Merger Efficiency and Welfare Implications of Buyer Power

1144 Discussion Papers Deutsces Institut für Wirtscaftsforscung 011 Merger Efficiency and Welfare Implications of Buyer Power Özlem Bedre-Defolie and tépane Caprice

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Merger Efficiency and Welfare Implications of Buyer Power Özlem Bedre-Defolie tépane Caprice July 011 Abstract Tis paper analyzes te welfare implications of buyer mergers, wic are mergers between downstream firms from different markets. We focus on te interaction between te merger s effects on downstream efficiency and on buyer power in a setup were one manufacturer wit a non-linear cost function sells to two locally competitive retail markets. We sow tat size discounts for te merged entity as no impact on consumer prices or on smaller retailers, unless te merger affects te downstream efficiency of te merging parties. Wen te upstream cost function is convex, we find tat tere are waterbed effects, tat is, eac small retailer pays a iger average tariff if a buyer merger improves downstream efficiency. We obtain te opposite results, anti-waterbed effects, if te merger is inefficient. Wen te cost function is concave, tere are only anti-waterbed effects. In eac retail market, te merger decreases te final price if and only if it improves te efficiency of te merging parties, regardless of its impact on te average tariff of small retailers. Keywords Buyer mergers, non-linear supply contracts, merger efficiencies, size discounts, waterbed effects. JE Classifications D43, K1, 4. Tis paper was circulated under title Inefficient Buyer Mergers To Obtain ize Discounts. Te first version was available in December 008. Te autors are grateful to ANR-DFG Researc Funding for te project entitled Market Power in Vertically Related Markets. We would like to tank for elpful comments Mark Armstrong, Caterine de Fontenay, Bruno Jullien, Patrick Rey, Cristian Wey, seminar participants at te Toulouse cool of Economics, Ecole Polytecnique (Paris, DIW (Deutsces Institut für Wirtscaftsforscung, Berlin, EARIE (jubljana, 009, IIOC (Boston, 009, and EEA-EEM (Barcelona, 009. European cool of Management and Tecnology (EMT, ozlem.bedre@esmt.org. Toulouse cool of Economics, GREMAQ and INRA. Tis paper as been completed wen tépane Caprice was visiting te DIW (Deutsces Institut für Wirtscaftsforscung, Berlin. 1

1 Introduction In recent years te grocery industry as undergone a dramatic consolidation. 1 A substantial number of acquisitions ave taken place between retailers serving different geograpic markets, for example, te expansion by ainsbury s and Tesco in convenience store retailing in te UK, acquisitions of stores from different local markets by Aold (Neterlands 3 or Carrefour (France. 4 In addition to grocery retailers, in te last decade many cable network operators from different geograpic markets ave declared teir interests to merge. For instance, in 004 te Kabel Deutscland Group (KDG, wic operates te former broadband cable network of Deutsce Telekom AG in all of Germany apart from tree regions, 5 proposed to acquire te network operators in tose regions. 6 Moreover, in 005 Is and Iesy, wic were two cable network operators active in different local markets, merged and became Unity Media 7 and in 010 te German cable network operator Unitymedia was acquired by iberty Global Europe Holding B.V. (GE of te Neterlands. 8 uc mergers between firms from different local markets do not raise any orizontal (anticompetitive concerns, owever, tey could significantly affect te bargaining position or buyer power of te merging firms wen purcasing inputs from a supplier. Te supplier migt ten cange its unit price to oter buyers wo could be te rivals of te merged entity in different markets. As a result, te buyer merger would modify te competitive conditions and consumer prices in te downstream markets. In particular, te effects of large grocery cains buyer power on consumers and on small independent retailers (e.g., convenience stores ave become one of te most controversial debate for anti-trust autorities and for academics. 9 Te common view is tat te exercise of buyer power by retailers may lower teir purcasing costs and terefore lead to lower consumer prices. 10 On te oter and, as argued by te UK Competition Commission, te exercise of buyer power by te merged entity would ave adverse 1 Te concentration ratio of te five largest retailers (C5 in te 15 member countries of te EU is on average 50% (IGD European Grocery Retailing, 005. Te UK s top four grocery retailers account for 65% of total retail sales (te Competition Commission, 008, p.9. In te U, C8 was 17.5% in 007, instead of 15.3% in 00. ee te U Census Bureau, Retail Trade, ttp://www.census.gov/econ/concentration.tml ee te groceries report prepared by te Competition Commission (008. 3 ee te European Commission s (EC cases M.183 (Aold/ICA Förbundet/CANICA, 000, M.161 (Aold/uperdiplo, 000 and M.604 (ICA Aold/Dansk upermarket, 001. 4 ee te EC s cases M.1904 (Carrefour/Gruppo G, 000, M.1960 (Carrefour/Marinopoulos, 000, M.115 (Carrefour/GB, 000, M. 45 (Carrefour/Aold Polska, 007 and M.5858 (Carrefour/Marinopoulos/Balkan JV, 010. 5 Bundesländer Hessen, Baden-Wuerttemberg and Nort Rine-Westpalia. 6 Is in Nort Rine-Westpalian, Kabel Baden-Württemberg (KabelBW and te Hessian cable operator Iesy. Bundeskartellamt (Germany s Federal Cartel Office proibited te proposed takeover due to te KDG s dominant position in Germany. ee ttp://www.bundeskartellamt.de/wenglisc/news/arciv/arcivnews004/004 08 4.pp 7 ee B7 /05 and Iesy Repository/Is, COMP/M.3674. 8 Te EC s case M.5734. 9 Inderst and Mazzarotto (008, Caprice and clippenbac (008 provide recent surveys on te buyer power debate. ee also te Federal Trade Commission reports (001, 003 in te U, te Competition Commission s reports (000, 008 in te UK, te EC s report (1999, and te EC s merger cases Kesko/Tuko (1997, Rewe/Meinl (1999 and Carrefour/Promodes (000. Inderst and affer (008 provide a nice discussion on buyer power as a merger defence. 10 Tis goes back to Galbrait s (195 countervailing power argument.

