The Effects of Vertical Integration on Competing Input Suppliers

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1 The Effets of Vertial Integration on Cometing Inut Suliers b R Preston MAfee Deartment of Eonomis Universit of Teas Austin, TX 787 Wednesda, Marh 03, 999 Preared for The Federal Reserve Bank of Cleveland Abstrat: When a downstream firm bus an inut sulier, the downstream firm an redue its osts of using that inut Other inut suliers tiall resond b riing more aggressivel, given the demand redution, whih tends to lower inut sul osts to other firms Thus a vertial merger ma lower rival's osts, rather than raise them I have benefited from the omments of Joe Haubrih and William Thomson

2 Vertial integration is a booming henomenon in man US industries The massive onsolidation of the defense industr has resulted in three or four latform develoers that rodue man of the omonents used in militar latforms Banking is onsolidating at a raid ae, with integration of related finanial servies (insurane, redit ards) along with inut servies (hek learing, aments, eletroni funds transfer) into the arent omanies Teleommuniations firms are merging, ombining able, wireless, loal wireline and long distane servies Simultaneousl, other firms are onentrating on their "ore ometen" and selling off related lines of business Automobile manufaturers, for instane, are inreasing their deendene on indeendent or semi-indeendent arts suliers What are the effets of vertial integration? There is a large literature that might reasonabl be desribed as disjointed Muh of the fous has been on roviding a rationale for oosing vertial mergers on antitrust grounds When a firm F bus an inut sulier (ustream firm) U that also sulies F's (downstream) ometitor, the firm an raise the rie of the inut to its downstream ometitor, thereb roviding an advantage in the downstream market This is the standard "raising rivals' osts" argument ioneered b Sheffman and Salo In etreme instanes, the vertiall integrated firm might refuse to sell to the ometitor If the inut sulier's rodut was neessar for rodution, F might be able to forelose its ometitors from the downstream market This aer will eamine an oosing effet to the well-known raising rival's ost theor In artiular, the analsis fouses on the reation of other inut suliers to vertial integration The main insight is that vertial integration, b reduing the demand for other inuts given easier aess to one, tends to lower the ries of the other inuts This, in turn, indues the vertiall integrated firm to sell its inut at a lower rie as well, whih ma redue the osts of all inuts Thus, aounting for the reation of substitute inut suliers ma reverse the onlusions of the raising rival's ost theor Struture of the Model The general form of the model is set out in Figure There are two ustream firms, X and Y, whih sell to two downstream firms The downstream firms sell to the final onsumers I will fous on the effets of firm vertiall integrating b urhasing firm X Suose that the roduts rodued the ustream firms are imerfet substitutes, and that, having urhased firm X, firm will ontinue to use some of the inuts sulied b Y Then vertial integration will affet firm Y's riing deision 3 An item like an airraft or a submarine is a latform, whih holds a variet of weaons sstems, detetion sstems like radar or sonar, and other sstems like landing gear, engines, et Ordover, Saloner and Salo, 990, is the best known treatment Salinger, 988 and Hart and Tirole, 990, also rovide related, and more general, analses 3 It might seem that servies suh as hek-learing are homogeneous However, distint banks have an advantage in being able to lear their own heks quikl, and large banks ma have a greater netting out of heks In addition, distint suliers of hek-learing ma have distint regional advantages

3 In this aer, I will set-aside the inentive to raise rival's osts, b assuming that firms and do not omete in the outut market Instead, the fous will be on the effets of vertial integration on the alternative inut sulier I find that vertial integration tends to lower ries of both inuts to firm The intuition is straightforward The urhase of firm X b firm lowers the rie of inut to firm, reduing firm 's demand for In resonse to this redution in demand b firm, firm Y lowers the rie of to both firms The resonse of the integrated firm is to lower the rie of X to firm When firm and omete imerfetl in the downstream market, the situation is less lear There are two diret effets of the merger First, the rie of to the ombined entit falls, tending to redue the rie of Seond, the rie of to firm should rise, tending to inrease the rie of Either effet an dominate, and the rie of ma rise or fall, deending on the etent of substitution between the oututs of firms and, and the substitutabilit of the two inuts Figure : Cometition Laout Ustream: Firm X Firm Y Downstream: Firm Firm Let i, i denote the demand for the two inuts b firm i I assume onstant returns to sale The timing is that the inut sellers simultaneousl set inut ries,, resetivel Then firms and hoose their inut quantities and outut ries

