Online Appendix for Merger Review for Markets with Buyer Power

Transcription

1 Onlne Appendx for Merger Revew for Markets wth Buyer Power Smon Loertscher Lesle M. Marx July 23, 2018 Introducton In ths appendx we extend the framework of Loertscher and Marx (forthcomng) to allow two products that are perfect complements for the buyer. We allow there to be some supplers who produce both of the products demanded by the buyer and others who produce only one. We can accommodate the possblty that the buyer has a preference for purchasng both products from the same suppler. Ths extenson s motvated n part by the proposed merger of olfeld servces frms Hallburton and Baker Hughes, whch posed challenges for competton authortes because of the mult-product nature of the mergng frms. 1 In partcular, exstng methodologes, whch typcally focus on ndvdual relevant anttrust markets, have lmted ablty to account for cost synerges assocated wth mult-product supplers, demand sde complementartes that cause buyers to prefer a sngle source for multple products, or the nteracton of these wth buyer power. 2 The extenson of Loertscher and Marx (forthcom- DepartmentofEconomcs,Level4,FBEBuldng,111BarryStreet,UnverstyofMelbourne,Vctora 3010, Australa. Emal: smonl@unmelb.edu.au. The Fuqua School of Busness, Duke Unversty, 100 Fuqua Drve, Durham, NC 27708, USA: Emal: marx@duke.edu. 1 The proposed merger was announced n 2014, but the partes ultmately abandoned attempts to merge n the face of opposton from the DOJ: Unted States of Amerca v. Hallburton Co. and Baker Hughes, Inc., Complant, Aprl 6, 2016, Case 1:16-cv UNA, hereafter DOJ Complant. 2 The argument that the DOJ put forward n ts opposton to the Hallburton-Baker Hughes transacton focused on effects wthn ndvdual product markets, gnorng possble synerges and complementartes, but then returned to these ssues as overarchng concerns that amplfed compettve concerns created by the transacton, notng that the mergng partes offer smlar types of ntegrated solutons, bundled servces, and other multple-product and servce combnatons. (DOJ Complant, p. 30)

2 ng) provded here allows one to address these ssues. Extenson to mult-product supplers In order to address cross-market ssues such as demand-sde complementartes, we consder a setup wth two products, A and B. The buyer has value zero for product A or B ndvdually, value v for the par of products A and B f purchased from two dfferent supplers, and value V v for the par of products A and B f purchased from the same suppler. Thus, the dfference between V v 0 captures demand-sde complementartes, whch are sometmes referred to as the value of one-stop shoppng. Ths mult-product extenson accommodates the case n whch supplers produce multple complementary products, as well as the case n whch products are locaton specfc, wth one product suppled n locaton A and the other n locaton B, where the buyer demands coverage that spans both locatons. Further, ths extenson can be nterpreted n terms of vertcally related products. For example, product A mght be the transportaton or marketng of product B, both of whch are demanded by the buyer. In that case, a merger of a suppler of A wth a suppler of B s a vertcal merger. Let M be the set of mult-product supplers, A be the set of supplers of only A, and B be the set of supplers of only B, wth M + A + B = n. The cost type of a mult-product suppler s the cost to that suppler of producng both products, whereas the cost type of a sngle-product suppler s the cost to that suppler of producng only one product. Thus, each suppler has a sngle-dmensonal type. Mult-product supplers can supply ndvdual products to the buyer for a commonly known proporton of ther jont producton cost, where we allow for the possblty of cost synerges n producton. Specfcally, the cost to mult-product suppler M of supplyng just product A s γ A c and of supplyng just product B s γ B c, where γ A,γ B < 1 and where γ A and γ B are known by the buyer. As a matter of notaton, we set γ A = γ A and γ B = γ B for M and γ A = γ B 1 for A B. Cost synerges are accommodated by lettng γ A + γ B > 1, whch mples that mult-product supplers can produce both products at a cost that s less than the sum of the costs of producng each separately. As n the sngle-product case, we model the merger of two supplers of substtute products (both producng A, both producng B, or both producng A and B) by assumng thatthemergedenttyhascosttypeequaltothemnmum ofthecosttypesofthemergng supplers. Wemodelamergedenttythatcombnes asuppler ofproductawthasuppler of product B as drawng ts cost type from the dstrbuton for the sum of the cost types 2