effects on oter, smaller, grocery retailers troug te waterbed effect - tat is, suppliers aving to carge more to smaller customers if large retailers force troug price reductions wic would oterwise leave suppliers insufficiently profitable. 11 Besides affecting purcasing terms in te upstream (input market, a merger migt enance te efficiency of some or all merging parties in te downstream market because te firms learn from eac oters management expertise, 1 improve teir tecnologies by te diffusion of knowow, save costs from reallocating distribution across different stores, benefit from synergies, or save on costs of capital. 13 In contrast, a merger migt reduce te efficiency of te merging parties eiter because communication would be more costly witin a larger firm 14 or due to te conflicting organizational cultures. 15 Wen deciding weter to approve a merger, anti-trust autorities assess te efficiency gains from te merger against te possible anti-competitive effects of te merger. 16 It is terefore important to understand ow te effects of a merger on efficiency interact wit its potential anti-competitive effects. Tis paper analyzes te implications of a buyer merger between two independent downstream firms on teir rivals and consumers. 17 Considering non-linear supply contracts, wic appear to be widespread practices, 18 we sow tat wen te supplier s cost is convex, te buyer merger leads to size discounts for te merged entity, but tese discounts are given troug fixed transfers, and terefore ave no impact on consumer prices or on te rival firms. 19 However, wen te merger generates some efficiency gains, we find tat buyer power leads to waterbed effects, tat is, iger average tariffs for te firms not involved in te merger (small firms. It also increases te total quantity in te final markets. On te oter and, if te merger deteriorates te efficiency of te merging firms, it could still be profitable due to te size discounts generated by te merger. In tis case, we obtain te opposite results: a buyer merger leads to anti-waterbed effects for te oter retailers and decreases te consumer surplus. If te supplier as a concave cost function, a profitable buyer merger is necessarily efficient and it also results in a iger total quantity in eac 11 Te Competition Commission s report (003, paragrap.18. ee also Guidelines in te applicability of Article 81 of te EC Treaty to orizontal cooperation agreements (001/C3/0, paragrap 16: Te primary concerns in te context of buying power are tat... it may cause cost increases for te purcasers competitors on te selling markets because eiter suppliers will try to recover price reductions for one group of customers by increasing prices for oter customers... For a general discussion of waterbed effects see Dobson and Inderst (007. 1 Farrell and apiro (1990. 13 ince larger firms usually ave better access to te outside capital markets. 14 Bolton and Dewatripont (1994. 15 Weber and Camerer (003. 16 Te EU Competition aw, Rules Applicable to Merger Control, 010, pp. 186-187. 17 We follow te literature by generating buyer power troug an endogenous process of a merger between te firms active in different markets (like in Inderst and Wey, 007; Inderst and Valletti, 011. In tis respect our paper differs from te earlier contributions by von Ungern-ternberg (1996, and Dobson and Waterson (1997, wo consider mergers between competing firms. 18 Empirical studies find evidence tat manufacturers and retailers use non-linear supply contracts in te markets for bottled water in France (Bonnet and Dubois, 010 and for yogurt in te U (Berto Villas-Boas, 007. Te supplier survey conducted by te GfK Group (007, on te bealf of te Competition Commission, supports te use of complex non-linear supply contracts in te UK grocery market. 19 Tis result is in parallel wit a statement in te European Commission Guidelines in te applicability of Article 81 of te EC Treaty to orizontal cooperation agreements (001/C3/0. 3

market, owever it leads to anti-waterbed effects on te small retailers. 0 We focus on one upstream firm producing wit a non-linear cost and supplying two competitive markets in wic tere are many retailers competing in quantities. 1 In te case of convex upstream cost, for simplicity, we assume tat retailers simultaneously make take-it-or-leave-it contract offers to te supplier, were te contracts determine a quantity and a tariff. Te supplier ten decides wic offer(s to accept. Finally, trade takes place according to accepted contracts. Wen te supplier as a concave cost, we assume sufficiently ig bargaining power for te supplier and consider contract equilibrium as a solution to te negotiation between te supplier and eac retailer, since oterwise te existence of equilibrium cannot be guaranteed. 3 Our paper contributes to te literature analyzing te sources and implications of buyer power. Cipty and nyder (1999 analyze te profitability of a buyer merger between retailers. Tey sow tat te effect of te merger on te merging entities buyer power (vis-à-vis one supplier depend on te curvature of te industry surplus. For example, if te surplus function is concave (wic migt be due to a convex cost of te supplier, te buyer merger results in size discounts for te merging parties. imilar to Cipty and nyder (1999, we model buyer power as an endogenous process wic originates from a buyer merger due to te convexity of te supplier s cost function and/or downstream efficiency generated by te merger. Different from Cipty and nyder (1999, we analyze te implications of buyer power on retail competition, rival retailers and consumer prices by introducing downstream competition in eac market. 4 Alternatively, Katz (1987 models buyer power as a retailer s ability to integrate backwards by paying a fixed cost. Wen te retailer gets larger, it could reduce te average cost of its alternative supply option and tereby get a better price from te supplier. Using te approac of Katz (1987, Inderst and Valletti (011 allow all competing retailers to ave access to a costly outside option and analyze te implications of a buyer merger on te wolesale prices offered by te main supplier, on retail competition and on final prices Tey sow tat, since a buyer merger creates size asymmetry between te retailers, it leads to a lower wolesale price to te merged entity and iger wolesale prices to te oter retailers, tat is, waterbed effects. Tey find tat waterbed effects are less significant wen te fixed cost of te alternative supplier is lower. As a result, buyer power migt increase te consumer surplus. Tis is found to be te case wen te retail prices are strategic complements and te fixed cost of te alternative supplier is sufficiently low. Intuitively, in tis 0 As long as retailers quantities are strategic substitutes. 1 Main results would be valid if we considered a different timing leading to price competition. For instance, first, retailers simultaneously make two-part tariff contract offers to te supplier, second, retailers wit accepted contracts compete à la (differentiated Bertrand and ten pay teir tariffs to te supplier accordingly. ee Bedre-Defolie and Caprice (009 for tis generalization. A more balanced bargaining power distribution in contract equilibrium (as defined in Crémer and Riordan, 1987 would lead to te same equilibrium quantities, but cange only te profit saring between te firms. 3 ee egal and Winston (003. 4 Alternatively, in te setup of Cipty and nyder, mit and Tanassoulis (011 introduce uncertainty on te supplier s volume of sales at simultaneous negotiations wit independent buyers. Wen te upstream cost is convex, tey sow tat a larger buyer migt pay a iger input price if te uncertainty is sufficiently ig. In tis case, wit a ig probability te suplier sells zero to te oter buyers wic increases its expected marginal cost wen it negotiates wit te large buyer. 4

