Concentration-Based Merger Tests and Vertical Market Structure

Transcription

1 Concentraton-Based Merger Tests and Vertcal Market Structure by Joshua S. Gans * Unversty of Melbourne Frst Draft: 8 th February 005 Ths Verson: 5 th June, 006 Ths paper derves a concentraton measure for markets wth multple vertcal segments. The measure s derved usng a model of vertcal contractng where upstream and downstream frms bargan blaterally and may be ntegrated. The resultng vertcal Hrschman-Herfndahl Index provdes a measure of the degree of dstorton n the vertcal chan as a result of both horzontal concentraton n a segment and the degree of vertcal ntegraton. Utlsaton of ths measure would allow competton authortes to dstngush between the dfferng compettve mpacts of upstream and downstream competton, the relatve sze of ntegrated frms n each segment and to provde a quanttatve threshold test for vertcal mergers. Journal of Economc Lterature Classfcaton Number: L40. Keywords: vertcal contractng, mergers, concentraton, Hrschman-Herfndahl ndex. * Thanks to Denns Carlton, Catherne de Fontenay, Stephen Kng, the edtor and an anonymous referee for helpful comments. Responsblty for all errors les wth me. All correspondence to Joshua Gans, E-mal: J.Gans@unmelb.edu.au. The latest verson of ths paper s avalable at

2 . Introducton The use of market share data to form concentraton ratos or ndexes have become a staple of safe harbour tests for horzontal merger analyss. The US Department of Justce bases ts measure of concentraton on the Hrschman-Herfndahl Index (or HHI). Ths ndex takes that sum of the squares of the market shares as a measure of concentraton. The test has two parts. Frst, the post-merger HHI s calculated and the level of concentraton of the market assessed. Markets wth an HHI above 800 are sad to be hghly concentrated, those between 000 and 800 moderately concentrated and those below 000 not concentrated at all. Second, based on the level of concentraton, the pre- and post-merger HHI s are compared. For unconcentrated markets, any merger s permssble. However, for moderately and hghly concentrated markets, only changes n the HHI of less than 00 and 50 respectvely wll usually be mmedately cleared. For mergers outsde of these ranges, the DOJ wll conduct further analyss as to the merger s compettve effects. There are many reasons why the HHI mght be used as a measure of concentraton n competton settngs. However, the ratonale that les at the heart of the present paper s grounded n the theory of Cournot olgopoly. If we take the Lerner ndex (that s, prce less margnal cost dvded by prce) as a measure of the level of welfare dstorton n a market, n a Cournot equlbrum, the average Lerner ndex across frms s the HHI dvded by the prce elastcty of market demand. In ths sense, the degree to whch a Perhaps the earlest formal dervaton of the HHI n a model of olgopoly was by Stgler (964). He modeled the lkelhood that a cartel mght be unstable n terms of the probablty a devatng member of that cartel mght attract a dsproportonate share of customers n ts favour. That share was nversely related to the HHI mplyng that for greater levels of concentraton a cartel mght be expected to be more stable. I thank the edtor for pontng out ths reference.

3 3 merger ncreases the HHI s an ndcaton of the degree to whch that merger reduces welfare. Ths use of the HHI has been subect to a number of crtcsms. Frst, f two frms wth pre-merger market shares of s and s are analysed, the ncrease n the HHI s usually assessed to be ss. Ths nvolves an mplct assumpton that the sum of market shares of the merged frms wll not change as a result of the merger. However, f ths was really the case, the merger would nvolve no welfare detrment; somethng that requres the merged partes to exercse market power by contractng ther market shares. Only by usng a full equlbrum model can one properly assess a merger s mpact (Farrell and Shapro, 990). Second, and on related lnes, ths analyss does not consder why a frm s market share may be what t s n the frst place. Typcally, a large market share mples lower producton costs and hence, the reallocaton of output followng a merger may, n fact, be welfare enhancng (Demsetz, 974). Fnally, competton authortes also have nformaton that flows from the fact that f a merger s proposed, t s lkely proftable for the mergng partes. Ths suggests that refnements n the way market shares are used to nfer ant-compettve effects can be utlsed. These crtques have not deterred competton authortes from usng the HHI as a threshold test for the desrablty of a merger. In part, ths reflects the fact that ths use of the HHI represents a conservatve threshold test n that, f a merger fals to pass t, further analyss of the full equlbrum effects would be possble. In addton, such an equlbrum analyss would be able to take nto account other market and technologcal condtons that may favour one olgopoly model over another. The semnal paper n ths stream s Farrell and Shapro (990), but Daughty (990), Levn (990) and McAfee and Wllams (99) offer alternatve perspectves. Fels, Gans and Kng (000) show how ths analyss could nform negotated undertakngs between competton authortes and merger partes.

