailers or by numbers of firms, the more detrimental was a ban on price discrimination. My examination of the influence of downstream substitutability separately from the number of downstream firms show that in the presence of upstream competition, the two indexes of downstream competition are not qualitatively similar. I demonstrated cases in which a ban on price discrimination is potentially welfare enhancing the more substitutable the downstream units, but the lower the number of downstream firms. V. Conclusions I identify a bargaining effect in intermediate-good markets that is not currently described in the literature. I show that below-cost pricing, i.e., a wholesale price lower than marginal cost, may arise as a device to facilitate a surplus transfer from the downstream level of an industry to an upstream supplier. Such a result applies when the upstream firm is threatened by a second, inferior source. The low-cost upstream firm would like to gain the largest share of the largest industry profit pie, but those two goals conflict since a decrease in the wholesale price reduces both the retailers disagreement payoffs and industry profit. This bargaining effect arises only when the low-cost supplier can commit to wholesale prices, a commitment which a ban on price discrimination would allow. The bargaining effect would be absent if price discrimination secret price cuts in particular were legal. Since equilibrium wholesale prices may be set below the dominant supplier s marginal cost, social welfare may rise with a ban on price discrimination on the intermediate-good market. The bargaining effect that I identified does not hinge critically on the assumption that the upstream firm offers a specific form of nonlinear tariffs, e.g., two-part tariffs. Relaxing this assumption and allowing the manufacturer to propose the same menu of contracts to both retailers, it can be shown that, though equilibrium wholesale prices and franchise fees will change from the two-part tariff case, the manufacturer is still not able to obtain the monopoly industry profit for itself, and so my qualitative results would go through. 7 7 See Marx and Shaffer (2004a, b) or Kolay et al. (2004) for an analysis of general nonlinear contracts.

13 EFFECTS OF BAN ON PRICE DISCRIMINATION 75 My results do hinge critically on the assumption that a breakdown in negotiation between the low-cost supplier and a customer is observable but not verifiable (in court), and therefore cannot be contracted upon. 8 Assume instead that breakdowns in negotiations over wholesale contracts are verifiable as well as observable, and are therefore contractible (as do, for example, Inderst and Wey, 2003). The supplier and one of the downstream firms, say D 1, can write a contract specifying what they will do in the event of a breakdown in negotiations between the supplier and D 2. If breakdown is a contractible contingency, different prices will be negotiated after a breakdown, and so the uniform price from the no-breakdown case will not affect breakdown values. Then, we recover Rey and Tirole s (2005) result that a ban on price discrimination reduces social welfare. Prices negotiated for the case in which both downstream firms are supplied do not carry over to the case of breakdowns and the monopoly industry profit is replicated. Another approach is to assume that all existing contracts are null after a refusal occurs, and thus renegotiated; this has similar implications for the welfare effects of a ban on price discrimination as does the assumption that breakdowns are contractible contingencies. I illustrated the effects of a ban on price discrimination, focusing in particular on the conditions under which a ban increases social welfare. I considered two linear-demand examples. My results contrast Rey and Tirole s (2005) finding in a model with an upstream monopolist that the more competitive the downstream segment, whether measured by substitutability in retailers or by numbers of firms, the more detrimental was a ban on price discrimination. In the presence of upstream competition, the two indexes of downstream competition are not qualitatively similar. An increase in competitiveness as indexed by substitutability in retailers enlarges the set of parameters for which a ban on price discrimination increases social welfare. An increase in competitiveness as indexed by the number of downstream firms has the opposite effect. Although the results in the downstream competitiveness paint a complex picture of the conditions under which antitrust authorities should view a ban on price discrimination favourably or not, I argue a ban on price discrimination is welfare enhancing when the cost difference between the suppliers is sufficiently narrow. This result is of practical importance since the upstream firm is generally not a pure monopolist in real-world cases. 8 The same distinction arises between Marx and Shaffer (2004c), who adopt the same assumption as I do, and Rey et al. (2005), who adopt the alternative assumption.