case te small retailers decrease teir price as a reaction to a more efficient rival and increase teir price due to waterbed effects, and te former effect dominates since te fixed cost is sufficiently low. Te assumption of linear contracts seems to be critical for teir results, since wit two-part tariffs, as a reaction to te retailers asymmetry, te supplier migt not cange te wolesale prices, but migt lower te fixed fee of te merged entity and increase te fixed fee of te oter retailers. Different from Inderst and Valletti (011, we consider non-linear supply contracts. In our paper, te buyer merger creates size asymmetry between te ex-ante symmetric retailers and so generates a size discount (a lower average tariff for te merged entity if te supplier s cost is convex: a larger retailer negotiates less at te margin of te supplier s cost. However, tis does not lead to a larger average tariff for a small firm unless te merger increases te efficiency of te merging parties. In te case of an efficient merger, te merged entity sells more at eac store and terefore lowers its average tariff even furter. Tis canges te bargaining position of te oter retailers and so leads to a iger average tariff for eac small retailer, tat is, tere are waterbed effects due to te convexity of te supplier s cost function. Wen quantities are strategic substitutes, te small firms sell less, competing against a more efficient rival, so te net effect of an efficient merger is not straigtforward. 5 We sow tat te total quantity in eac market is iger post-merger. On te oter and, if te supplier s cost is concave, te size of a retailer increases its average price, and so a buyer merger would be profitable only if it generates efficiency. In tis case, te buyer merger results in a lower average tariff for te oter retailers, tat is, tere are anti-waterbed effects. Despite paying a lower average tariff, we sow tat eac small retailer sells less post-merger since tey face a more efficient rival and quantities are strategic substitutes. As in te convex case, we find tat te efficient merger increases te total quantity in eac market. Majumdar (006, Cen (003 and Bedre-Defolie and affer (011 provide analyses of waterbed effects in a context of ex-ante asymmetric retailers (a dominant or large retailer and competitive fringe or small firms. Majumdar (006 sows tat waterbed effects exist since te large retailer wants to own more stores to increase its rivals costs (te spot price for smaller retailers as tere are fewer small stores over wic te upstream fixed cost can be spread. 6 Modeling buyer power as an exogenous bargaining strengt of te dominant firm, Cen (003 and Bedre-Defolie and affer (011 illustrate anti-waterbed effects on competitive fringe firms. 7 Cen (003 finds tat an increased buyer power lowers te final price, but te oter papers conclude tat te impact of buyer power on final prices is not clear. Te next section presents our bencmark model wit a convex upstream cost. In ection 3 we solve for te equilibrium of te bencmark. ection 4 analyzes te implications of a profitable buyer merger. In ection 5 we extend our analysis to te case were te supplier as a concave 5 Wen quantities are strategic complements, small firms sell more as a result of an efficient merger, so te efficient merger always increases te total quantity. 6 Majumdar (006 considers a large retailer wic could contract wit two perfectly competitive manufacturers outside of te spot market and, moreover, could appoint one or bot of te manufacturers wic ten commit(s to production by sinking a fixed cost. 7 Bedre-Defolie and affer (011 sow tat by offering a lower wolesale price to te fringe firms, a supplier could increase its outside option and tereby capture a iger rent from a more powerful dominant retailer. 5

cost function. Finally, we discuss te case of strategic complementarity and conclude in ection 6. Te Model We consider a vertical industry were one monopoly supplier sells its product to two locally competitive retail markets. In eac local market n identical retail stores resell te product of te supplier competing in quantities, were n. Te supplier s cost of producing Q units is C (Q, wic is assumed to be twice continuously differentiable, strictly increasing, C (Q > 0, and strictly convex, C (Q > 0. 8 Retailers ave constant marginal cost of retailing c. et Q denote te total quantity sold in local market ( = 1,. uppose tat for, te inverse market demand is given by P (Q, wic is twice continuously differentiable and downward sloping, P (Q < 0. We make te following assumption on te demand function, Assumption 1. P (Q + QP (Q < 0 for any Q, to ensure tat te second-order condition for te existence and uniqueness of an equilibrium is satisfied. Te supply contracts are assumed to be quantity-forcing contracts. Te contract of retailer i specifies quantity q i to be delivered to retailer i and money transfer t i to be made from retailer i to te supplier, for i = 1,..., n. We assume tat retailers ave all te bargaining power vis-à-vis te supplier. 9 Hence, retailers simultaneously make take-it-or-leave-it contract offers to te supplier wo in turn decides weter to accept tese offers or not. Te retailers wit accepted contracts buy te agreed quantity and pays its tariff. Retailers ten re-sell te quantity tey purcased to consumers. Retail competition is terefore à la Cournot, were quantities are determined by signed supply contracts between retailers and te supplier. 30 et T denote te total transfers made: T = n t i, and Q denotes te total quantities sold: Q = n q i. Moreover, T [i] (respectively Q [i] refer to te sum of all transfers (quantities except for i=1 te tariff paid (quantity sold by retailer i. imilarly, Q [i] denotes te sum of all quantities for i=1 local market except for te quantity sold by retailer i. Wit tis notation, te profit of te supplier is written as π U = t i + T [i] C ( Q [i] + q i, 8 We extend te analysis to concave cost in ection 5. 9 Tis assumption is for simplicity. Te main qualitative results would go troug if we allowed for sared bargaining power in contract equilibrium were quantity-forcing contracts are determined by simultaneous and secret bilateral negotiations between te supplier and retailers, as in Allain and Cambolle (011, for example. Te proofs of tis extension are available upon request from te autors. 30 We discuss te case of strategic complementarity in ection 6. 6