4 4 Nonetheless, wth one recent excepton, all of these analyses of the compettve effects of mergers and the approprate use of market shares as threshold ndcators of concern neglect the vertcal structure of markets. Ths s somewhat surprsng as many competton authortes beleve that ncreasng levels of vertcal ntegraton n the market can gve rse to ant-compettve concerns. 3 Such belefs suggest that the level of concentraton n a sngle vertcal segment may not reflect the level of ant-compettve potental arsng from mergers n and across that segment and that changes n such concentraton may not capture the full ant-compettve mpacts of a merger. Hence, t would be desrable to have a measure of concentraton that reflected vertcal ssues n markets. Gven ths, n ths paper, I consder concentraton-based tests that take nto account the degree to whch merged partes are vertcally ntegrated. In so dong, I utlse recent developments n the theory of vertcal contractng that gves a general approach to the competton ssues that arse from vertcal ntegraton. Those developments descrbe the nature of competton when contractng over nput supply terms are negotated and, n so dong, demonstrate how vertcal ntegraton can be utlsed as a means of leverage market power across vertcal segments. Importantly, as I wll show, ths theory gves rse to a natural Cournot-type equlbrum outcome that makes t possble to derve approprate concentraton ndexes readly comparable wth the HHI (and ndeed collapsng to t n a specal case). The recent theory of vertcal contractng was a reacton to the Chcago School crtque of vertcal merger analyses that stated that ntegraton could not be an nstrument 3 The US DOJ (987) and the Australan Competton and Consumer Commsson (994) are explct n ther acknowledgement that mergers that ncrease the level of vertcal ntegraton can be undesrable.

5 5 for the leverage of market power as frms wth such power could leverage that power through arms-length contractng arrangements and non-lnear prcng. Hart and Trole (990) were the frst to develop a specal model that demonstrated that when an upstream monopolst negotated wth downstream frms blaterally and blateral agreements could not easly be observed by outsde partes then a vertcally separated monopolst would be constraned to offer supply terms that dsspated monopoly rents downstream. Put smply, each downstream frm dd not trust the monopolst to offer supply terms consstent wth a monopoly outcome and the monopolst could not commt to those terms publcly. The end result was an olgopolstc outcome across the ndustry despte the exstence of market power n the upstream segment. Ths baselne result was subsequently demonstrated to be robust to alternatve assumptons on compettve nstruments (O Bren and Shaffer, 99), nformaton (McAfee and Schwartz, 994; Segal, 999; Rey and Verge, 004), contractng nstruments (McAfee and Schwartz, 994; Segal and Whnston, 003), contract tmng (Gans, 006), barganng power (de Fontenay and Gans, 005) and the presence of upstream competton (de Fontenay and Gans, 005). In ths envronment, vertcal ntegraton s a means of restorng ndustry-wde monopoly outcomes (Rey and Trole, 003). Put smply, rent dsspaton occurred because an upstream frm was tempted to offer downstream frms secret dscounts; mposng negatve compettve externaltes on other downstream frms. That ncentve s mtgated when the upstream frm s ntegrated downstream as such secret dscounts to ndependent frms harms ts own ntegrated unt. In some cases, the ntegrated frm has no ncentve to supply nputs to other downstream frms and foreclosure and an ndustrywde monopoly result. In general, vertcal ntegraton, partcularly by frms wth upstream

6 6 or downstream market power, s a means of rasng nput prces and softenng the strength of competton downstream (de Fontenay and Gans, 005). In the next secton, I take ths approach to vertcal contractng and ntegraton and use t to derve modfed or vertcal HHI (VHHI) that reflects the average degree of Lerner-type dstorton across the vertcal chan. In so dong, n Secton 3, I demonstrate the followng: () that n the absence of any vertcal ntegraton, VHHI becomes the HHI based solely on downstream market shares; () the VHHI changes f there are vertcally ntegrated frms who are net nput supplers; (3) the compettve mpact of upstream and downstream mergers are dstnct; n partcular, horzontal mergers amongst nonntegrated upstream frms have no mpact on the average Lerner ndex; (4) that vertcal mergers that ncrease downstream market shares or ncrease the degree to whch ntegrated frms are net supplers wll ncrease dstortons whle vertcal ntegraton creatng a net nput demander has no mpact on the VHHI. Fnally, I argue that the VHHI offers a more approprate bass for a threshold test based on market shares than the current HHI. Of course, whle the recent theory of vertcal contractng and ntegraton yelds an elegant, consstent and general theory and moreover, a smple VHHI based on general demand and technology assumptons there are other theores of vertcal relatons n the lterature. The most promnent of these nvolves upstream frms settng smple posted prces to downstream frms and frms n each vertcal segment compete as Cournot olgopolsts. Downstream frms then compete on the bass of these prces or, f they are vertcally ntegrated, on the bass of margnal cost (Salnger, 988). Vertcal ntegraton, therefore, nvolves potental compettve effects but also effcency gans as the

