Vertical Contracting When Competition for Orders Precedes Procurement *

Transcription

1 Vertcal Contractng When Competton for Orders Precedes Procurement * by Joshua S. Gans ** Unversty of Melbourne Frst Draft: 30 th June, 2003 Ths Verson: 29 th March, 2004 Ths paper reverses the standard order between nput supply negotatons and downstream competton and assumes that competton for orders takes place pror to procurement of nputs n a vertcal chan. In an envronment where procurement negotatons nvolve no prvate nformaton and no restrctons on the form of prcng, t s found that olgopolstcally compettve outcomes wll result despte the presence of an upstream monopolst. It s demonstrated that vertcal ntegraton s a means by whch the monopolst can leverage ts market power downstream to the detrment of consumers. However, t does so, not by foreclosng on ndependent downstream frms, but by softenng the compettve behavour of ts own ntegrated unts. Thus, the paper provdes a smple ratonale for ant-compettve vertcal ntegraton n an envronment that respects the usual Chcago school assumptons. Journal of Economc Lterature Classfcaton Number: L42 Keywords. vertcal contractng, vertcal ntegraton, monopolsaton, barganng, competton. * I thank Yongmn Chen, Stephen Kng, Lesle Marx and semnar partcpants at the Unversty of Melbourne for helpful dscussons and comments. Responsblty for all errors remans my own. ** Melbourne Busness School, Unversty of Melbourne, 200 Lecester Street, Carlton VIC 3053 Australa. All correspondence to: J.Gans@unmelb.edu.au. The latest verson of ths paper s avalable at

2 1. Introducton Vrtually all models of vertcal supply contractng assume that an upstream frm commts to the terms of nput supply contracts pror to downstream frms makng ther own producton and marketng decsons. 1 Ths means that downstream frms compete wth one another wth full knowledge of at least ther own supply condtons. Whle ths tmng t rarely gven any ustfcaton, t would appear to apply most naturally n envronments where nput supply terms can be changed or renegotated less frequently than customer orders (for nstance, where customers are relatvely mpatent or goods are relatvely pershable so that downstream frms need to have secure supply terms n place before competng for them). There are many nstances, however, where ths standard tmng does not apply and where, n realty, competton for customer orders precedes commtment to procurement terms. Here are four clear examples: Buldng and archtectural contracts where nput requrements are generally unknown pror to recevng a customer order. The provson of large scale servces to government or frms (n defense or nformaton technology) nvolves competton for contracts that precede procurement decsons regardng captal equpment supples and human captal expertse n on-gong legal and consultng servces (Kamen, L and Samet, 1989). If customer swtchng costs are substantal, competton for those customers takes place at a tme well n advance of when consumpton of the requste servces wll be requred. Electrcty and gas retalng where customers (both resdental and ndustral) are sold forward contracts before supply agreements to obtan the necessary stock or supples are set (Stahl, 1988). 1 Ths occurs for models where upstream frms smply post nput prces (e.g., Waterson, 1980) or where they negotate those nput prces wth downstream frms (e.g., Rey and Trole, 2003).

3 2 Indeed, t s qute concevable that procurement contracts may be subect to hold-up and ex post renegotaton once customer contracts are n place. In ths stuaton, common to analyses of vertcal relatonshps n the ncomplete contracts lterature (Hart, 1995), modelng procurement negotatons as occurrng followng the marketng of servces to customers would be necessary to fully capture the lack of commtment power nherent n some supply agreements. For these reasons, ths paper reverses the stages n the standard approach to vertcal contractng and explores the mpact on ths on two key questons n that lterature: (1) f there s a monopoly n upstream supply, n a perfect nformaton envronment, can that monopoly power be leveraged downstream? and (2) does vertcal ntegraton have an ant-compettve or strategc effect n ths settng? The frst queston s one whch the Chcago school has consstently answered affrmatvely leadng to a concluson that there s no further ant-compettve role for the actons n the second queston (Bork, 1978). It s only where there s ncomplete nformaton where there s both a negatve answer to the frst queston and, consequently, a cause for concern over vertcal ntegraton (see Rey and Trole, 2003, for a recent survey). To ths end, competton for orders s assumed to take place pror to negotatons over procurement wth a sngle upstream suppler. It s demonstrated that ths modelng change has profound mplcatons for the level of competton n downstream markets. Specfcally, even n an envronment of complete (publc) nformaton and flexblty regardng the nature of ex post procurement, olgopolstcally compettve outcomes result n the ndustry. In contrast, for the same contractual and nformatonal space, the standard approach would yeld a monopoly outcome wth the upstream supply able to commt to nput supply terms that maxmse ndustry proft (.e., the Chcago school concluson). In the standard approach, t s only by restrctng the nformaton or contract space that more compettve outcomes emerge. 2 2 Hart and Trole (1990), O Bren and Shaffer (1992), McAfee and Schwartz (1994) and Segal (1999) analyse the outcomes that emerge when supply negotatons between one downstream frm and the upstream monopolst are not observed by other downstream frms. In ths settng, dependng upon the contract space, dfferent types of olgopolstc outcomes can emerge (see Rey and Trole, 2003). Indeed, McAfee and Schwartz (p.220) conectured that f sales were determned pror to nput negotatons, a smple olgopolstcally compettve outcome would not emerge. It s demonstrated here that ths s not the case and a Cournot outcome s an equlbrum outcome.