and te profit of retailer i, wic is active in market, is equal to π i = [ P (Q [i] + q i c ] q i t i. 3 Equilibrium Contracts and Payoffs Consider te contract coice of retailer i, taking te oter contracts as given. Retailer i cooses (q i, t i by maximizing its profit subject to te participation constraint of te supplier: max q i,t i [[ P (Q[i] + q i c ] q i t i ] s.t. T [i] + t i C ( Q [i] + q i πu[i] = T [i] C ( Q [i] (1 were te disagreement payoff of te supplier wit retailer i, π U[i], is te supplier s profit wen te negotiation wit retailer i fails. In equilibrium, te participation constraint of te supplier is binding, tat is, t i (q i = C ( ( Q [i] + q i C Q[i] ( since oterwise te retailer could increase its profits by raising t i. In oter words, in equilibrium, eac retailer pays a tariff equal to its cost contribution. Plugging te equilibrium tariff ( into te retailer s profit, we re-write retailer i s problem as max q i ([ P (Q[i] + q i c ] q i [ C ( Q [i] + q i C ( Q[i] ]. Te first-order condition caracterizes retailer i s best reply quantity to te quantities of oter retailers as, q BR i (Q [i], Q [i], 31 P ( Q [i] + q i qi + P ( Q [i] + q i = c + C ( Q [i] + q i (3 In equilibrium, eac retailer cooses a quantity wic maximizes te bilateral profit wit te supplier. Using te fact tat te markets are symmetric, condition (3 yields te equilibrium quantity, qi = q : P (nq q + P (nq = c + C (nq, (4 were te equilibrium quantity of local market and of te industry are respectively Q = nq and Q = nq. Hence, eac retailer pays t = C (nq C ((n 1 q. (5 and earns π = [P (nq c] q [C (nq C ((n 1 q ]. (6 31 Assumption 1 ensures tat te second-order condition olds. 7

4 Buyer Merger and ize Discounts We extend te model by introducing a single large retailer as a result of a merger between two independent stores. Te merged entity ( now operates two stores wic are active in different retail markets and makes a quantity offer to te supplier to distribute it troug its stores. A small retailer,, operates only one store, and tus makes a quantity offer to te supplier to distribute it at tat store. et q and q denote, respectively, te total quantity delivered by te large retailer and a small retailer (using symmetry, all small retailers buy te same quantity. We terefore ave Q = q + (n 1q, Q = Q. We allow for te possibility tat te merger affects not only te size but also te downstream efficiency of te merging parties. et c + µ be te marginal cost of retailing at eac store of te large retailer. Wen µ = 0, te merger as no effect on retail efficiency. However, wen µ < 0 (respectively µ > 0, te merger improves (deteriorates downstream efficiency. For instance, te merger could result in some economies of scale downstream or oter types of synergies and/or increase te costs of communication and coordination witin te merged entity. If te efficiencies generated by te merger are iger (lower tan te inefficiencies produced by te merger, we say tat µ < 0 (µ > 0. For te small retailers te marginal cost of retailing is still equal to c. Te merged entity cooses (q, t by maximizing its total profit from operating two stores subject to te participation constraint of te supplier: [ [ max P (Q [] + q ] q,t (c + µ q ] t s.t. t C ( Q [] + q C ( Q[] After plugging te binding constraint into te problem, te optimality condition caracterizes te best reply quantity of te large retailer to te oter retailer s quantities, q BR (Q [], Q [] : ( P Q [] + q q ( + P Q [] + q = c + µ + C ( Q [] + q were Q [] = (n 1q and Q [] = (n 1q. By te Implicit Function Teorem, observe tat te large retailer sells more wen te merger is more profitable, q µ < 0. Te small retailers coose teir contracts by solving problem (1, for i =, and tus teir best reply quantities are caracterized by (7 (8 P ( Q [] + q q + P ( Q [] + q = c + C ( Q [] + q. (9 By taking te total derivative of te first-order condition, we illustrate tat te small retailer s 8

equilibrium quantity decreases in te large retailer s quantity, q = P ( Q[] + q q + P ( Q [] + q C ( Q [] + q q P ( Q [] + q q + P ( Q [] + q ( < 0, C Q [] + q due to Assumption 1 and te convexity of te cost. Te solution to equations (8 and (9 caracterizes te equilibrium quantities after te merger, q te small retailer are, respectively, π (µ = [P (Q π (µ = [P (Q (c + µ] q c] q and q. Te profit of te large retailer and [C (Q C (Q q ], (10 [C (Q C (Q q ]. Comparing te optimality conditions before, (3, and after te merger, (8 and (9, gives us te following results: emma 1 Wen a buyer merger as no impact on retail efficiency, µ = 0, it does not cange te equilibrium quantities sold at eac store: q = q = q. Equilibrium transfers t and t are suc tat te large retailer pays a lower average tariff tan te small retailers, wic pay exactly te same tariff as before te merger: t (0 = C (nq C ( (n 1 q < t, t (0 = t. Intuitively, te large retailer negotiates a larger quantity wit te supplier wic as a convex cost function, and tus as a iger incremental contribution to te industry profit tan te small retailers. As a result, te large retailer pays a lower average tariff, tat is, gets size discounts. emma 1 implies tat te merging parties earn more tan tey would get if tey were separated, π (0 = [P (nq c] q [C (nq C ( (n 1 q ] > π, wic proves te profitability of te merger: Corollary 1 A buyer merger, wic as no impact on retail efficiency, µ = 0, is always profitable, since it brings size discounts. ize discounts for te large retailer alter neiter equilibrium quantities nor te profits of te small retailers, tat is, tere is no waterbed effect: π (0 = π. 9