7 7 successve mark-up or double margnalsaton problem s elmnated. For ths reason, n Secton 4, I consder a vertcal concentraton measure based on a model of successve Cournot olgopoly. Wth some assumptons on demand and technologes, ths s able to yeld a concentraton measure that whle more nformatonally burdensome than the VHHI s related to t and can potentally be appled n regulatory settngs. In Secton 5, I compute both concentraton measures to consder the analyss of the compettve mpact of the Exxon-Mobl merger on the Calfornan petroleum market. A fnal secton concludes. As alluded to earler, one other paper consders concentraton tests takng nto account vertcal structure and ntegraton. Hendrcks and McAfee (005) provde an alternatve model of outcomes n wholesale markets wth many upstream and downstream frms. Based on supply functon equlbra models, they focus on the ablty of upstream frms to exercse market power and downstream frms to exercse monopsony power and use ths to derve an ndex of equlbrum dstorton n the wholesale market. Ther analyss dentfes the balance between ntegrated frms nput supply and demand as crtcal n creatng any Lerner-type dstortons and derve a modfed HHI that reflects ths. The man dfference between ther approach and the standard vertcal contractng lterature s that ther model desgn offers a means of uncoverng a sngle market clearng lnear prce when upstream and downstream frms exercse market power (smlar to the smple posted prces vertcal model). In contrast, the vertcal contractng lterature focuses on envronments where wholesale markets are governed by sets of blateral negotatons that permt non-lnear prces. Not surprsngly, ths latter approach leads to

8 8 no Lerner-type dstorton n the wholesale market taken on ts own; the very dstorton Hendrcks and McAfee set out to quantfy. In realty, the dfference n approaches corresponds to dfferences n the type of wholesale market beng modeled. Hendrcks and McAfee consder general mass markets for nputs where downstream frms may or may not compete drectly whereas the vertcal contractng lterature focuses on nputs suppled to competng downstream frms where nput terms are formed by negotatons rather than posted prces.. Baselne Model and Concentraton Index Here I provde a model of vertcal contractng. It s based on de Fontenay and Gans (004) who consder blateral barganng between two upstream frms and two competng downstream frms. Unlke other models, ths structure allows for competton n multple vertcal segments and hence, s an approprate bass for the consderaton of a concentraton ssues across segments. It represents a strct generalsaton, n terms of both frm numbers and the nature of upstream and downstream producton technologes, over exstng models n the lterature. Suppose there are N frms n an ndustry ndexed =,, N. Each frm (potentally) operates n an upstream and a downstream vertcal segment. Frm s downstream market share s s whle ts upstream market share s σ. The products of frms n the downstream market are perfect substtutes from a fnal consumer perspectve. The (nverse) market demand for that fnal good s denoted by P(Q); wth the usual propertes where Q s total downstream producton. For smplcty, I wll assume that Q s smply the sum of all upstream nputs; although all of the results below go through

9 9 wthout ths assumpton. Frm s upstream costs are a contnuously dfferentable functon, C (.) whle ts downstream costs (net of nput payments) s a contnuously dfferentable functon, c (.). Notce that, n prncple, whle fnal goods are homogeneous, ntermedate nputs may not be and ntegrated frms may have a lower or hgher cost structure than non-ntegrated ones. Blateral Barganng I follow the standard tmelne n the recent vertcal contractng lterature: STAGE (Barganng): Barganng over nput supply terms takes place between each frm. STAGE (Producton): Producton takes place and payoffs are realsed. As n the vertcal contractng lterature, t s assumed that there are a set of blateral Nash barganng games between upstream and downstream pars. Each upstream-downstream par negotates over prce and quantty supply terms. For example, and bargan over terms specfyng a quantty of nputs purchased, q, and a lump-sum transfer, p pad by to. The precse game theoretc relatonshp between the set of Nash bargans s not modeled here. Those negotatons could be smultaneous (as n Segal, 999; and O Bren and Shaffer, 004) or sequental wth passve belefs (as n McAfee and Schwartz, 994; and de Fontenay and Gans, 005). Ether approach leads to the same outcome wth regard to nput quanttes traded: that parwse negotatons between frms over nput supply terms wll satsfy blateral effcency. That s, when pars cannot contract or observe the outcomes of other negotatons durng ther own, there exsts an equlbrum where they undertake those negotatons holdng the outcomes of others as fxed. Ths means that the