4 Raising Rival's Costs The standard raising rival's ost theor is best elained b eliminating firm Y In this ase, X is a monool sulier of the inut If is neessar for rodution, the merged firm has the abilit to forelose from rodution Even if is not neessar, but valuable for rodution, the merged firm an raise the ost of to, thereb raising 's osts Even in this simle senario, the rie harged for X to firm an fall Suose and barel omete in the final outut market Moreover, suose firm has signifiantl more inelasti demand for X, so that the monool rie for firm eeeds the monool rie for firm Prior to vertial integration, the rie of will be between the two monool ries After the merger, the rie of will fall to aroimatel the monool rie for firm Moreover, insofar as firms and do omete, the monool rie for firm will fall, sine firm is now a more aggressive ometitor with its lowered marginal osts ost-merger The standard analsis fouses on the ase where X and Y are ournot ometitors with onstant marginal osts In this ase, if the merged firm uses its own inuts and withholds outut from firm, firm is faing a monool, and will generall eeriene higher inut ries This is true even when firm Y is atuall several firms ometing in ournot ometition, although the more firms in the inut sul market, the smaller is the effet The results onerning ournot inut sul generalize to inreasing marginal osts With inreasing marginal osts, firm ma either wish to sell or bu from firm Y even after the merger with firm X However, onsider the smmetri ase, so that X looks like Y and looks like Post merger, firm does not need to bu from firm Y, and thus an inrease the osts to firm via a refusal to sell This literature served an imortant role, b showing that vertial mergers had the otential to forelose ometition downstream However, the literature has foused rimaril on the bad effets of mergers, without eamining the otential for good effets on rivals Lowering Rival's Costs I start the analsis using the demand for inuts as rimitives To failitate the analsis, I distinguish the ries firm X harges firms and With indeendent downstream demands, the effet of the merger of X and is to hange the inut rie of to firm Firm X earns rofits on its sale to firm of: π ( ) (, ) I divide firm Y's rofits into the omonents earned on firm and firm : 3

5 ψ ( ) (, ), ψ ( ) (, ) Using numerial subsrits to denote artial derivatives, rofit maimization ields: π ψ + ψ 0 The diret effet of the merger of X and on the inut sul ries is to lower from its monool level to marginal ost Beause of the assumed indeendene of the demands for the oututs of and, the merged entit will hoose the rie of to maimize and firm Y will maimize the sum of and I am assuming that firm Y an't rie-disriminate If both inut suliers an rie disriminate, nothing hanges to the ries harged to firm If firm Y an rie disriminate but firm X ould not, then the merger ermits firm X to rie disriminate, sine the onl relevant rie is that harged to As a onsequene, will inrease if firm 's demand for X is less elasti than firm 's demand for X This will have effets on the rie of Y, usuall of the same diretion Differentiating the first order onditions, one obtains: π ψ ψ π + ψ d d + ψ 0 d 0 0 This gives: d d d π ψ Stabilit imlies that π ( ψ + ψ ) π ψ > 0 π ψ The terms and are similar in that the reresent the effet of a ometitor's rie inrease on the marginal rofitabilit of a rie inrease for the firm If the inut riing game is one of strategi omlements, then these terms are ositive Alternativel, and equivalentl, if an inrease in the rie of one inut makes the demand for the other inut less elasti, these ross-artials will be ositive It an be shown that if the downstream rodution funtions are CES with onstant returns to sale, and demand is onstant u to a hoke rie (whih is tantamount to 4

6 assuming that downstream quantit is eogenous), then the ross-artials are ositive This seial ase will be elored in the numerial simulation given below When these inut rofit ross-artials are ositive, then d d d > 0, d > 0 Thus, the effet of the merger, whih lowers the rie of to firm through the elimination of firm X's marginalization, lowers both of the inut ries to firm, as well as the rie of Y to firm This result is intuitive The redution in the rie of X to firm makes firm 's demand for more elasti, sine firm now has a less eensive substitute This auses Y to lower the rie of 4 The lower rie of indues a reation from the ombined firm it lowers the rie of Numerial Eamle A numerial eamle illustrates and quantifies the effets desribed in the theor Suose that the two downstream firms an sell one unit eah at a rie suffiientl high that eah firm will alwas bu inuts suffiient to rodue one unit The downstream firms have a CES rodution tehnolog with onstant returns to sale and arameter ae[½,] 5 : q ( + ) Let the marginal rodution osts of the ustream firms be No Vertial Integration Without vertial integration, the downstream firms minimize + st q This gives: +, +, 4 This is where the assumtion that Y an't rie disriminate is ritial If Y ould rie disriminate, the redution in the rie of X to firm would redue Y's rie to firm, but not Y's rie to firm 5 For a, onl one inut is hosen For a<½, demand is inelasti and the inut riing equations solve with infinite ries 5