ince we consider non-linear supply contracts and, in equilibrium, eac contract is bilaterally optimal olding te oters contracts fixed, te buyer merger results in a transfer of profits from te supplier to te large buyer witout affecting quantities and retail prices. Te parties always want to merge to increase teir size and negotiate a better deal wit te supplier. Wen te supplier as strictly increasing incremental production costs, a small buyer negotiates at te margin, were incremental costs are ig. In contrast, if two (or more small buyers merge, tey account for a larger fraction of te supplier s total sales, and tus negotiate less at te margin, tereby paying a lower price per unit. Wen te buyer merger improves retail efficiency, µ < 0, te parties always want to merge for two reasons: To extract discounts from te supplier and to benefit from te efficiencies generated by te merger. On te oter and, if te merger deteriorates downstream efficiency, µ > 0, it migt still be profitable. Tis would be te case, for example, wen te inefficiency produced by te merger is low enoug to be compensated by te gains from size discounts. emma If te merger generates less efficiencies (or more inefficiencies, te equilibrium profit of te merged entity decreases, tat is, µ π < 0. Te merger s efficiency (or inefficiency affects te merged entity s profit troug two cannels. First, wen µ decreases, becoming more efficient (or less inefficient increases its margin and so its profit. econd, wen te merged entity becomes more efficient (or less inefficient, te rival retailers quantities cange. ince retailers quantities are strategic substitutes, te small retailers sell less as a reaction to a more efficient (or less inefficient merger, tat is, dq dµ te large retailer earns more wen its rivals sell less, > 0. Moreover, π q = (n 1 [ q [ C (Q C (Q q ]] < 0, because te inverse demand is decreasing and te upstream cost is convex. As a result, te large retailer s profit decreases in µ: dπ dµ dπ dµ = π dq q dµ q < 0. Note tat a buyer merger is always profitable if µ = 0 (see Corollary 1 and tat we ave < 0 from emma. By continuity, we sow tat Corollary Tere exists µ > 0 suc tat for any µ < µ, a buyer merger is profitable. A buyer merger affecting downstream efficiency is going to cange te equilibrium quantities due to te efficiency impact of te merger. Proposition 1 If a buyer merger generates downstream efficiency, µ < 0, we ave q < q < q and Q < Q, 10

Inversely, if a buyer merger produces downstream inefficiency, µ > 0, we ave q < q < q and Q < Q. Corollary 3 As a result of a buyer merger affecting downstream efficiency, te total cange in te small retailers quantities is lower tan te cange in te merging parties quantities: (n 1 q q < q q. Wen te merger improves te efficiency of te merging parties, eac store of te merged entity as a competitive advantage against te small retailers and so sells more tan before. Tis implies tat eac small retailer sells less after te merger. Te first-order effect of te efficiency gains on te large retailer s quantity dominates te second-order effect on te small retailers quantities. Hence, te total quantity increases after an efficient buyer merger. ymmetric intuition applies for an inefficient buyer merger. ince te supplier as a non-linear cost function, te canges in quantities modify te average tariff paid by te small and te large retailers. Te large retailer could furter obtain more size discounts since it is asking for a larger quantity and te small retailers are buying a lower quantity. As a result, eac small retailer negotiates more at te margin, and so pays a iger average tariff. To see tis let t (q and t (q denote a small retailer s transfer for a given q wen te oter retailers sell teir equilibrium quantities, respectively, before and after te merger. Before te merger a small retailer pays and after te merger it pays t (q = C (q + (n 3q + q C (q + (n 3q. t (q = [C (q + (n 3q + q C (q + (n 3q ]. Consider for instance te canges after an efficient merger (µ < 0. From Corollary 3, we ave q t q > (n 3 (q q. A small retailer pays more for any volume of sales q, t (q > (q, because its cost contribution is iger wen te oter retailers total quantity is iger. ymmetrically, for an inefficient merger, a small retailer pays a lower average tariff post-merger since te oter retailers total quantity is lower: q q > (n 3 (q q. Tis discussion illustrates te effects of a buyer merger on te average tariff of a small retailer. ince we consider non-linear supply contracts, we define a waterbed effect as an increase in te average tariff of a small retailer due to te merger. If te merger decreases te average tariff of a small retailer, we say tat tere are waterbed effects. Te following lemma summarizes our results on waterbed effects: emma 3 As a result of an efficient buyer merger, eac small retailer pays a iger average tariff for a given volume of sales, tat is, tere are waterbed effects. Conversely, an inefficient buyer merger results in a lower average tariff for a small retailer, tat is, anti-waterbed effects. 11