10 0 quantty of nputs traded wll be such that the ont profts of both partes are maxmsed holdng fxed the quantty of nputs expected to be traded as a result of other parwse negotatons. It s ths equlbrum, whch s the man focus of the vertcal contractng lterature, whch wll be the focus of ths paper. Lerner Index for a Vertcal Chan Consder a representatve negotaton between frms and over q (that quantty suppled by to ) and p (the payment from to ). That s, n ths negotaton, s the downstream frm whle s the upstream frm (even though each potentally has operatons n the other vertcal segment). The profts of and (wrtten to hghlght ths quantty and prce) are: ( ) π k k k = PQ ( ) q + q p p c( q,.) + p C(.) k k k 's Downstream Profts 's Downstream Profts 's Upstream Profts 's Upstream Profts π = PQ ( ) qk pk c(.) + p + pk C( q,.) k k k () () Blateral effcency mples that the two frms wll agree to a quantty (q ) that maxmses the sum of () and () takng as gven all other nput prces and quanttes. Ths s equvalent to solvng: ( ) max PQ ( ) q + q c( q,.) + PQ ( ) q C( q,.) q k k k k (3) Ths mples that: C c PQ ( ) + P ( Q) ( q + q ) = 0 C k k k q q c P q ( ) ( ) q P Q q k k + qk = = + P P ε ( s s) (4) where ε = P/ PQ s the market prce elastcty of demand. Ths s the Lerner ndex for

11 the entre vertcal chan n ths model. Notce that t depends only on downstream market shares and not upstream shares. The ntuton for ths s that, n blateral negotatons, both frms take nto account mpacts of changes n nput supply between them on ther downstream profts and ths depends on ther downstream market shares. The only upstream mpacts come through margnal costs but these depend upon the absolute (rather than relatve) level and nature of ther upstream outputs. Vertcal Hrschman-Herfndahl Index Let HHI = N s. Utlsng (4), the average Lerner ndex for the ndustry can be derved. N Proposton. The average Lerner ndex s ε s ( / s + σ q Q) = = HHI N s ( q / Q ε + ε σ ). = All proofs are n the appendx. Here q s the level of nternal supply. Notce that the hgher s ths, the lower s the average Lerner ndex. Ths s because nternal supply smply maxmses ndvdual profts as opposed to blateral profts that are maxmsed n determnng other supply terms and so there s no nternalsaton of compettve externaltes n ths case. Thus, as q ranges from 0 to mn{ σ, s} Q, for all, the average Lerner ndex moves from ε HHI to N ε s max{, } s σ =. Indeed, there s a sense n whch ths latter measure provdes a sold bass for an approprate concentraton measure. Corollary. Suppose that, for all, q mn { s, σ } ε N s max{ s, σ }. = = Q. The average Lerner ndex s

12 The assumpton here mples that f s σ then = 0 and f s q σ then q = 0. It amounts to an assumpton that each frm does not care about the source of ts nput supply but that f t provdes nputs nto ths market, then t wll demand those nputs frst before sourcng them from others. From ths corollary, t s easy to see that the approprate concentraton ndex for ths type of model s, VHHI N s max{ s, σ }. As an ndex t shares wth the smple N = structure of HHI = s beng a sum of squared market shares and a value between 0 (n the case of perfect competton n both vertcal segments) and 0,000 (n the case of a downstream monopolst). As such, t s readly comparable to the thresholds establshed for the applcaton of the HHI; ncludng equal frm sze equvalency comparsons. It s perhaps nstructve, at ths pont, to consder the dfferences between the HHI and VHHI by way of a smple example. Imagne that there s one vertcally ntegrated frm, two ndependent downstream frms and one ndependent upstream frm. Suppose that all frms are symmetrc wthn ther segment and that downstream frms have no costs (other than nput payments) whle upstream frms have cost functons of the form, C(.) = q. Let fnal market demand s lnear, PQ ( ) = Q. In ths stuaton, pror to any merger, t s straghtforward to calculate that the ntegrated frm wll not supply ndependent downstream frms n equlbrum and wll produce output of 5 6 whle the ndependent upstream frm wll supply 6 6 ; dvded equally amongst the two downstream 5 frms. Thus, P = 6. If, however, ndependent upstream frm merged wth one of the ndependent downstream frms, t s easly to calculate that, followng ths merger, the remanng ndependent downstream frm would not receve any supply n equlbrum.

13 3 The two ntegrated frms would splt the market and each supply 5 leadng to a prce of 3 5 ; a lower quantty and hgher prce than pror to the merger. The nterestng thng about ths example s that tradtonal merger analyss (where the pre-merger shares of the mergng frms are summed and concentraton measures calculated), utlsng the HHIs only would not have revealed any ssue. The upstream and downstream HHIs are 504 and 3353 respectvely both pre- and post-merger. In contrast, the VHHI rses from 3353 (the same as the downstream HHI) pror to the merger to 498. Thus, utlsng t would have dentfed concerns worthy of closer examnaton. 3. Implcatons for Merger Analyss In ths secton, I consder the mplcatons of utlsng VHHI for the purpose of merger analyss. In so dong, downstream mergers, upstream mergers and vertcal mergers are evaluated n turn. Downstream Mergers When all downstream frms n an ndustry are net buyers of upstream nputs, VHHI = HHI and horzontal mergers wll approprately be evaluated usng the HHI. Vertcal separaton of all downstream frms or, conversely, the lack of external trade between ntegrated frms would smlarly satsfy ths condton. If some frms are ntegrated and net supplers of upstream nputs, then for the purposes of measurng post frm concentraton, VHHI > HHI. Put smply, n ths stuaton, downstream competton s unlkely to follow a pure Cournot outcome and so the HHI understates the level of concentraton. Nonetheless, even n ths stuaton, f two