4 3 The ntuton behnd the result here s smple. Downstream frms antcpate supply negotatons when they compete ex ante. If those ex post negotatons are effcent (.e., they maxmse blateral surplus), so long as the order prce exceeds the margnal cost of the nput requrements for that order, procurement wll take place. Moreover, as an effcent surplus s shared by the downstream frm, that frm nternalses the effcent upstream supply choce when competng for orders wth other downstream frms. The result s an olgopolstcally compettve outcome wth upstream supply takng place n a productvely effcent manner. The exstence of compettve outcomes generates scope for vertcal ntegraton to rase ndustry profts. It s demonstrated that vertcal ntegraton can acheve an ncrease n ndustry profts by softenng downstream competton. However, t does ths, not by foreclosng on non-ntegrated downstream frms, but nstead by provdng ncentves for ntegrated unts to weaken ther own compettve choces. 3 That s, vertcal ntegraton results n a contracton n nternal supply and an expanson n external supply. So whle ntegraton under standard vertcal contractng can generate a stuaton where rval s costs rse to the detrment of competton, here rvals compettve advantages are stmulated. Nonetheless, by vrtue of ts monopoly poston, the upstream frm approprates part of the ncrease n ndustry rents that occurs. Ths s a novel mechansm for ant-compettve vertcal ntegraton and, all the more sgnfcant n that t does not arse from problems assocated wth prvate nformaton or restrctons on the form of nput prces. The remander of the paper proceeds as follows. Next, several papers, where competton for orders precedes procurement n vertcal contractng, are dentfed and ther relatonshp to the present paper explored. In the next secton, vertcal contractng when the upstream monopolst s not ntegrated downstream s examned and the man result that, even n an envronment of complete nformaton, olgopolstcally compettve outcomes result despte the presence of a monopoly bottleneck. Secton 3 then consders the effect, proftablty and welfare effects from vertcal ntegraton n ths context. 3 Ths stands n contrast to the post-chcago approach to vertcal mergers that focuses on the way a vertcal ntegrated frm can commt to rase rval s costs. (see Rordan and Salop, 1995). In general, ths s done by commttng to hgher nput prces to ndependent downstream frms than s mplct wthn the ntegrated frm (see Ordover, Saloner and Salop, 1990; Chen, 2001 and Rey and Trole, 2003).

5 4 Secton 4 extends the baselne model to the case of Bertrand prce competton downstream and to consder the roles of contngent agreements and exclusve dealng. A fnal secton concludes. Related Lterature There are a handful of antecedents to ths paper n the lterature. Stahl (1988) examnes a model of prce settng downstream frms who procure nputs from a compettve set of upstream supplers. In one varant of hs model, t s assumed that competton downstream s for forward contracts and bddng for nputs takes place later. He demonstrates that ths leads to (Walrasan) compettve outcomes across the entre vertcal chan. As wll be demonstrated below (Secton 4), hs model s dstnct n that a sngle nput prce s set (there s no prce dscrmnaton n the wholesale market) and downstream frms otherwse have all the power n that market. In contrast, the model here presumes that the sngle upstream frm bargans one-on-one wth each downstream frm, gvng t some barganng power and also permttng dscrmnatory nput prcng outcomes. Consequently, n ths settng the Walrasan outcomes derved by Stahl do not hold. Moreover, Stahl does not analyse how vertcal restrctons mpact on downstream market outcomes. Kamen, L and Samet (1989) also consder an envronment where bddng for customer (n ther case a sngle customer contract) precedes procurement. Ther model focuses on a stuaton where frms are vertcally ntegrated but that, for effcency reasons, f one frm wns a contract t may want to subcontract part of the contract wth the losng frm. They demonstrate that the dstrbuton of barganng power mpacts on the compettveness of bd competton ex ante. Specfcally, f the losng frm has lots of barganng power ex post, ths weakens ex ante prce competton. Smlarly, below t s demonstrated that strong upstream barganng power (under vertcal separaton) weakens ex ante prce competton. The strength of the contrbuton here relates to ts comparson wth the standard vertcal contractng lterature and ts focus on how changes n vertcal

6 5 structure mpact on downstream competton. Nether of the earler papers examne these ssues Vertcal Contractng Ths secton provdes the baselne result of the paper that when competton for orders precedes procurement negotatons, olgopolstcally compettve outcomes (namely, Cournot competton) result. Moreover, ths outcome s unque. Notaton Let {1,..., N} denote an ndvdual downstream frm. Frm has nverse demand curve, P( x, x ), whch s a functon of t own output, x, and a vector of the output of others, x -. It s assumed that (.) P s non-ncreasng n each of ts arguments, for all, and that 2 P P x x x x < for all and. 5 Downstream frms face no other costs, save for the costs of procurng nputs, px. In order to sell x unts of output, frm requres y = x unts of the nput. Intally, t s supposed there s a sngle provder of nputs to all downstream frms (U). U has costs descrbed by a non-decreasng functon, Cx ( 1,... xn ). Denote C( x1,... xn) as the margnal cost of supplyng an addtonal unt to. Sometmes t s convenent to refer to Cx (, x ) and C ( x, x ) n order to focus attenton n varatons n x holdng x - as gven. It s assumed that, P(0,0) > C (0,...,0). Tmelne STAGE 1: Each downstream frm competes for orders n the downstream market. An order comprses an average prce over a fxed quantty of orders 4 Rey and Trole (2003) look at a make to order specfcaton whereby nput prcng terms are agreed upon ex ante but actual nput supply quanttes are determned followng downstream competton. The key feature of the approach here s to assume that no supply commtments (n ether prce or quantty) are made pror to downstream competton for orders. 5 These assumptons are made to guarantee the exstence and unqueness of an nteror Cournot equlbrum (Vves, 1999).

7 6 ( P, x ). Competton nvolves downstream frms choosng x takng the order quantty of other frms ( x ) as gven. STAGE 2: Each frm who wshes to procure a postve quantty negotates wth U over the prce pad per unt of nput requred ( p, y ). These negotatons are blateral. STAGE 3: Downstream frms who reach an agreement wth U produce. Those who do not reach an agreement wth U for all of ther orders ncur default costs. STAGE 4: Payments are made and payoffs are realsed. The Cournot case where downstream frms choose the order quanttes they would lke to acheve and the market prce adusts accordngly (as assumed for Stage 1) s the focus of the paper. However, n a later secton, t wll be demonstrated that all of the man results of the paper carry over to the Bertrand case. In Stage 2, barganng takes place blaterally. Fx an order for the sequence of negotatons, say begnnng wth 1 and then through to N. The precse order turns out not to matter. Blateral negotatons take the followng form: wth probablty λ, U makes a take-t-or-leave-t offer of ( p, y ) to downstream frm but wth probablty 1-λ, gets to make a take-t-or-leave-t offer to U. If the offer s reected, there s no procurement between U and otherwse the accepted offer becomes the agreed procurement terms. The outcome s observed by all other downstream frms who play the same blateral barganng game as ther turn comes up. It wll be demonstrated that ths smple barganng game mplements the blateral Nash barganng soluton wth asymmetrc barganng powers. 6 It s worth emphassng at ths pont that t s assumed here that λ [0,1). Ths s n contrast to the common assumpton n the vertcal contractng lterature that U can make take-t-or-leave-t offers to downstream frms (McAfee and Schwartz, 1994; and Segal, 1999). When orders precede procurement, ths assumpton cannot be meanngfully appled as downstream frms would receve no profts regardless of what they dd to compete for orders. Whle ths wll not change the olgopolstcally compettve outcome 6 For ths reason, any multlateral negotaton game that gves U and the payoffs they would receve under asymmetrc Nash barganng wll generate the same equlbrum outcomes n what follows.