Te net effect of te merger on a small retailer also depends on ow te merger canges its gross profit. et π (q (respectively, π (q denote a small retailer s profit for a given quantity q wen te oter retailers sell teir equilibrium quantities before te merger (respectively after te merger. Before te merger, a small rival retailer gets and after te merger it gets π (q = [P (q + (n q + q c] q t (q, [ ( q π ] (q = P + (n q + q c q t (q. As a result of an efficient merger, te gross profit of a small retailer decreases since te market price decreases due to te increase of te total quantity sold by its rivals. Te reduction in te gross profit and te increase of te tariff lead to lower profit for te small retailer. ymmetrically, an inefficient merger increases te gross profit of a small retailer by increasing te final price. As a result of te price increase and te reduction in its tariff, te small retailer earns more. Proposition As a result of an efficient (respectively inefficient buyer merger, eac small retailer earns less (respectively more profit for a given volume of sales. 5 Extension: concave upstream cost Wen te upstream cost is concave, tere exists no Nas equilibrium in pure strategies if te retailers ave all te bargaining power and make take-it-or-leave-it offers to te supplier. 3 avoid tis problem of inexistence, we allow for distributed bargaining power between te supplier and retailers. More specifically, we assume tat supply contracts are determined by simultaneous and secret bilateral negotiations between te supplier and retailers. We look for a contract equilibrium suc tat tere is no bilateral incentive for te supplier and any retailer to alter te terms of teir contract. By definition, a contract equilibrium is immune to any bilateral deviation, olding oter retailers supply contracts fixed. 33 A contract equilibrium is terefore a vector of supply contracts, (q, t, suc tat for i, (q i, t i maximizes te bilateral profits π U + π i of te upstream firm and retailer i, taking (Q [i], T [i] as given. 3 In a candidate equilibrium eac retailer offers te cost contribution of its quantity to te supplier s total cost of production, but ten te supplier s profit would be negative due to te concavity of te cost. ee egal and Winston (003. 33 Crémer and Riordan (1987 introduce te contract equilibrium concept in a setup were te interdependence between bilateral supply contracts is due to te non-linearity of te supplier s cost and due to asymmetric information between te supplier and its independent customers. O Brien and affer (199 re-define contract equilibrium in a setup were te interdepence between bilateral supply contracts comes from te downstream competition between retailers. Our contractual setup is a combination of tese two setups since we look for a contract equilibrium of bilateral supply contracts negotiated simultaneously and secretly between locally competitive retailers and te supplier wic as a concave cost function. To 1

ince te upstream cost is concave, te quantities could be strategic complements. We terefore assume tat te supplier s cost is not so concave tat te quantities are strategic substitutes: Assumption 1a. P (Q q + P (Q C (Q < 0 for any q Q. 34 Moreover, to ensure tat te equilibrium profit of eac retailer is decreasing in its rival s quantity of sales, we assume tat a cange in a rival s sales affects te revenue of te retailer more tan its effect on te retailer s cost contribution: 35 Assumption 1b. P (Qq < C (Q C (Q q for any q Q. For example, a quadratic concave cost, C (Q = aq + b Q wit b < 0, and linear demand satisfy bot Assumption 1a and 1b if b > P (Q. Consider a vector of contracts wic simultaneously solve asymmetric Nas bargaining solutions between te supplier and eac retailer. Te disagreement payoff of te upstream firm wit retailer i, π U[i], is te supplier s profit wen te negotiation wit retailer i fails, taking te oter supply contracts as given: π U[i] = T [i] C ( Q [i]. (11 Eac retailer s disagreement payoff wit te supplier is zero since tere is no alternative supplier. Te Nas bargaining problem between te supplier and retailer i is described by te disagreement points (π U[i], 0 and te relative (exogenous bargaining power of te supplier vis-à-vis te retailer, α (0, 1. 36 ince te supplier and retailer i could sare te gains from trade troug fixed tariff t i, at any Nas bargaining solution, te supplier and retailer i set q i to maximize teir bilateral profits π U + π i taking te oter supply contracts (Q [i], T [i] as given. Hence, any asymmetric Nas bargaining equilibrium is a contract equilibrium wit a particular distribution of rents (O Brien and affer, 199. For a given α, te contract equilibrium (q, t is te simultaneous solution to wic is ( α max πu π U[i] π 1 α q i,t i for i = 1,..., n, (1 i [ ( ( ( ] α [( ( ] 1 α (qi, t i = arg max t i C q i + Q q i,t [i] C Q [i] P q i + Q [i] c q i t i. i Using te fact tat all markets are symmetric, q i = q, te first-order conditions of problem (1 yield te optimal quantities, P (nq q + P (nq = c + C (nq. (13 34 Under tis assumption, te second-order conditions of te optimization problems are also satisfied. 35 Observe tat tis assumption is always satisfied for a convex cost. Moreover, for a concave cost were te concavity of te cost function decreases at larger quantities, tat is, C (. < 0, Assumption 1a implies Assumption 1b. 36 Parameter α captures any exogenous factor wic affects te supplier s relative bargaining power. 13

power: Te optimal tariffs are used to sare te bilateral profits wit respect to te relative bargaining t = α [P (nq c] q + (1 α [C (nq C ((n 1 q ]. (14 Eac retailer s equilibrium payoff is equal to its sare over te incremental contribution to te industry profit: π = (1 α [[P (nq c] q [C (nq C ((n 1 q ]], (15 and te supplier earns π U = n {α [P (nq c] q + (1 α [C (nq C ((n 1 q ]} C (nq. (16 To ensure tat te supplier s equilibrium profit is non-negative, we define tresold α at wic π U = 0 (see te Appendix for te explicit definition of α and assume tat te supplier s bargaining power is sufficiently ig, α α As before, we introduce a single large retailer as a result of a merger between two independent stores. et (q, t and (q, t denote, respectively, te total quantity delivered and te tariff paid by te large retailer and a small retailer (given tat, by symmetry, all small retailers buy te same quantity, and pay te same tariff in a contract equilibrium. We terefore ave Q = q + (n 1q, Q = Q. For a given α, te contract equilibrium for a small retailer maximizes te joint profit of te supplier wit te small retailer. Te optimality condition yields to: ( ( ( P Q [] + q q + P Q [] + q = c + C Q [] + q. (17 were Q [] = q + (n q and Q [] = q + (n 3 q. imilarly, te contract equilibrium for te merged entity leads to te optimality condition: ( P Q [] + q q ( + P Q [] + q ( = c + µ + C Q [] + q. (18 were te large retailer s cost is c + µ, Q [] = (n 1q and Q [] = (n 1q. Te simultaneous solution to equations (17 and (18 caracterizes te equilibrium quantities for a contract equilibrium after te merger, q and q.37 Te optimal tariffs are used to sare te bilateral profits wit respect to te relative bargaining power. Te tariff paid by te large retailer and te tariffs paid by te small retailers are respectively: 37 Compared to te case were te retailers ave all te bargaining power, te pre-merger (respectively post-merger equilibrium quantities are te same. In oter words, bargaining power distribution in a contract equilibrium does not affect te equilibrium quantities, but only affect te equilibrium profit saring between te firms. 14