14 4 frms, and, merge who are net buyers, then the change n VHHI wll be ss ; the same as t would be usng the HHI. In these cases, merger analyss wll prmarly focus on downstream market shares. It s only where at least one of the mergng frms s a net suppler of upstream nputs that the change n concentraton wll be s ( s + σ ) (f only s a net suppler) and s σ + s σ (f both and are net supplers). In both of these cases, the upstream shares of one or both frms become relevant n evaluatng the merger. In ths stuaton, t s smply not possble to use a functonal market separaton along vertcal lnes to evaluate the mpact of the merger. Upstream Mergers When nput supply terms are determned by blateral barganng, a clear mplcaton s that, under vertcal separaton, upstream market structure does not matter for overall quantty and prce downstream. Ths s a drect mplcaton of (4) and a generalsaton to the case of upstream competton of results that non-ntegrated upstream monopoles are unable to leverage ther market power downstream. 4 Recall, that when frms are not ntegrated (or more generally ntegrated frms are net buyers of nputs) the average Lerner ndex for the whole vertcal chan does not depend on upstream market shares. Hence, should upstream frms merge, the VHHI would be unchanged. Whle at a broad level ths suggests that competton authortes should vew purely upstream and purely downstream mergers dfferently, when there s vertcal 4 Ths outcome s contaned n both de Fontenay and Gans (004) and O Bren and Shaffer (004). The latter paper then consders how restrctons on the ablty of mult-product frms to bundle may gve rse to welfare effects from upstream mergers.

15 5 ntegraton, the strong result that upstream mergers (absent other effcences) are welfare neutral s potentally weakened. For example, f a vertcally ntegrated frm and a nonntegrated upstream frm merge and σ + σ > s, then the change n the VHHI as a result of that merger wll be s(max{ σ s,0} + σ ). Thus, the greater the upstream market share of the mergng frms, the greater the ncrease n VHHI. In addton, the greater the degree of vertcal ntegraton amongst mergng frms, the greater the potental competton concern from upstream mergers. Vertcal Mergers Whle the above analyss ndcates the potental changes n horzontal merger analyss based on alternatve vertcal market structures t s n the analyss of vertcal mergers that the VHHI s at ts potentally most useful. To date, competton authortes have not been able to provde brght-lne safe harbour tests for vertcal mergers. The USDOJ (984) alludes to the degree of concentraton n a vertcal segment as beng of ssue n ts evaluaton but there s no further gudance beyond ths. To be sure, the level of upstream competton does, n fact, play an mportant role n mtgatng adverse compettve consequences from vertcal mergers (de Fontenay and Gans, 004). But precsely how much competton s requred for ths has to date been unknown. The VHHI provdes gudance on ths front. Frst, t provdes a baselne measure of the level of relevant concentraton over the entre vertcal chan to determne whether an ndustry facng a vertcal merger should be consdered concentrated or not. Second, t suggests that the nature of the vertcally ntegrated frm; that s, whether t ends up a net suppler of nputs or not s mportant. Fnally, t provdes a way of consderng mergers

16 6 between frms wth dfferng degrees of vertcal ntegraton. To see ths, let s begn wth a stuaton where no frm n an ndustry s ntegrated. A merger between any upstream and downstream frm s pure vertcal ntegraton. Imagne that there are 4 equal szed upstream frms and 0 equal szed downstream frms. In ths case, pror to the merger the upstream HHI s 500, the downstream HHI s 000 as s the VHHI. If one upstream and one downstream frm merge, the upstream and downstream HHI s reman unchanged whlst the post-merger VHHI becomes 50. In ths case, f we appled the same thresholds as the USDOJ utlsng the VHHI, ths would be regarded as a moderately concentrated ndustry and hence, the merger would volate those thresholds. In contrast, magne that there are 8 downstream frms wth market shares of 0% each and an addtonal frm wth a market share of 0%. In ths case, f that larger downstream frm should merge wth an upstream frm, the pre- and post-merger upstream and downstream HHI s would be 500 and 300 respectvely whle the pre- and postmerger VHHI s would be 300 and 400. Utlsng the USDOJ thresholds, ths merger agan n a moderately concentrated ndustry would ust satsfy the threshold for a safe harbour. Thus, despte effectvely a hgher presumptve level of concentraton n each vertcal segment and a merger creatng a sgnfcantly larger frm n the second example that merger s potentally less ant-compettve. The reason s that whle at least 60 percent of the ntegrated frm s output wll be sold to other downstream frms n the frst case, only 0 percent wll be sold to those frms n the second. Thus, the potental for negotatons wth those frms to have a sgnfcant overall effect on competton s much