8 7 below from beng an equlbrum, any equlbrum outcome s possble. 7 As such, t s assumed throughout that U s barganng power (λ) s bounded away from 1 although on occason I look at the outcomes of the lmtng case as λ approaches 1. A crtcal set of assumptons n vertcal contractng s what each downstream frm can observe about the outcomes of negotatons wth other frms. One possblty s that there s complete observablty where each frm knows the order and prce level of ts rvals. In ths stuaton, each would be able to nfer the outcomes of negotatons. Indeed, ths s a natural assumpton gven that the outcomes n Stage 1 wll comprse an equlbrum. The alternatve s that downstream frms cannot observe negotated outcomes. Ths s the usual assumpton n the vertcal contractng lterature; although there t s to capture the noton that U cannot commt not to engage n secret dscountng wth an ndvdual frm. Here, gven that competton for orders precedes procurement negotatons, the secret dscountng motve s not present. For ths reason, attenton s confned to the complete nformaton case throughout ths paper provdng the closest comparson wth Chcago school assumptons. Nonetheless, t wll be readly apparent that all of the results carry over to the ncomplete nformaton case. There s one mportant restrcton on the contractng space that s mplct n the specfcaton of the barganng game above. An offer from U or a downstream frm s smply a prce and quantty par that does not change regardless of the outcomes of other negotatons. Thus, agreements cannot be made contngent upon the outcome of later negotatons. Nonetheless, the realsed agreements n negotatons can stll nfluence the outcomes of later negotatons as those agreements are observed. 8 Ths smplfes the 7 It should be noted here that n the standard lterature wth prvate nformaton, many equlbrum outcomes are possble. The case that s the focus of most attenton n that lterature s the one that yelds a Cournot outcome (see Rey and Trole, 2003). However, that case requres an assumpton of passve belefs (somethng that may not be reasonable n many crcumstances). Indeed, t s also possble that the ntegrated monopoly outcome could arse under alternatve belef assumptons (McAfee and Schwartz, 1994). The advantage n ths paper s that wth λ [0,1), the equlbrum outcome s unque and s the appealng Cournot case. 8 In ths way, the type of rent shftng analysed by Marx and Shaffer (2002) s stll possble. What s not possble s an agreement that allowed the downstream frm to earn a large penalty f a later procurement agreement was reached. It s demonstrated below that such agreements may allow rent shftng (so that the order of negotatons mattered for ndvdual payoffs) but does not change the overall welfare and compettve outcomes.

9 8 analyss but as s demonstrated later n the Secton 4, the man qualtatve conclusons of the paper contnue to hold. Fnally, n Stage 3, two mportant assumptons are made: (A1) There s an exogenous default cost, d > 0, per unt of orders unfulflled. (A2) The total level of default payments cannot exceed the profts of the downstream frm. The frst assumpton smplfes the analyss consderably and, as wll be demonstrated, t does not play a crtcal role. The second assumpton s an assumpton that, to some extent, a downstream frm s udgment proof. That s, any damages award cannot exceed the ablty of the frm to pay that award. In ths case, ablty to pay s measured by downstream frm profts. (A2) smplfes the analyss consderably. If t were not present ths would have a mnor mpact on the strength of downstream competton but otherwse the results n ths paper would be unchanged. Barganng Outcome Take a set of orders { P, x } 1 N =. Then: Proposton 1. If () P + d C( x, x ) for all, and () Px C ( x, x ), then y = x and E[ px] = λpx + (1 λ) ( C( x, x ) C(0, x ) ), for all. All proofs are n the appendx. It wll turn out that, n equlbrum, condton () s always met. Wth ths, the proposton states that the soluton to any blateral negotaton s the same as the Nash barganng outcome. 9 Ths requres condton () that, f all orders are flled, ndustry profts are postve. Notce that t s concevable that ths mght not be the case even f condton () s satsfed f C(.) s not weakly concave (e.g., U has szeable fxed costs). 9 Note that there s no ssue here of the form of upstream prcng. Essentally negotatons are over what proporton of the order to fulfll and the payment for that. The payment can take a per unt form (as has been done here) or a non-lnear schedule. Essentally, however, t s the lump sum that matters and the form of the prce s smply made for notatonal convenence.

10 9 Ex Ante Competton for Orders In Stage 1, each chooses x to maxmse: P( x, x ) x E[ p( x, x ) x] where the expected procurement costs are as n Proposton 1. Let { x ˆ } N = 1 be the set of equlbrum orders. Ths results n the followng: Proposton 2. In any subgame perfect equlbrum, f P ( x ˆ, x ˆ ) x ˆ C ( x ˆ ˆ 1,..., x N), then { x ˆ } N = 1 satsfes: xˆ arg max P( x, xˆ ) x C( x, x ) for all. ˆ x Thus, the outcome s a Cournot olgopoly outcome where upstream supply s effcently provded. Ths mrrors results n the vertcal contractng lterature where procurement precedes orders and there s ncomplete nformaton. 10 Here, however, observatonally, upstream prces may be lnear and not nvolve lump sum payments. Despte ths, for a gven order, procurement s effcent and does not nvolve the negatve consequences of double margnalsaton that would normally arse when upstream prces are lnear and downstream competton s mperfect. What s also notable here, however, s that ths outcome occurs n a complete nformaton envronment and s ndependent of the degree or nature of product dfferentaton and the allocaton of barganng power. As McAfee and Schwartz (1994) demonstrate, when λ = 1 (.e., U has all of the barganng power) and downstream products are perfect substtutes for one another, the unque equlbrum outcome s the same as would be acheved by an ntegrated monopoly. That outcome s acheved because n ex ante sequental negotatons for nputs, U can commt to sgn an agreement wth a sngle frm (the last one n the sequence) and approprates all of the ndustry returns. Here that outcome s only possble f N = 1. In the standard vertcal contractng case (where procurement precedes orders), as products become dfferentated and/or relatve barganng power changes, t s not possble to provde a charactersaton of the outcome; t s lkely to depend on both of these parameters. Where orders precede procurement, however, the Cournot outcome occurs regardless of the allocaton of barganng power or the nature of downstream 10 See Hart and Trole (1990) and Segal (1999). de Fontenay and Gans (2002) provde a general treatment.