t (µ = α [P (Q t (µ = α [P (Q (c + µ] q c] q + (1 α [C (Q C (Q q ], (19 + (1 α [C (Q C (Q q ]. Te profits of te large retailer and te small retailers are respectively: π (µ = (1 α [[P (Q π (µ = (1 α [[P (Q Te profit of te supplier is, (c + µ] q c] q [C (Q C (Q q ]], (0 [C (Q C (Q q ]]. π U (µ = α [[P (Q (c + µ] q + (n 1 [P (Q c] q ] (1 +(1 α [[C (Q C (Q q ] + (n 1 [C (Q C (Q q ]] C (Q. As we did for te pre-merger case, we define tresold α (in te Appendix suc tat for α α te supplier s equilibrium profit is positive post-merger. Hence, wen te supplier s cost is concave, te sufficient condition to ensure tat te supplier earns non-negative profit in equilibrium is tat Assumption. α Max { α, α }. Wen a buyer merger as no impact on retail efficiency, i.e., µ = 0, it is never profitable due to te concavity of te upstream cost function. More precisely, comparing te large retailer s profits before and after te merger, (15 and (0, sows tat π (0 = (1 α [P (nq c] q [C (nq C ( (n 1 q ] < π. emma 4 Te equilibrium profit of te merged entity increases in te level of efficiency of te merger, i.e., µ π < 0. By Assumption 1a retailers quantities are strategic substitutes, so te small retailers sell less as a reaction to a more efficient merger, tat is, dq dµ retailer earns more wen its rivals sell less, > 0. Moreover, by Assumption 1b, te large π q = (1 α (n 1 [ q [ C (Q C (Q q ]] < 0 As a result, te large retailer s profit decreases in µ: dπ dµ = π dq q dµ (1 αq < 0. For µ = 0, we previously sowed tat te merger is not profitable, π (0 < π. By emma 15

4, we know tat µ π < 0. ince te pre-merger profit of a merging entity, π, is constant in µ, by continuity of te merged entity s profit in µ, we sow tat Corollary 4 Tere exists a tresold µ < 0 suc tat for any µ < µ, te buyer merger is profitable. Te corollary implies tat wen te cost function is concave, te merger is profitable only if it improves efficiency. We moreover sow tat te merger canges te equilibrium quantities in te same way as an efficient merger in te case of convex cost (see Proposition 1. Proposition 3 If a buyer merger is profitable, we ave q function < q < q and Q < Q. To analyze te merger s impact on te equilibrium tariff of te small retailers, we define t (q, x, y = α [P (x + q c] q + (1 α [C (y + q C (y], for q, x, y > 0. We ave t (q, x, y is decreasing in x and also in y, since P (. < 0 and C (. < 0. Before te merger, te transfer of a small retailer for a given quantity is equal to t (q, x, y for x = (n 1 q and y = (n 1 q. After te merger, for te same quantity, te small retailer pays transfer t (q, x, y for x = Q ince Q > Q, q > q and q q and y = Q q. < q (from Proposition 3, we get x = Q q > Q q = (n 1 q = x and y = Q q > (n 1 q = y. We tus sow tat t (q, x, y < t (q, x, y for any q, tat is, te small retailer pays less post-merger. emma 5 As a result of a profitable buyer merger, eac small retailer pays a lower average tariff for a given volume of sales, tat is, tere are anti-waterbed effects. Te lemma sows tat te efficient merger increases te profit of a small retailer by reducing its average tariff. On te oter and, te efficient merger decreases eac small retailer s revenue by lowering te retail price in eac local market. Hence, te net impact of te merger on a small retailer s profit is not straigtforward. Under Assumption 1b, we sow tat te negative effect of te merger dominates te positive effect: Proposition 4 As a result of a profitable buyer merger, eac small retailer earns less for a given volume of sales. 6 Discussion and Conclusions Tis paper analyzes te welfare implications of efficient or inefficient buyer mergers, wic are mergers between retailers from different markets. More precisely, we focus on te interaction between merger efficiency and buyer power concerns in a setup were one manufacturer wit a non-linear cost function sells its product to two locally competitive retail markets. 16

Te European Commission as identified two potential concerns arising from buyer power: first, lower purcasing costs for powerful buyers migt not be passed on to final consumers; second, tere migt be waterbed effects, tat is, lower tariffs for powerful buyers migt be at te expense of iger tariffs for less powerful buyers. Our paper supports te first concern if te buyer merger as no efficiency effect. In tis case, we formally sow tat even if a larger buyer obtains size discounts from te supplier, tere is no pass-on of lower purcasing costs to consumer prices wen supply contracts are non-linear. Wit regard to te second concern, we find tat tere are waterbed (respectively, anti-waterbed effects if a buyer merger increases (respectively, decreases te retail efficiency of merging parties and te upstream cost function is convex. Wen te cost function is concave, tere are only antiwaterbed effects. Te merger s effect on efficiency is te only determinant of te implications for te consumer surplus. In eac retail market, te merger decreases te final price if and only if te merger improves te efficiency of te merging parties, regardless of its impact on te average tariff of small retailers. Different from te literature, in our paper if a waterbed effect exists, it always increases te consumer surplus. Besides te results summarized above, our analysis would ave interesting implications for retail markets supplied by te same manufacturer and were te merged entity is not active, wic we refer to as independent markets. Wen te upstream cost is convex, an efficient merger would lead to a iger retail price in eac independent market troug increasing te average tariff of eac retailer in tose markets. Tis means tat, by contrast to te markets were te merged entity is active, waterbed effects lead to a iger retail price in eac independent market. Te opposite result olds if te merger is inefficient, in wic case te merger decreases te price of eac independent market due to anti-waterbed effects. Te same mecanism applies wen te supplier as a concave cost, in wic case anti-waterbed effects originate from te efficiency of te merger. We consider te case were quantities are strategic substitutes, since tis was te most interesting scenario in our framework. In tis case a small retailer sells less as a reaction to a more efficient rival (a store of te merged entity. Wen te upstream cost function is convex, tis furter deteriorates te bargaining position of a small retailer and so increases its average tariff, lowering its quantity even furter. Hence, in tis case it is not straigtforward weter tis negative effect of an efficient merger is dominated by te quantity expansion of te merged entity. However, if quantities were strategic complements, te impact of an efficient merger on te final prices would be straigtforward since eac small retailer sells more wen its rival is more efficient. Our work could be extended to deal wit te long-run implications of buyer power on upstream investment, like in Inderst and Wey (007, and Battigalli et al. (007. Anoter promising researc avenue is allowing for upstream competition (see, for instance, de Fontenay and Gans, 007. 17