17 7 lower. These examples demonstrate the usefulness of the VHHI measure. Not only does t take nto account upstream and downstream competton where relevant but t also takes nto account the lkely poston of the vertcally ntegrated frm. When that frm s not a sgnfcant net suppler of nputs, then the lkely ant-compettve effects arsng from t are lkely to be lower. But the VHHI also allows us to consder more carefully the overall ndustry-wde effects of a vertcally ntegrated and a non-ntegrated frm. For nstance, buldng on the frst example, suppose that the vertcally ntegrated frm there (wth a 0% downstream and 5% upstream share) was to merge wth another downstream frm. In ths case, because the only segment both frms operated n would be the downstream segment, t s lkely that competton authortes would evaluate the merger on that bass. In that case, the downstream HHI would change from 000 to 300 and be regarded as presumptvely ant-compettve. In contrast, usng the VHHI, the merger would change t from 50 to 400. Whle stll presumptvely ant-compettve, the magntude of the change n concentraton n sgnfcantly less. Put smply, the nomnally horzontal merger makes the ntegrated frm a relatvely smaller net suppler and ths effect mtgates the usual ant-compettve concerns based on an analyss of concentraton n a sngle segment. 4. Concentraton Measures n Successve Cournot Olgopoly In some markets, frms may not be able to negotate over non-lnear prces and may be constraned to offer lnear ones. As s well known, ths gves rse to the problem

18 8 of double margnalsaton: a problem that can be resolved by vertcal ntegraton. Consequently, a vertcal merger may have an ant-compettve effect of the type descrbed earler along-sde a pro-compettve one n terms of elmnatng double markups. It s, therefore, nstructve to consder a vertcal concentraton measures that takes each of these effects nto account. Here I derve a measure of concentraton based on the successve Cournot olgopoly model of Salnger (988). Lke Salnger, I mpose assumptons of lnear demand and costs. The basc tmelne of the model s as follows: STAGE (Wholesale Market Competton): Upstream frms compete n Cournot quantty competton for the sale of nputs to downstream frms. STAGE (Downstream Market Competton): On the bass of wholesale market prces, downstream frms operate as Cournot compettors n competton for fnal consumers. Thus, n contrast to the prevous model based on blateral barganng, nput prces are smple per unt prces only and hence, wll nvolve upstream frms earnng a margnal above ther margnal cost for external sales. Gven ths set-up, the followng proposton states the analogue to the concentraton measure derved n Proposton. Proposton. Under lnear downstream demand and costs, the vertcal HHI n the successve Cournot olgopoly model s: N N N N N ε σ + ε s Q ε qs + Q ε = = = = Notce that ths s the sum of the upstream and downstream HHI s less a term that reflects the lack of dstorton for nternal trade wthn a frm and plus a dstorton reflectng the concentraton of external trade between frms. q.

19 9 There are some nterestng thngs to note about ths ndex. Frst, f all frms are vertcally ntegrated and dentcal then t smply becomes the HHI for a sngle segment. Second, f no frm s vertcally ntegrated, the ndex becomes: N N N N ε σ + ε s + Q ε = = = = q (5) Notce that for the case where there are two upstream and downstream monopolsts, ths becomes 3/ε. Ths mples that the equlbrum level of ε would have to be greater than 3. Ths reflects the multple dstortons arsng from double margnalsaton. Fnally, notce that for a bottleneck monopolst n a segment wth perfect competton n the other segment, the ndex reduces to. Fnally, x = q and consder the followng smplfcaton: Corollary. Suppose that, for all, q = mn[ s, σ ] Q and for all (,), s σ q = max[0, s ] ( q x σ ), then ( s mn[ s, σ])( σ mn[ s, σ ]) ( mn[, ] ) N N N N ε max[, σ ] ε σ ( σ ) s σ = = = =. VHHI = s s + s + Thus, ths concentraton measure s smlar to the one based on the contractng model but wth the addtonal dstortons from double margnalsaton and the addtonal dstorton (or removal of dstorton) based on whether a frm s a net suppler (or net buyer) n the wholesale market. In ths model, all other thngs beng equal, horzontal mergers are dstortonary whle vertcal mergers mprove effcency. However, what ths allows s for a consderaton of these offsettng effects when vertcal mergers occur that ncrease horzontal concentraton n ether or both upstream and downstream markets. We demonstrate how ths apples n the next secton.