11 10 products and upstream technology. Whle the charactersaton s both sharp and robust, t does, however, rely on the dentfcaton of the nature of downstream competton. 11,12 4. Vertcal Integraton The key feature of the results derved thus far s the fact that, n an envronment wth complete nformaton, olgopolstcally compettve outcomes emerge despte the presence of an upstream monopolst. Competton emerges because there s no mechansm by whch the monopolst can commt to nput prcng outcomes that mpact on downstream competton. A lack of commtment also drves the emergence of compettve outcomes n the standard vertcal contractng lterature. There, however, an upstream monopolst cannot commt not to engage n secret dscountng n an envronment where there s mperfect nformaton. In that envronment, a move to complete nformaton would gve the monopolst the ablty to embed multlateral contngences nto ndvdual supply contracts so as to ensure a monopoly outcome ndustry-wde. Vertcal ntegraton, however, provdes an alternatve means by whch the monopolst can acheve commtments to softer downstream competton n the absence of feasble contractual mechansms. That possblty s examned here. Suppose that U purchases one or more downstream frms. In ths stuaton, the ntegrated unts wll be able to base ther orders drectly on the U s margnal cost. However, as n Chen (2001), ntegrated unts wll also have regard to the potental profts U mght earn from non-ntegrated frms. Nonetheless, t s frst useful to note that for a gven set of orders, the barganng outcomes between U and any ndvdual downstream wll be as n Propostons 1. Ths s because, n each blateral negotaton, ont surplus depends only upon the value of the 11 Other models of vertcal contractng rely on ths too. Generally, downstream competton s assumed to be Bertrand wth the outcomes drven by the types of nput prcng contracts that are feasble. 12 It s worth notng that the above equlbrum also remans an equlbrum when there s ncomplete nformaton regardng procurement contract outcomes. As s commonly assumed n the standard vertcal contractng lterature, suppose that retalers hold passve belefs regardng the outcomes of other negotatons. In ths case, f a retaler receves an offer other than that consstent wth the Cournot equlbrum outcome, t does not revse ts belefs about the outcomes of other negotatons. For ths reason, a devaton by the manufacturer cannot mpact on other negotatons and hence, wll gve t no advantage.

12 11 order and the mpact on upstream costs. It does not depend upon the terms acheved by other ndependent frms or U s own downstream dvsons. Let xˆ ( I ) be the equlbrum order and prce of an ndependent when I frms are ntegrated and let zˆ ( I) be those for an ntegrated unt. It s easy to see that zˆ ( N) = x ; * that s, f all downstream frms are ntegrated, a monopoly outcome s possble; so complete ntegraton wll be (weakly) preferred by all frms relatve to non-ntegraton or partal ntegraton. What s more nterestng are the comparatve statc results regardng the effect of partal ntegraton. Proposton 3. Suppose that each s symmetrc and I < N. In any subgame perfect equlbrum, f E[ pxˆ ] z < 0 (for all and ) then, () zˆ ( I) < xˆ (0), () xˆ (0) < xˆ ( I), () 1 xˆ ( I) N Izˆ ( I ) + ( N I ) xˆ ( I ) < ; and (v) Nxˆ (0) > Izˆ ( I) + ( N I) xˆ ( I). A necessary condton for () to (v) not to hold s that E[ pxˆ ] z > 0. The proposton demonstrates that f the revenues U expects to receve from ndependent downstream frms falls as ntegrated output expands then ndustry output and hence, consumer surplus wll be lower as a result of ntegraton. Moreover, ths occurs because U has an ncentve to contract the output of ts ntegrated unts relatve to what they would sell f they were not ntegrated. Ths, n turn, leads to an expanson n ndependent sales and an ncrease n ther market share. Thus, the ant-compettve effect of ntegraton here s not foreclosure (a reducton n ndependent output) but precsely the opposte. Indeed, ndependent frms beneft from ntegraton. The ntuton behnd Proposton 3 can be llustrated by focusng on the Cournot case wth symmetrc downstream frms sellng a homogenous product. In ths stuaton, ndependents stll solve: xˆ( I) argmax P( Izˆ+ ( N I 1) xˆ+ x) x C( Izˆ+ ( N I 1) xˆ+ x) whle an ntegrated frm solves: x zi ˆ( ) arg max ( ( ) ˆ) ( ) E[ ˆ( ) ˆ z PIz+ N IxIz+ N I pizx] CIz ( + ( N Ix ) ˆ) Integrated unt revenues Payments from ndependents where pˆ( Iz) xˆ λp( Iz ( N I) xˆ) xˆ (1 λ) ( C( Iz ( N I) xˆ) C( Iz ( N I 1) xˆ) ) = Integraton means that when consderng ther sales level, ntegrated unts take nto account ther mpact on (a) the revenues receved externally from ndependent unts; and