14 76 STÉPHANE CAPRICE Acknowledgements I thank the referee and, especially, the editor of this special issue Christopher Snyder for their incisive comments. I also thank Patrick Rey and Mike Waterson for their helpful comments on an earlier version of this paper. I thank S.F. Hamilton, C. Wey and the participants to INRA-IDEI (Toulouse, 2004), ESEM (Madrid, 2004), IIOC (Atlanta, 2005) conferences and the IO seminar at the Economics Department of the University of Warwick. This work was finalized when I was visiting fellow at the Economics Department of the University of Warwick. Appendix Proof of Proposition 1. Recall w i maximizes: (w i c)yi BR (w i,y i ) + π i BR (w i,y i ) π i(c,w i ) + (w i c)y i. (12) The last two terms of (12) are independent of w i, hence we need only consider the effect of w i on the first two terms. Differentiating (12) with respect to w i and applying the envelope theorem (that is, noting that yi BR (w i,y i ) maximizes π i(w i,y i,y i ) and satisfies the relevant first-order condition), equilibrium wholesale prices satisfy (w i c) ybr i (w i,y i ) w i = 0. (13) Since yi BR (w i,y i )/ w i < 0, for (13) to hold, wholesale prices must satisfy w i = c, i = 1, 2. Because of the assumption of quantity competition, multilateral deviations are not an issue here (See Rey and Vergé, 2004). The expressions for firms profits follow from the fact that the retailers incentive compatibility constraints (the constraints that the retailers not resort to the alternative supply) bind. Q.E.D. Proof of Proposition 2. The low-cost supplier s payoff is u(w, w) = (w,w) 2 π i (c,w). (14) i=1 Let (w,c ) denote the derivative of (14), where the first argument of is the wholesale price of the low-cost supplier and the second argument is the cost the downstream firm pays in the event of a breakdown. The first-order condition from maximization of (14) is 0 = (w,c ), or, dividing through by 2,

15 EFFECTS OF BAN ON PRICE DISCRIMINATION 77 [ yi (w, w) 0 = (w c) + y ] i(w, w) y i (w, w) + πbr i (w, y i (w, w)) w i w i w i [ + πbr i (w, y i (w, w)) y i (w, w) + y ] i(w, w) y i w i w i πbr i (c,y i (w, c [ )) y i (w, c ] ). (15) y i w i Noting that, by definition, w m = arg max w (w,w), substituting w = w m into expression (15) yields (w m,c ) = πbr i (c,y i (w m,c )) y i [ y i (w m,c ) w i ]. (16) Equation (16), together with the fact that π i (w i,w i )/ w i > 0, implies (w m,c )<0. Since the objective function (14) is concave, the equilibrium wholesale price satisfies w i = w nd w m, i= 1, 2. (17) The expressions for firms profits follow from the fact that the retailers incentive compatibility constraints (the constraints that the retailers not resort to the alternative supply) bind. Q.E.D. Proof of Proposition 3. Comparative statics reveal that dw nd (c )/dc > 0. Applying the implicit function theorem to the first-order condition (15) shows that the sign of dw nd (c )/d c is the same as the sign of (w nd,c )/ c since / w<0 due to the concavity of the upstream firm U s objective. Now (w nd,c ) c = 2 π i (c,w nd ) w i w i. (18) The assumption that the cross-partial derivative 2 π i (w i,w i )/ w i w i is negative implies that expression (18) is positive. Q.E.D. Proof of Proposition 4. Recall the definition of (w,c ) as the first-order condition that is proportional to expression (15). The first step in the proof is to show that, if we set w =c in the first argument and c =c in the second argument, then (c,c) is negative. Substituting w = c into (15), we have [ (c,c ) = πbr i (c, y i (c, c)) y i (c, c) + y ] i(c, c) y i w i w i πbr i (c,y i (c, c [ )) y i (c, c ] ). (19) y i w i