20 0 5. Applcaton As an llustraton of how these concentraton measures may be useful n provdng gudelnes for merger analyss, I consder here (as dd Hendrcks and McAfee, 005) the mpact of the Exxon and Mobl merger on the Calforna petrol retalng market. Hendrcks and McAfee (005) study ths market because of ts relatve solaton to the rest of the Unted States (for transportaton and regulatory reasons). However, ther focus s not on concentraton measures as a threshold test for compettve concern but on a full analyss of the mpact of the merger on ntermedate and fnal good prces. Nonetheless, usng the threshold tests here yelds smlar conclusons. Table presents nformaton on the market shares of petrol refnng and retalng partcpants n Calforna. 5 Notce that both Mobl and Exxon have larger downstream market shares than upstream ones. Thus, each s a net purchaser n the wholesale petrol market and wll reman so followng the summaton of ther market shares. 5 The data s from Hendrcks and McAfee (005) who themselves utlse data from unpublshed work by Leffler and Pullam (999).

21 Table : Market Shares (Based on Sales) Company Upstream (Refnng) Market Share (%) Downstream (Retalng) Market Share (%) Chevron Tosco Equlon Arco Mobl Exxon Ultramar Paramount.3 0 Kern Koch 0 0. Vtol 0 0. Tasoro 0 0. PetroDamond 0 0. Tme 0 0. Glencoe 0 0. Table reports varous concentraton measures. The frst two columns are the pre- and post-merger concentraton measures based on a smple summaton of market shares (as would occur n threshold tests). Notce that, for the frst three measures, the threshold requrements for the USDOJ would not be met as ether the post-merger measure was hghly concentrated or the merger rased the concentraton measure by more than 00 ponts. Notce, however, that the percentage ncrease n the VHHI (Contractng) measure (9.6%) s greater than the VHHI (Cournot) measure (7.%) because the latter nvolves an effcency beneft as a greater proporton of wholesale market trade s nternal to an ntegrated frm whle the former nvolves a large ncrease n downstream concentraton; somethng that causes greater compettve dstortons n the contractng model.

22 Concentraton Measure Table : Concentraton Measures Pre-Merger Post-Merger Post-Merger wth Exxon Refnery Dvestture Post-Merger wth Exxon Retal Dvestture Upstream HHI Downstream HHI VHHI Contractng VHHI Cournot Dvesttures may have also been consdered as optons to resolve vertcal problems. Notce that f Exxon s refnery assets were dvested to an ndependent compettor, then ths would resolve an upstream concentraton ssues (meetng USDOJ thresholds) but both VHHI measures exhbt a contnung problem as downstream concentraton has ncreased. In contrast, dvestture of Exxon s retal assets would result n a sgnfcantly reduced ncrease n VHHI (Contractng) whle beng neutral n comparson wth a full merger for VHHI (Cournot). Ths suggests that a retal dvestture would be more desrable than an upstream dvestture n ths nstance. Put smply, the most compettve damage appears here to be comng from the ncrease n downstream concentraton relatve to upstream concentraton. 6 Ths s not to suggest that concentraton measures alone should dctate whether a merger should be opposed by competton authortes. 7 Here, however, n establshng threshold gudelnes for compettve concern, measures that take nto account vertcal ssues can be very useful n cases where proposed mergers nvolve partes wth market power n one or both vertcal segments. Moreover, for mergers that are purely vertcal, 6 Interestngly, concentratng on the wholesale market effects, Hendrcks and McAfee s (005) model suggested that a downstream dvestture would acheve lttle as the balance of trade between frms would largely be unaltered relatve to a full merger. In contrast, an upstream dvestture would brng about a relatvely more balanced wholesale market and fewer dstortons. 7 See Hendrcks and McAfee (005) for an argument n favour of broader smulatons.

23 3 these measures provde a new approach to settng quanttatve gudelnes. 6. Concluson In concluson, the analyss here demonstrates that the evaluaton of mergers nvolvng or creatng ntegrated frms s more nuanced than purely horzontal mergers wthout any cross-segment mpacts. Vertcal mergers create ant-compettve concerns through a dfferent path than the unlateral effects created by pure horzontal mergers. In addton, horzontal mergers nvolvng ntegrated frms can sometmes create outcomes that balance the usual ant-compettve concerns regardng such mergers. The use of the VHHI rather than a segment-level HHI as the bass for threshold tests captures these dfferng effects. Of course, t would also be nstructve to buld the analyss here nto the equlbrum analyses lke Farrell and Shapro (990). After all, lke horzontal mergers n Cournot olgopoles, vertcal ntegraton when there s upstream competton may also not be prvately proftable (de Fontenay and Gans, 005). As such, the fact that a vertcal merger s proposed contans addtonal nformaton regardng ts lkely ant-compettve effects. That type of analyss s, however, left for future work.