3 of the two mergng supplers. 3 Analogously to the sngle-product case, we assume that market outcomes correspond to the allocaton and payments of the optmal mechansm wth the objectve that s a weghted average of buyer surplus and socal surplus, wth weght β {0,1} on buyer surplus. Thus, focusng on the case wth buyer power and usng the conventon that subscrpts on vrtual type functons ndex supplers, when the type vector s c, 4 quanttes traded n the pre-merger market (and analogously for the post-merger market) are determned by the maxmzer of the set {0} {V Γ (c )} M { v γ A Γ (c ) γ B j Γ j(c j ) } M A,j M B, j as follows: If there exsts M such that V Γ (c ) s a maxmzer, then q A (c) = q B (c) = 1; otherwse, f there exst M A and j M B wth j such that v γ A Γ (c ) γ B j Γ j(c j ) s a maxmzer, then q A(c) = qb j (c) = 1; otherwse, zero s a maxmzer and there s no trade. The allocaton rule s monotone. For the case wthout buyer power, vrtual type functons are replaced by the dentty functon. Gven the allocaton rule, expected buyer surplus s E c [ M qa (c)qb (c)(v Γ (c )) + M A,j M B, j qa (c)q B j (c) ( v γ A Γ (c ) γ B j Γ j (c j ) ) In the domnant strategy mplementaton for the mult-product setup, payments to supplers are defned by multple threshold cost types as descrbed n Lemma 1. Lemma 1. There exst threshold cost types that defne the domnant-strategy mplementaton of the optmal drect mechansm wth objectve β(buyer surplus) +(1 β)(socal surplus), (1) ]. subject to ncentve compatblty and ndvdual ratonalty. Proof of Lemma 1. Gven c, possble threshold types for suppler are c AB,, c A,, c B,, c AB,A, c AB,B, c B,A, and c A,B, where c X,Y s defned so that for cost types below c X,Y 3 For a merger that combnes a sngle-product suppler wth a mult-product suppler, varous approaches can be consdered, but we do not deal wth ths case. 4 In the drect mplementaton, each agent reports a type c [c,c] to the buyer. As descrbed n Lemma 1 below, one can structure transfers n the drect mplementaton so that reportng truthfully s a domnant strategy for every agent of every possble cost type. Whether the optmal drect mechansm wth mult-product frms permts a descendng clock-aucton mplementaton s left for future research. 3

4 and above the next lower threshold, suppler supples product X, and for cost types above c X,Y and below the next hgher threshold, suppler supples product Y, where denotes the empty set. For example, for the case wth buyer power, f for a gven c, suppler supples both A and B, then V Γ (c ) max 0,max j M j ( (V Γ j (c j )), max v γ A k Γ k (c k ) γ B j Γ j (c j ) ). (2) k M A j M B j k If the hghest element n curly brackets on the rght sde of (2) does not nvolve suppler, then there exsts a cost type for suppler, c AB,, such that f suppler reports a cost less than c AB,, suppler supples A and B, but f suppler reports a cost greater than c AB,, suppler supples nothng. The cost type c AB, s the threshold type for suppler between supplyng both A and B and supplyng nothng. However, f the hghest element n curly brackets on the rght sde of (2) nvolves suppler, then the threshold types must account for that. Fxng the cost types of supplers other than, as the cost type of suppler vares, the set of products that suppler supples also vares. For example, t may be that for low cost types, suppler supples A and B, but for ntermedate cost types, suppler supples only A, and for hgher cost types, suppler supples nothng. In ths case, the cost types defnng the cutoffs between the regons n type space would be denoted c AB,A and c A,. Other threshold types are defned analogously. In all cases, the threshold types for suppler depend only on the cost types of the other supplers. Gven the cost vector for the supplers, the denttes of the tradng supplers, and the threshold types for the tradng supplers, payments n the domnant strategy mplementaton are as shown n Fgure 1. As we show, the payments defned n Fgure 1 correspond to the domnant-strategy mplementaton of the optmal mechansm for the mult-product setup. To see that domnant strategy ncentve compatblty s satsfed, suppose that supplers other than report truthfully. If suppler does not trade when t reports truthfully, then all threshold types for suppler are less than c, and so any report that results n suppler tradng gves suppler a payment that s less than c, and so no devaton s proftable. If suppler does trade when t reports truthfully, then a downward devaton r < c only changes suppler s payoff f r s less than a type threshold that s less than c. For example, f suppler s a mult-product suppler and f r < c AB,A < c < c A,, 4