13 12 (b) the revenues acheved nternally by other ntegrated unts. The frst effect may be postve or negatve and, as t plays a crtcal role n Proposton 3, t s examned n detal next. On the other hand, the second effect s the same as would occur f downstream frms were to merge and, ceters parbus, mples that ntegrated frms wll contract output relatve to when they were not ntegrated. It s for ths reason that a suffcent condton for an overall reducton n ntegrated frm and overall output s that ntegrated sales reduce U s external revenue and that an output expanson necesstes as postve external revenue mpact. When I = 1, the external revenue mpact drves the outcomes entrely (as there s no nternal revenue mpact). In ths stuaton, what s the mpact of ntegrated sales on external revenue? Note that: E[ pzx ˆ( ) ˆ] = λ { Px ˆ + (1 λ ) ( C ( z+ ( N 1) xˆ ) C ( z+ ( N 2) xˆ ) ) z (1) Increased Competton Improved Barganng Poston There are two effects here. Frst, f an ncrease n sales by ntegrated unts rases the ncremental cost of supplyng a gven ndependent unt, ths mproves U s relatve barganng poston. If supply to ndependents s less attractve at the margn ths rases the prce extracted from them. Second, an ncrease n ntegrated sales reduces the downstream prce. Ths reducton s shared by the ndependent frm and U, reducng U s external revenues. These two effects a barganng effect and a competton effect (potentally) have opposng mpacts on the ncentves of an ntegrated frm to ncrease ts sales downstream. Indeed, f the competton effect outweghs the barganng effect, that ncentve s reduced; ntegrated unts wll generate fewer orders, n equlbrum, than ther ndependent downstream rvals. In the end, overall downstream quantty s reduced followng ntegraton, lowerng consumer surplus. On the other hand, a relatvely strong barganng effect may turn ntegraton nto what Fudenberg and Trole (1985) termed a top dog strategy. Ceters parbus, ths effect causes the ntegrated frm to be more aggressve downstream, rasng nternal supply at the expense of external supply. Whle ths harms ndependent downstream frm, t benefts consumers as total quantty ncreases. When wll one effect domnate? Re-arrangng (1), and assumng that x ˆ > 0 :

14 13 E[ pzx ˆ( ) ˆ] < ( )0 < ( ) z λ > ( ) λ C ( z+ ( N 1) xˆ) C ( z+ ( N 2) xˆ) 1 λ P (.) xˆ C ( z+ ( N 1) xˆ) C ( z+ ( N 2) xˆ) P C ( z+ ( N 2) xˆ ) (2) Thus, the competton effect domnates the barganng effect when () ncremental upstream costs are ncreasngly convex and () U s barganng power s hgh. Note that when upstream costs exhbt ncreasng returns or have a constant margnal cost, external revenues necessarly fall as the ntegrated frm generates more downstream orders. As such, ncreased ntegrated sales make t more desrable to reach ndependent deals at the margn (mprovng an ndependent s barganng poston). In contrast, when upstream costs are convex, t s ncreasngly costly for U to serve another ndependent unt when t has a hgh level of nternal supply. Ths commts t to a hgher prce from those ndependent sales. In terms of barganng power (λ), note that when λ s close to 1, an ntegrated frm places most weght on the downstream value from ndependent sales (that s the downstream prce receved). As such, t nternalses ths compettve externalty when choosng sales quantty from ts own dvson; reducng ts own sales n order to soften downstream competton. Interestngly, n equlbrum, ths wll mean that ndependent frms wll generate hgher orders and profts relatve to the stuaton where U was not ntegrated. The relatve salence of the competton and barganng effects can be easly seen n a specfc example. Suppose that N = 2, I = 1, P= 1 z x Cz ( + x) = α( z+ x) + β( z+ x) 2 wth α < 1. Wth ths, the respectve equlbrum quanttes are: (1 α)(1+ 2 β)(1 λ) ˆx = and ẑ = 2. 1 α (1 ) + (4 6) β λ β λ λ Notce that when β = 0 (costs are lnear), then 3 4 β (1 λ) + β(4λ 6) λ 1 α (1 λ )(1 α ) 3 λ 3 and xˆ = > zˆ = λ and as λ goes to 1, partal ntegraton acheves the ntegrated monopoly outcome. Ths s acheved by U completely foreclosng on ts nternal dvson ( z ˆ = 0). Note also that (2 λ )(1 α) 2(1 ) xˆ + zˆ = 3 λ α 3, the non-ntegrated outcome (wth equalty at λ = 0). Consderng now the case where β > 0, note that (2) becomes: 2β λ ( ) β > (3)

15 14 The rght hand sde of (3) s ncreasng n β (a measure of the convexty of upstream costs). (3) s a necessary and suffcent condton for xˆ > ( ) zˆ and xˆ + zˆ > ( ), the 2(1 α ) 3+ 4β non-ntegrated outcome. Note, however, that at λ = 1, ntegraton always results n a reducton n ndustry output. In summary, when competton for orders precedes negotatons over procurement, there s a novel mechansm for ant-compettve vertcal ntegraton. Dependng upon the nature of upstream costs, so long as U s barganng power s suffcently hgh, t wll contract ts nternal supply (perhaps completely) n order to mtgate negatve effects from ntense competton downstream. In contrast, n tradtonal models of vertcal contractng, ntegraton results n an expanded market share for ntegrated frms at the expense of ndependent ones (potentally foreclosng on them). Ths s because the compettve externalty n those models s taken nto account n barganng wth ndependent frms whle ntegrated frms are suppled only on the bass of ther own downstream revenues. 13 In effect, reversng the tmng of procurement and competton for orders swtches the supply agreements (external and nternal) compettve externaltes are nternalsed. Equlbrum Integraton Whle the precedng analyss has examned the consequences of vertcal ntegraton, there s a queston over the level of vertcal ntegraton U mght choose. To be sure, as complete ntegraton acheves the ndustry monopoly outcome, there appear to be gans to trade from all downstream frms beng acqured by U. So, at frst blush, one mght be tempted to conclude that a smlar logc mght apply to ntegraton of a sngle frm. However, as already noted, f upstream costs are convex and U s barganng power s suffcently low, ndustry profts fall as a result of partal ntegraton. For such ntegraton to be proftable U s mproved barganng poston would have to outwegh any loss as a result of hgher competton downstream, even before takng nto account any acquston costs for downstream frms. 13 See Hart and Trole (1990) and also de Fontenay and Gans (2002) for the case where downstream retalers have some barganng power.