7 Firm X hooses to maimize: π ( ) Routine alulations ield: 0 ( ) + For a>½ and >, this equation haraterizes a maimum A smmetri solution to the first order onditions ield: As afi, the goods beome erfet substitutes, and ries fall to marginal osts Vertial Integration When firms and X merge, firm an urhase at rie In this ase, the ombined entit will rie to maimize 6 : π ( ) ( ) + As before, this gives the first order ondition: 0 ( ) + Firm Y faes a more omliated roblem, as firm Y will generall sell to both firms and, and these two firms generall fae distint inut ries for Firm Y hooses to maimize 6 Beause the vertiall integrated firm is assumed not to omete with firm, downstream rofits an be ignored However, if there is a small level of ometition, then downstream rofits must be inluded here, dramatiall omliating the analsis 6

8 7 While losed forms for the first order onditions eist (and are suffiient to haraterize equilibrium in the range of of a osited), it is not ossible to solve the first order onditions for the equilibrium ries eliitl, as the ries enter these equations in omle was Consequentl, I have used Mathematia 30 to find the roots of the first order onditions, and to grah the outome, as a funtion of a To simlif the alulations, note that an be set to unit without loss of generalit (ries measured in ost units) In addition, for saling uroses, it is useful to lot the marku redutions assoiated with vertial integration, rather than the atual ries Thus, the ries relative to the non-integrated ries are lotted, in artiular lotting (for z,): When P z is, there is no ost redution, while P z equal to zero would be ometitive or marginal ost riing The outome is lotted in Figure Several observations emerge ψ ) ( ) )( ( ) ( ) )( ( z z z P Figure : The inut markus under vertial integration, as a roortion of the marku without vertial integration, grahed against a

9 First, the redutions in inut ries are signifiant, on the order of 5% or 0% Seond, firm Y redues rie more than firm X This should be a reasonabl general roert, sine firm X is resonding to firm Y's rie redution In smmetri models suh as the one eamined, the rie of the unintegrated inut should fall more than the rie of the integrated inut (to the rest of the world) In asmmetri models, there is an additional effet As an indeendent firm, firm X ried to serve both firms and, and therefore firm X's rie is an average of the two monool ries assoiated with and After the merger, firm X will rie onl for firm ; this ould inrease or derease the ost-merger rie The effet identified in the aer, however, should ontinue to hold, using the monool rie for firm as a benhmark, rather than the monool rie for both downstream firms Third, the markus are not monotoni in a This is interesting beause the ries are monotoni, with ries diverging as afi½, and ries going to osts as afi Simulations suggest that the marku on is below the marku without vertial integration (as a roortion of the vanishing marku absent vertial integration) even in the limit While ries are more indiative of the asmmetri effets on the individual inut suliers, firm rimaril ares about its marginal ost In Figure 3, the marginal ost is lotted, relative to the marginal ost without vertial integration Figure 3: The marginal ost of firm under vertial integration as a roortion of the marginal ost without vertial integration, grahed against a 8