5 Threshold types c AB, c AB,A c AB,B c AB,A c AB,B < c A, < c B, < c A,B < c B,A < c B, < c A, Suppler s type Products supples Payment to suppler c < c AB, A and B c AB, c < c AB,A A and B c AB,A +γ A (ca, c AB,A ) c (c AB,A,c A, ) A only γ A c A, c < c AB,B A and B c AB,A +γ B (c B, c AB,B ) c (c AB,B,c B, ) B only γ B cb, c < c AB,A A and B c AB,A +γ A (ca,b c AB,A +γ B (cb, ) c A,B ) c (c AB,A,c A,B ) A only γ A ca,b +γ B (cb, c A,B ) c (c A,B,c B, ) B only γ B cb, c < c AB,B A and B c AB,B +γ B (cb,a c AB,B +γ A (c A, ) c B,A ) c (c AB,B,c B,A ) B only γ B cb,a +γ A (ca, c B,A ) c (c B,A,c A, ) A only γ A c A, Fgure 1: Threshold types n the mult-product setup wth assocated payments then under truthful reportng suppler supples A, for a payoff of γ A ca, under report r, suppler supples A and B, for a payoff of c AB,A +γ A (c A, ( ) c AB,A ) c = (1 γ A ) c AB,A c +γ A c A, γ A c < γ A ca, γ A c, γ A c, but where the nequalty uses c AB,A c < 0 and γ A < 1 for a mult-product suppler, and so the devaton s not proftable. A smlar analyss shows that no other downward devaton s proftable. If suppler reports r > c, then ts payoff s only affected f r s greater than a type threshold that s greater than c. For example, consder a mult-product suppler, wth c < c AB,A a payoff of c AB,A < r < c A,. Then under truthful reportng, suppler supples A and B for +γ A (c A, c AB,A ) c, but under report r, suppler supples only A, and so the devaton s not for a payoff of γ A ca, γ A c, whch s less for any c < c AB,A proftable. Smlarly, no other upward devaton s proftable. 5

6 Usng the setup descrbed above, one can analyze a merger n the mult-product envronment. Merger of supplers of complements Our framework also allows us to consder the merger of suppler 1 producng only product A wth suppler 2 producng only product B, whch s a merger of supplers of complements. As mentoned, these complementary products could be two nputs used together by the buyer, or nputs n dfferent geographc locatons for a buyer that demands coverage for both locatons, or vertcally related products, such as a product and ts dstrbuton. To llustrate effects, consder the case of n = 2. Let Γ be the vrtual cost functon for a suppler who draws ts cost type from the dstrbuton that s the convoluton of G 1 and G 2. Even f the vrtual cost functons for supplers 1 and 2 are bounded on [c,c], Γ s necessarly unbounded on [2c,2c]. 5 If v 2c, then a buyer wthout power purchases both before and after the merger, payng 2c n both cases. Thus, the buyer s quantty and payment are not affected by the merger, but t benefts from one-stop shoppng f V > v. Consderng a buyer wth power, f v Γ 1 (c)+γ 2 (c) 2c, then the buyer purchases beforethemergerandpays2c. Afterthemerger, thebuyeronlypurchasesf Γ(c 1 +c 2 ) V, n whch case the buyer pays Γ 1 (V), whch s less than 2c because V < Γ(2c) =. By revealed preference, the buyer s expected surplus followng the merger s greater than f the buyer commtted to always purchase from the merged entty at prce 2c, whch would be ncentve compatble and generate the same surplus as n the case of no merger. Thus, wth buyer power, the buyer s expected surplus ncreases as a result of a merger, and more so the greater s the buyer s value for one-stop shoppng. Thus, we have the followng result: Proposton 1. Assumng v Γ 1 (c) + Γ 2 (c), a merger of monopoly supplers of complementary products ncreases a buyer s expected surplus f the buyer has buyer power or has a postve value for one-stop shoppng, and the effect on expected buyer surplus s ncreasng n the value of one-stop shoppng. Ths result s consstent wth the usual ntuton that the merger of supplers of complementary products typcally produces benefts for the buyer. 5 Thedenstyoftheconvolutonsg m (c) = c c g 1(x)g 2 (c x)dx,andsog m (2c) = c c g 1(x)g 2 (2c x)dx = 0, whch follows because g 2 (2c x) s zero for all x [c,c). 6

7 References Loertscher, S. and L. M. Marx (forthcomng): Merger Revew for Markets wth Buyer Power, Journal of Poltcal Economy. 7