16 15 To see these ssues more clearly t s worthwhle returnng to the smple 2 frm example used above. Note frst that when β = 0 (so upstream costs are lnear), the profts of an ntegrated U and an ndependent downstream frm are: 2 (1 α ) 2 (3 λ ) whle, under non-ntegraton, they were: (1) (1 α ) (1 λ ) πu = and π (1) = 2, 2 2 πu (0) 9 (1 α) λ 2 (3 λ ) 1 2 = and π (0) = (1 α) (1 λ). Notce that: π (1) > π (0) and π (1) π (0) wth equalty at λ = 0. Thus, ntegraton n U U ths case s always welfare reducng. However, π (1) > π (0) + π (0) only for λ > U U Ths means that even f U could purchase a downstream frm at ts non-ntegrated proft level, t may not be worthwhle as ntegraton only rases blateral surplus when U s barganng power s suffcently hgh. Turnng to the convex cost case, t s straghtforward to demonstrate that π (1) π (0) f and only f 2β λ 1+ 2β >. Ths s not surprsng as otherwse the ndependent frms output would be reduced by ntegraton. Fgure 1 depcts the ranges of ( λ, β ) over whch ntegraton s blaterally proftable and socally desrable (where the β = 0 vertces corresponds to the constant margnal cost case). 14 Thus, for ntermedate levels of U s barganng power, ntegraton s not blaterally proftable. However, as β gets larger, the range where ntegraton s not blaterally proftable les between ( +,1]. Thus, when 2β 1 2β costs are convex, ntegraton wll not be blaterally proftable unless λ s suffcently low (where there s a strong barganng effect from ntegraton; somethng not present n the constant margnal cost case). Moreover, n ths stuaton, ntegraton wll result n lower ndustry output and tend to nvolve foreclosure on the ndependent downstream frm. Nonetheless, as costs become ncreasng convex, vertcal ntegraton wll only occur f t s socally desrable. Fgure 1: Proftablty and Socal Desrablty of Vertcal Integraton 14 In fact, the range where ntegraton s proftable s where: β β+ 22 β + 8 β β+ 120 β β + 36 β [0, ) (,1] 1+ 2β 2 2(1 + β )(1+ 2 β ) λ.

17 16 Proftable & Socally Undesrable Unproftable & Socally Undesrable 2β λ = 1+ 2β β Proftable & Socally Desrable λ These consderatons carry over to the many frm case but nvolve an addtonal negatve mpact on blateral surplus that comes from the horzontal ntegraton mpact of vertcal ntegraton. As demonstrated by Salant, Swtzer and Reynolds (1983), horzontal mergers between Cournot compettors may be unproftable when the man benefcares of the merger are outsde rvals. Here, f vertcal ntegraton nvolves more than one downstream unt, a smlar effect occurs. Those unts prcng are now coordnated and n equlbrum wll, ceters parbus, lead to a reducton n ther market share and earnngs. For ntegraton to be proftable, the mpact on external revenue wll have to outwegh any losses assocated wth horzontal ntegraton. 5. Other Consderatons Ths secton consders varous extensons of the baselne model to demonstrate the robustness of the qualtatve results above.

18 17 Bertrand Prce Competton Consder a stuaton where prce s the strategc varable n Stage 1; that s, downstream frms are Bertrand compettors. In ths case, f there s suffcent product dfferentaton so that an equlbrum exsts where each downstream frm has postve orders wth prce chosen above upstream margnal cost, the outcome s smlar to that n Proposton 2. That s: Proposton 4. Let Pˆ { P ˆ} N = 1 where: Pˆ argmax ( ˆ) ( ( ˆ), ˆ P Px ( )) P C x P x ˆP for all. If x ˆ ( P) > 0 for all, and Px ˆ ˆ ˆ ˆ Pˆ ( P) C ({ x ( )}), then n any subgame perfect equlbrum, where retaler chooses P n Stage 1, realsed orders are { ( Pˆ )} N. x = 1 The key condton here s that despte prce competton, there s an nteror soluton where all retalers take postve orders n equlbrum. Of course, whenever fnal goods are close enough substtutes an nteror Bertrand equlbrum may not exst. In the perfect substtutes case, some downstream frms may realse no orders n equlbrum and ths wll, n turn, mpact upon ex post barganng over procurement. To assst n analysng ths case, t s supposed here that when two or more downstream frms choose the same lowest prce, then each has an equal chance n provdng all of the orders; that s, these are not shared. Ths assumpton means that some ndetermnacy that arses wth Bertrand competton under convex costs wll be avoded. For the homogenous goods case, let X ( P) = x ( P) denote the aggregate demand functon. The followng proposton characterses the resultng equlbrum. Proposton 5. Suppose that downstream products are homogenous and upstream costs are strctly convex. Then, n any subgame perfect equlbrum, only one retaler receves orders where: Pˆ P( P+ d) yp ( ) dx( P) = CyP (%( ),0) and yp ( ˆ) = mn[ X( Pˆ), C 1 ( Pˆ + d)]. { } The ntuton behnd ths result s very smple. Downstream frms wll bd the prce down as far as possble n order serve the entre market; ndeed, they wll bd the prce down to a pont where they expect to earn zero profts. Notce that f there are convex upstream costs, ths wll nvolve a prce less than margnal cost and could also nvolve a stuaton where some orders are not fulflled (for d suffcently low). Fnally, gven that a

19 18 downstream frm wth orders wll share any remanng surplus wth U, n bddng ther profts to zero, the downstream frm necessarly dsspates any ndustry rents (or quasrents). Thus, there are always some orders unfulflled and the damage payments assocated wth ths balance any ndustry profts from orders that are fulflled. There are several mportant thngs to note about ths equlbrum. Frst, notce that a pure strategy equlbrum exsts even when upstream costs are convex. Ths s n contrast to the usual analyses of Bertrand competton n that case: where there s typcally a mxed strategy equlbrum nvolvng prce above margnal cost. A key feature of the model that drves unqueness of the equlbrum outcome s that d > 0. If d = 0, then the equlbrum exstence problems that occur for Bertrand competton between frms wth convex costs re-emerge (Vves, 1999). Second, Stahl (1988) found that when upstream supply was perfectly compettve (arsng from prce takng frms wth an upward slopng supply curve), that when orders proceeded procurement, there exsted a subgame perfect equlbrum where fnal good prce equaled ndustry margnal cost. Stahl confned attenton to the case where d was so hgh that downstream frms found t optmal never to default on orders. However, more crtcally, he assumed that procurement entaled the same prce for each unt suppled. Thus, a retaler settng a prce below upstream margnal cost was sure to make a loss; drvng hs Walrasan equlbrum outcome. Here, a Walrasan equlbrum does not exst when upstream costs are convex. Ths s because, n contrast to Stahl (1988), barganng does not constran the per unt nput prce pad to equal upstream margnal cost. 15 Even when downstream frms have all of the barganng power (.e., λ = 0), they may fnd t optmal to prce below upstream margnal cost ncurrng losses on margnal unts or damages for unfulflled orders. In ths case, the equlbrum s socally neffcent nvolvng over-producton relatve to the Walrasan case Another dfference between the model here and that of Stahl (1988) s the need for and senstvty to te breakng rules. Whle Stahl nvestgates alternate rules, here no such rule s needed as ex post barganng drves outcomes towards a sngle retaler. 16 The ablty to effectvely prce dscrmnate n procurement s the key factor drvng the non-walrasan outcome. Even f there were more than one upstream frm, f the procurement prce allowed nframargnal payments below upstream margnal cost, the same qualtatve outcomes would result.