16 78 STÉPHANE CAPRICE Substituting c = c for the second argument in (19), (c,c)= πbr i (c, y i (c, c)) y i (c, c). (20) y i w i The first factor in (20) is negative since retailers products are substitutes. The second factor in (20) is positive. To see this, note y i (w i,w i ) w i = ybr i (w i,y i (w i,w i )) y i y i (w i,w i ) w i. (21) Both factors on the right-hand side of (21) are positive, hence the whole expression is positive. Hence the whole expression in (20) is negative. This establishes that (c,c)<0. The second step in the proof is to note that the concavity of upstream firm U s objective function implies that w nd (c)<c. The remainder of the proof follows readily. Because w nd (c ) is an increasing function of c and because w nd (c)<c, by continuity there exists a threshold value c such that the sign w nd (c ) c is negative for c < c. Q.E.D. Proofs of Propositions 5 and 6. Begin with the first example, with linear inverse demand given by Equation (10). The equilibrium wholesale price satisfies { { 8c 2γ w nd = min w m 2 (1 + c)+ γ 3 (1 + c)+ 4γ(c }} c), max, 0 (22) 2(4 2γ 2 + γ 3 ) where w m = 2c + γ(1 + c). 2(1 + γ) The threshold value such that w nd = c is c = 2γ(1 c) γ2 (1 c)+ 4c. (23) 4 Differentiating (23) with respect to γ yields c γ = 1 (1 γ)(1 c)>0. (24) 2 Next, turn to the second example, with linear inverse demand function given by (11). The equilibrium wholesale price satisfies { { c(1 + n) (1 n)(1 2nc w nd = min w m }} ), max, 0 (25) 2(1 n + n 2 )

17 EFFECTS OF BAN ON PRICE DISCRIMINATION 79 where w m c(1 + n) (1 n) =. 2n The threshold value such that w nd = c is c = 1 c + 2cn. (26) 2n Differentiating (26) with respect to n yields c c) = (1 < 0. (27) n 2n 2 Q.E.D. References Avenel, E. and S. Caprice (2006) Upstream Market Power and Product Line Differentiation in Retailing, International Journal of Industrial Organization, forthcoming. Bork, R. (1978) The Antitrust Paradox. New York: Basic Books. Chen, Y. and M. H. Riordan (2004) Vertical Integration, Exclusive Dealing, and Ex-post Cartelization, Boston University working paper. DeGraba, P. (1990) Input Market Price Discrimination and the Choice of Technology, American Economic Review, 80, Hart, O. and J. Tirole (1990) Vertical Integration and Market Foreclosure, Brookings Papers on Economic Activity, Microeconomics, Inderst, R. and C. Wey (2003) Bargaining, Mergers, and Technology Choice in Bilaterally Oligopolistic Industries, RAND Journal of Economics, 34, Katz, M. (1987) The Welfare Effects of Third-Degree Price Discrimination in Intermediate Goods Markets, American Economic Review, 77, Kolay, S., G. Shaffer, and J. A. Ordover (2004) All-Units Discounts in Retail Contracts, Journal of Economics & Management Strategy, 13, Marx, L. M. and G. Shaffer (1999) Predatory Accomodation: Below-Cost Pricing without Exclusion in Intermediate Goods Markets, RAND Journal of Economics, 30, Marx, L. M. and G. Shaffer (2004a) Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity, and Uniformity: Comment, American Economic Review, 94, Marx, L. M. and G. Shaffer (2004b) Opportunism and Menus of Two-Part Tariffs, International Journal of Industrial Organization, 22, Marx, L. M. and G. Shaffer (2004c) Upfront Payments and Exclusion in Downstream Markets, Duke University working paper. McAfee, R. P. and M. Schwartz (1994) Opportunism in Multilateral Vertical Contracting: Nondiscrimination, Exclusivity and Uniformity, American Economic Review, 84, O Brien, D. P. and G. Shaffer (1992) Vertical Control with Bilateral Contracts, RAND Journal of Economics, 23, Rey, P., J. Thal, and T. Vergé (2005) Slotting Allowances and Conditional Payments, IDEI working paper.

18 80 STÉPHANE CAPRICE Rey, P. and J. Tirole (2005) A Primer on Foreclosure, forthcoming, in M. Armstrong and R. Porter (eds.), Handbook of Industrial Organization, volume 3. Amsterdam, Elsevier. Rey, P. and T. Vergé (2004) Bilateral Control with Vertical Contract, RAND Journal of Economics, 35, Segal, I. and M. Whinston (2003) Robust Predictions for Bilateral Contracting with Externalities, Econometrica, 71, Yoshida, Y. (2000) Third-Degree Price Discrimination in Input Markets: Output and Welfare, American Economic Review, 90,