10 Firm 's marginal ost is lowered u to 8½% This amount is, of ourse, less than the redution enjoed b firm, but substantial nevertheless Disussion of Banking Aliations Reentl, the Federal Reserve Sstem studied the imliations of its eit from the rovision of retail aments servies, suh as hek-learing and eletroni aments For man ommunit banks, eseiall those in rural markets, the remaining roviders of these servies would be vertiall integrated ometitors Moreover, as Osterberg and Thomson (998 - this issue) show, branhing deregulation is leading to the onsolidation of both the ustream and downstream markets in banking The etant industrial organization literature suggests that inreased vertial integration in banking ouled with onsolidation in the inter-bank market ma have deleterious effets on downstream banking ometition However, the literature itself is a oor guide to the likelihood of anti-ometitive effets First, muh of the literature was driven in an attemt to understand how vertial mergers might matter for antitrust enforement In artiular, the Claton At, whih rovided ourts with the abilit to blok a variet of vertial raties, reeded a lear understanding of an irumstanes in whih vertial integration might be harmful to ometition As a onsequene, a literature develoed to show that vertial integration ould matter in a negative wa, rather than assessing the likelihood that vertial integration is harmful to ometition Seond, muh of the literature fouses on the ournot model, rimaril for tratabilit reasons While ournot ometition might be a reasonable haraterization of downstream ometition for ustomers, where firms' aaities are relativel infleible, at least omared to ries, ournot ometition seems like a oor model of the rovision of man of the ustream servies suh as hek-learing, where aait onstraints are unlikel to bind Results from models emloing ournot ometition ustream ma not be aliable to integration in the banking industr Third, the ke ingredient of the raising-rivals'-osts stories is that the rime motivation for vertial integration is damaging ometitors One lausible future for the banking industr involves a handful of ver large, interstate banks, along with a large number of relativel small, loal banks The large banks will offer banking, mortgage, insurane, finane, and other servies, rimaril oerate eletroniall, and be vertiall integrated into most or all areas of finanial servies In ontrast, the loal banks will be rimaril rural, offering ersonalized servie, and reating a market nihe b eloiting the suerior information and goodwill that loal interation rovides These different stles of banks will not likel omete with eah other in the minds of most ustomers The large banks will omete strongl with the other large banks, at least until their numbers are whittled down to three or four in an given region The rural banks will onl fae the threat that their best (largest) ustomers are indued to use the large, ineensive banks; for most ustomers, a given rural bank will omete with other rural banks 9

11 In this senario (whih is not the result of an stud on m art), the rural banks will not omete signifiantl with the large banks As a onsequene, the are unlikel to be a target of anti-ometitive vertial integration, nor are the likel to be harmed b the redution in the number of large vertiall integrated banks The largest banks ma attemt to harm eah other b their riing of banking servie inuts, but these banks are in the best osition to fend for themselves The lowering rivals' osts stor of this aer is inaliable to the resent analsis so long as the Federal Reserve remains a rovider of hek learing and other servies at some reasonable fasimile of ost As a onsequene, the onl mehanism b whih rural banks ould benefit through vertial integration of large banks is if the Federal Reserve is ineffiient, so that a mehanism for rie redutions eisted Pries an't be lowered below minimum ost Conlusion The standard analsis of the effets of vertial integration on ometitors emhasizes the inentive of the vertiall integrated firm to forelose its downstream rivals, or raise their osts While this effet is natural in some aliations, there is an off-setting effet on suliers of substitute inuts If firms and omete suffiientl weakl in the outut market, the effet on other inut suliers ma dominate the forelosure effet, ausing vertial integration to benefit downstream rivals while harming ustream ometitors The harm to the ustream ometitors, however, is to redue their markus over marginal ost, that is, harm to their monool ower A signifiant aset of the effet of vertial integration is that both the un-merged inut sulier and the vertiall integrated firm lower their inut ries The mehanism is that the merger eliminates the marku on the inut b the urhased firm The other inut sulier redues its ries in resonse to this lower rie substitute for the merged firm The vertiall integrated firm lowers its inut ries to the rest of the world in resonse to the lowered rie of the other inut sulier Simulations with onstant elastiit of substitution rodution funtions indiate otential redutions in marginal osts of the downstream ometitor of as muh as 8½% Referenes Hart, Oliver, and Jean Tirole, "Vertial Integration and Market Forelosure," Brookings Paers on Eonomi Ativit: Miroeonomis, Seial Issue, 990, Ordover, Janusz A,, Garth Saloner and Steven C Salo, "Equilibrium Vertial Forelosure," Amerian Eonomi Review, 80, number, Marh 990, 7-4 Salinger, Mihael, "Vertial Mergers and Market Forelosure," Quarterl Journal of Eonomis, 03,, Ma 988,

12 Salo, Steven C and David T Sheffman, "Cost-Raising Strategies," Journal of Industrial Eonomis, 36 number, Setember 987, 9-34

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