24 4 Appendx Proof of Proposton and Corollary To fnd the average Lerner ndex, we take (4) and multply t by N N N Q q ε ( s + s ) + Q q ε s = = N N N N Q q ε s ε ( σ q / Q) s Q ε qs = = = = + + N N N ε ε ε σ = = = = ( s q / Qs ) + ( q / Qs ) + ( q / Qs ) N N ε s ε = = = + ( σ mn{ σ, s }) s N N ε s ε ( σ mn{ σ, s}) s = = = + N N ε s ε max{0, σ s} s = = N ε = = + N ε s s s = ( max{0, σ }) = + = q and sum: s max{ s, σ } (6) Proof of Proposton Workng backwards, n ths model, f s non-ntegrated, ts downstream profts are gven by: PQx ( ) c( x) px. Maxmsng ths wth respect to x (holdng other downstream quanttes as gven) gves the (nverse) nput demand functon: c p = P( Q) + P ( Q) x where x = q (.e., the sum of nputs purchased from x upstream frms, as ndexed by ). Upstream frms compete n Cournot for downstream customers based on downstream ndvdual demand. Note that those demands are nterdependent. Hence, p q c = P ( Q) + P ( Q) x x

25 5 p q k = P ( Q) + P ( Q) x Upstream frms solve: max { q } pq + P( Q) x c( x) p x C( q). Here we use x to denote s downstream quantty whle q denotes ts upstream quantty. Ths gves frst order condtons of: p p p C q + p + q + P ( Q) x q = 0 q q q k, k l q for all (7) p c p C k q k + P ( Q ) + P ( Q ) x ( x q ) = 0 for = (8) q q q q Note that (7) mples that: c ( x ) c P ( Q) + P ( Q) x q + P( Q) + P ( Q) x + P ( Q) x + ( P ( Q) + P ( Q) x ) q ( P ( Q) + P ( Q) x )( x q ) = 0, x k k q ( P ( Q) + P ( Q) x ) q ( P ( Q) + P ( Q) x )( x q ) + P ( Q) x c c C + ( P ( Q) ) q + P( Q) + P ( Q) x x 0 x q = ( ) ( ) c c C x x q P( Q) + P ( Q) q q + q + q + x + P ( Q) xq x ( x q ) q = + ( ) ( ) c c C x x q PQ ( ) + P ( Q) q + x+ q + P ( Q) xq x q = + C (9) Smlarly (8) mples: c c k k x x ( P ( Q) + P ( Q) x ) q + P( Q) + P ( Q) x ( P ( Q) + P ( Q) x )( x q ) = 0 ( ) c k k x PQ ( ) + P ( Q) x + q q x + q + P ( Q) xq ( P ( Qx ) )( x q ) = + ( ) PQ ( ) + P ( Qq ) + P ( Q) xq x c c C ( x q) x x q + = + It s useful to note that, f downstream demand and costs are lnear (.e., c 0 x C q c x P ( Q) = 0 = ), all FOCs are ndependent of x (that s, q and q do not depend upon s downstream market share). Let σ and s denote s upstream and downstream market shares. From (9) and (0) we can derve the dstorton from each quantty decson: C q and (0)

26 6 P ( ) c C c P ( Q) xq x q x q q = ( σ + s + q / Q) P P ε ( ) c C c P Q xq x x x q + q x = P ε σ ( ) ( ) P P () () Note that f downstream demand has a constant elastcty, ε, then these become: P c C c x q q = ( + s + q / Q) ( + ) ( q / Q)( s s) P P ε σ ε ε ( ) c C c x q x = ( + ) ( / )( ) P ( q Q s s ) ε σ ε ε ( x q ) The vertcal HHI s constructed by takng a weghted average of the above dstortons wth respect to each share of the nput trade as a functon of total output (that s, assgnng weghts of q / Q). Fnally, take the weghted sum of the Lerner ndexes: P P q Q q P c x P C q N N N Q q ε ( σ s q / Q) Q q εσ = = = N N N N N N N N Q ε qσ Q ε qs Q ε qs Q ε q Q ε qσ = = = = = = N N N Q ε qσ Q ε qs Q ε = = = = q s + = + N N N Q ε q = = N N N N N Q ε qσ Q ε xs Q ε qs Q ε q = = = = = + + N N N N N ε σ ε s Q ε qs Q ε q = = = = = + + Proof of Corollary Gven these assumptons, ( s mn[ s, σ])( σ mn[ s, σ ]) ( mn[ s, ] ) σ N N N N N N Q q Q qx = s s σ = = = = = mn[, ]

27 7 Wth ths we have ( s mn[ s, σ])( σ mn[ s, σ ]) ( mn[, ] ) N ( s mn[ s, σ])( σ mn[ s, σ ]) ( mn[, ] ) σ ( s mn[ s, σ])( σ mn[ s, σ ]) ( mn[, ] ) σ N N N N N ε σ + ε s s mn[ s, σ ] + s σ = = = = = N = ε HHI + HHI + s mn[ s, σ ] + = Up Down s = = N N N N ε s max[ s, σ ] + ε σ ( σ s) + s = = = =

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