20 19 Moreover, t could also be the case that consumer surplus s lower than mght be acheved n an ntegrated monopoly. Whether ths s so depends upon the ratonng rule for consumers as to who receves orders and who does not. In partcular, t s possble to magne an equlbrum wth d arbtrarly small whereby all orders are receved by a retaler wth a very low prce but very few consumers are actually served. In ths stuaton, consumer surplus generated n the ndustry s low so that consumers as a whole would be better off wth a downstream monopoly. However, ths type of equlbrum reles on the lack of sophstcaton of consumers who wllngly accept the lowest prce offer wthout thnkng further about what they mght receve. An extenson of the model to the case of sophstcated consumers s left for future work. Fnally, t s worth consderng the effect of vertcal ntegraton n the Bertrand envronment. When an nteror equlbrum exsts, then we cannot say whether there s a change towards nternal versus external supply followng ntegraton. Nonetheless, prces of all downstream frms rse as the ntegrated frm softens prce competton. In the homogenous goods case, an ant-compettve effect reles on there beng only one ndependent downstream frm. Ths s because downstream competton cannot be softened n that case f there are two ndependent frms. In that case, the ntegrated downstream frm s completely foreclosed n the downstream market. Contngent Agreements Throughout the paper t has been assumed that procurement agreements cannot be made contngent upon the outcome of later agreements. The mpact of that assumpton can be readly demonstrated for the N = 2 case. In ths case, f a contngent agreement were possble, U and the frst downstream frm (call ths frm 1) n the negotatons could agree that f U were to supply a postve quantty to the second downstream frm, U would have to pay the frm 1 a penalty, f. Gven the complete nformaton assumptons n ths paper, ths agreement would be observed by frm 2 and would be seen as reducng ts gans from trade wth U. Formally, the agreement wth frm 2, would nvolve an expected payment: ( ) E[ px] = λpx + (1 λ) f+ Cx (, x) Cx (,0) (4)

21 20 so long as f Px C( x, x ) + C( x,0). For a gven f satsfyng ths constrant, the gans from trade between frm 1 and U become: Px C( x, x ) + C(0, x ) + f. In ths case, they wll agree to Thus, f = Px C( x, x ) + C( x,0) ( ) as ths maxmses ther ont profts. E[ px] = λ Px C( x, x) (1 λ) C(0, x) + Px + C( x,0) Gven ths, U s expected payoff s λ( ) Px C( x, x ) + Px (1 λ) C(0, x ), frm 1 s s ( (1 λ) Px + C(0, x ) C( x, x )) whle frm 2 s s 0. If we suppose that each downstream frm has a non-zero probablty of beng the frst to negotate wth U, t s easy to see that the equlbrum outcome from ex ante competton s the same n ths case as n Proposton 2. Interestngly, f U were to vertcally ntegrate wth one of the frms, rent shftng would no longer be possble and the equlbrum outcome would be as n Proposton 3. So, as before, ntegraton causes a contracton n ndustry output as the output of ntegrated downstream unts s reduced. Thus, the effects of vertcal ntegraton on competton and welfare reman the same as before. However, as the dstrbuton of ndustry rents under non-ntegraton has changed n partcular, t has moved n favour of U the returns to ntegraton wll have been reduced. Exclusve Dealng In the standard vertcal contractng lterature, exclusve dealng s seen as a way n whch upstream monopolsts can restore monopolstc outcomes downstream. Here, an exclusve deal would be a contract sgned wth a retaler that prevents U from dealng wth other downstream frms. On the face of t, such a contract would allow a sngle frm to generate orders at the monopoly prce, f t excludes other frms from generatng orders (as t may f downstream frms beleved those orders would not be fulflled). However, would exclusvty prevent other downstream frms from competng for orders? It won t f those frms can stll procure the necessary nputs to fll those orders. 17 Thus, perfect rent shftng s possble (Marx and Shaffer, 2003).

22 21 To consder ths, suppose that an exclusvty deal s sgned but that some other frms succeed n generatng orders. U and ts exclusve partner could choose to enforce ther agreement and leave those orders unflled. To do so, however, would nvolve mssng a surplus creatng opportunty. As Segal and Whnston (2000) note (when that opportunty s created by new entry), there exst many multlateral barganng outcomes (between the downstream frm, U and ts exclusve partner) that would allow the addtonal surplus to be splt three ways ex post. 18 Moreover, whether an order was flled or not would be drven by the same effcency crtera as n Proposton 1; that s, f the order prce above upstream margnal cost. Thus, t s easy to see that a downstream frm who generates an order ex ante wll be able to receve a share of the surplus created by that order ex post. Under multlateral barganng outcomes such as the Shapley value, ndependent retalers wll receve a one thrd share of ths value and hence, wll compete to maxmse t n Stage 1 competton. Thus, the equlbrum outcome of Proposton 2 wll reman. Nonetheless, an exclusve deal wll stll be advantageous for U and the downstream frm concerned as t allows them ontly to approprate more rents n ex post barganng over procurement. 19 Exclusve dealng, n contrast to vertcal ntegraton, does not actually change the nature of competton for orders and hence, has no ant-compettve effect. 5. Conclusons The contrbuton of ths paper has been to stand the usual approach to vertcal contractng on ts head and consder competton for orders as takng place pror to procurement negotatons. Ths change not only captures realty n some vertcal markets but also generates sharp and robust predctons regardng the ablty of monopolsts n a vertcal chan to leverage ther market power n downstream markets. 18 See also Aghon and Trole (1987) and Sper and Whnston (1995). 19 Ths pure barganng effect from exclusvty has been noted by Segal and Whnston (2000) and Segal (2003). If there are some stpulated damages then these would be rrelevant n ex post negotatons except n terms of ensurng that U and ndependent downstream frm dd not break off and reach a blateral agreement and pay the stmulated damages. Thus, exclusvty would work n a smlar way to contngent agreements as analysed above. In ether case, appropraton of rents s all that s acheved by exclusve dealng.