APPENDIX Proof of Proposition 1: We do te proof for µ > 0. A symmetric argument would sow te claim for µ < 0. First step: Q < Q Before te merger, te first-order condition for equilibrium quantity q is given by were Q = nq. P (Q q + P (Q = c + C (Q. umming te condition for all retailers in a local market gives: P (Q Q + np (Q = nc + nc (Q. ( After te merger, equilibrium quantities for te large firm (, and a small firm ( are respectively given by te first-order conditions (see (8 and (9: q q + P (Q = c + µ + C (Q, + P (Q = c + C (Q. umming te conditions for all retailers in a local market, we obtain Q + np (Q = nc + µ + nc (Q. (3 ince µ > 0, we ave nc + µ > nc and comparing expressions ( and (3, we ten obtain: Q + np (Q nc (Q > P (Q Q + np (Q nc (Q. From our assumptions, P (Q Q + P (Q < 0, P (Q < 0 and C (Q > 0, we deduce tat P (Q Q + (n + 1 P (Q nc (Q < 0, wic implies tat P (QQ + np (Q nc (Q is decreasing in Q, we terefore ave Q < Q and, Q < Q by multiplying by. econd step: q < q We sow te claim by contradiction: From our assumptions, P (Q Q + P (Q < 0 and P (Q < 0, we deduce tat P (Q y + P (Q < 0 for any 0 < y < Q (for P (Q < 0, P (Q y + P (Q < 0 since P (Q < 0, and for P (Q > 0, P (Q y + P (Q < 0 since P (Q y + P (Q < P (Q Q + P (Q for any 0 < y < Q and P (Q Q + P (Q < 0 wic implies tat P (Qy + P (Q is decreasing in Q. Moreover, since C (Q > 0, we ave P (Qy + P (Q C (Q wic is decreasing in Q. 18

From Q < Q, we ten obtain: y + P (Q C (Q > P (Q y + P (Q C (Q. uppose now tat, q > q, te result is tat: q + P (Q C (Q > P (Q q + P (Q C (Q, since P (Qy + P (Q C (Q is decreasing in y (P (Q < 0. Using te following first-order conditions: P (Q q + P (Q = c + C (Q, and q + P (Q = c + C (Q, we obtain q + P (Q C (Q = P (Q q + P (Q C (Q, tat is, we reac a result tat contradicts te inequality at te beginning. Terefore, by contradiction we sow q < q. Tird step: q < q q Inequalities Q < q. Proof of Proposition 3 < Q (from te first step and q < q (from te second step imply tat We follow te same metodology as in te convex case (see te proof of te Proposition 1. Te proof is now for µ < 0. First step: Q > Q Before te merger, te first-order condition for equilibrium quantity q is given by were Q = nq. P (Q q + P (Q = c + C (Q, umming te condition for all retailers in a local market give us: P (Q Q + np (Q = nc + nc (Q. (4 After te merger, te equilibrium quantities for te large firm (, and a small firm ( are respectively given by te first-order conditions (see (18 and (17: q q + P (Q = c + µ + C (Q, + P (Q = c + C (Q. 19

umming te conditions for all retailers in a local market, we obtain Q + np (Q = nc + µ + nc (Q. (5 ince µ < 0, we ave nc + µ < nc and comparing expressions (4 and (5, we sow tat Q + np (Q nc (Q < P (Q Q + np (Q nc (Q. (6 From Assumption 1a for q = Q n, we ave P (Q Q n + P (Q C (Q < 0. Multiplying te bot sides by n proves tat P (Q Q + np (Q nc (Q < 0 and terefore P (Q Q + (n + 1P (Q nc (Q < 0, since P (Q < 0. Tis implies tat P (Q Q + np (Q nc (Q is decreasing in Q. As a result, inequality (6 proves tat Q > Q and Q > Q. econd step: q > q Assumption 1a, P (Q q + P (Q C (Q < 0 for any q Q, and P (Q < 0 ensures tat te function P (Qq + P (Q C (Q is decreasing in Q. ince Q > Q (from te first step, we ave q + P (Q C (Q < P (Q q + P (Q C (Q. (7 Using te first-order condition of a small retailer before and ten after te merger, respectively, P (Q q + P (Q = c + C (Q, q + P (Q = c + C (Q, we obtain q + P (Q C (Q = P (Q q + P (Q C (Q, Te latter togeter wit inequality (7 imply tat q > q, since P (. < 0. Tird step: q > q Inequalities Q > Q (from te first step and q > q > q. q Proof of Proposition 4 We define function (from te second step imply tat π (q, x, y = (1 α ([P (x + q c] q [C (y + q C (y], for q, x, y > 0. We ave π (q, x, y is decreasing in x, but is increasing in y, since P (. < 0 and 0