23 22 Sgnfcantly, n an otherwse Chcago School envronment wth none of the usually consdered mpedments to procurement negotatons prvate nformaton or restrcted prcng optons t s demonstrated that the strength of downstream competton constrans the ablty of bottleneck monopolsts to generate monopoly levels of fnal good prces. Ths, n turn, provdes a motvaton for vertcal ntegraton for purely strategc reasons. However, when t comes to ant-compettve effect, that vertcal ntegraton s used, not to foreclose on ndependent frms, but to weaken the compettve mpetus comng from ntegrated downstream unts. Thus, the model here generates predctons regardng the effects of vertcal ntegraton that are testable and dstnct from those arsng from the standard vertcal contractng lterature. The fact that reversng the tmng of competton for orders and procurement negotatons can generate such dfferent results n otherwse dentcal envronments suggests the mportance of future research nto the determnants of the tmng of wholesale and output market contracts. These are undoubtedly related to ssues of uncertanty, flexblty and the relatve ablty to re-negotate supply contracts based on the realsaton of orders n downstream markets. The standard lterature assumes that no renegotaton s possble whle here t has been assumed that no ex ante contractual commtment can be made. In most ndustres, the truth no doubt les somewhere n between and s related to more fundamental condtons n the contractng envronment.

24 23 Appendx Proof of Proposton 1 Workng backwards, gets the chance to make an offer, gven condton (), wll make an offer of y and = x py = C( y, x ) C(0, x ) whch wll be accepted by U. On the other hand, f t gets a chance, U wll make an offer that solves: max p, (, ) subect to ( ypy C yx P p) y d( x y). Solvng the constrant for py and substtutng ths nto the obectve gves: max Py C( y, x ) d( x y ) y Note that, gven condton (), ths mples that the entre order would be flled (.e., y = x ) whle evaluatng p y at ths pont and takng expectatons mples E[ px ] as stated n the Proposton. Gven ths, we need only check that a devaton from ths offer by U would not change the offers made n any subsequent negotaton. Note that the prces of other negotatons do not enter U s problem so any devaton would have to be on the bass of order level. In ths case, a devaton could only feasbly nvolve a reducton n nput quantty (.e., to x < x ). For ths to be accepted, the prce n that order would adust but more crtcally, ether () the revenue receved n subsequent orders would fall or () some orders would not be flled n those orders. In ether case, U receves a reducton n ther overall payoff. Hence, no devaton would be proftable. Proof of Propostons 2 and 4 Assume that the condtons of Proposton 1 hold. Then, frm expects to receve: P( x, x ) x λp( x, x ) x (1 λ) ( C( x, x ) C(0, x ) ) f t generates x orders. It chooses x to maxmse ths holdng x - constant. If all downstream frms do the same, ths gves x ˆ as defned n the proposton. Note that ths mples that: Proposton 1). P( x, xˆ ) C ( x, xˆ ) = x > 0 P( x, xˆ ) x (confrmng the condton of The proof of Proposton 4 proceeds along the same lnes wth the nterorty of the equlbrum ensurng the relevant condton of Proposton 1. Proof of Proposton 3 A non-ntegrated frm, I, has the same frst order condton as n the nonntegrated case: P( xˆ ( I), xˆ, zˆ ) x + P( xˆ ( I), xˆ, zˆ ) = C ( xˆ ( I), xˆ, zˆ ) (5)

25 24 whle for a gven ntegrated unt, U chooses z that satsfes: ( ) P ( zˆ ( I), xˆ, zˆ ) zˆ ( I) + zˆ + P( zˆ ( I), xˆ, zˆ ) E[ p ( ˆ ( )) ˆ z I x] + ( N I) = C ( ˆ ( ), ˆ, ˆ z I x z ) z (6) Evaluatng (6) at xˆ ( I) = xˆ (0) and zˆ ( I) = xˆ (0), t s easy to see that f p ( zˆ ( I)) xˆ z < 0, then the RHS s less that the LHS so that, f xˆ ( I) > xˆ (0), then zˆ ( I) < xˆ (0) (as quantty choces are strategc substtutes). Evaluatng (5) where xˆ ( I) = xˆ (0) but zˆ ( I) < xˆ (0), mples that the RHS s greater than the LHS, so that xˆ ( I) > xˆ (0). Ths gves () and (). It s easy to see that () s equvalent to Izˆ ( I) < Ixˆ ( I) whch holds gven () and (). Summng up (5) and (6), and usng symmetry, we have: P(.) Izˆ ( I) + I( I 1) zˆ ( I) + ( N I) xˆ ( I) + NP(.) ( ) E[ p ( ˆ ( )) ˆ z I x] + I( N I) = NC ( ˆ ( ), ˆ, ˆ z I x z ) z (7) If we evaluate (7) at xˆ ( I) = xˆ (0) and zˆ ( I) = xˆ (0) t s easy to see that f E[ p ( zˆ ( I)) xˆ ] z < 0 then aggregate equlbrum output under ntegraton must be lower than that under non-ntegraton. Fnally, note that because () to (v) not to hold s that P(.) zˆ ( I ) < 0, a necessary condton for the nequaltes E[ p ( zˆ ( I)) xˆ ] z > 0. Proof of Proposton 5 The proof proceeds n two parts. Frst, consder the outcomes of stage 2 barganng when there s a sngle downstream frm wth postve orders (as wll occur f two or more frms set the lowest downstream prce) and where P + d < C ( x,0). In ths case, U makes an offer that solves: max p, (,0) ypy C y subect to ( P p ) y d( x y ) 0. If t gets a chance, the downstream frm makes an offer that ( ) solves: max Py p y d( x y ) subect to py C( y,0). So long as ( p, y) % % yˆ { y P d C( y,0) } ( P + d) y C( y,0) dx, both of these yeld: ( ) expectaton, E[ pyˆ ] = λ ( P+ d) yˆ dx + (1 λ) C( yˆ,0). + = and, n Consder an equlbrum where all downstream frms set a prce equal to the proposton. By assumpton, only one frm receves postve orders, that s ˆP as n X ( P ˆ).