Horizontal mergers for buyer power. Abstract

Transcription

1 Horzontal mergers for buyer power Ramon Faul-Oller Unverstat d'alaant Llus Bru Unverstat de les Illes Balears Abstrat Salant et al. (1983) showed n a Cournot settng that horzontal mergers are unproftable beause outsders reat by nreasng ther output. We show that ths negatve effet may be ompensated by the postve effet that horzontal mergers have on the buyer power of mergng frms n nput markets. Bru aknowledges partal fnanal support from the Spansh Mnstry of Eduaton projet PB and Faulí-Oller from projet SEJ /ECON and from the IVIE. Ctaton: Faul-Oller, Ramon and Llus Bru, (008) "Horzontal mergers for buyer power." Eonoms Bulletn, Vol. 1, No. 3 pp. 1-7 Submtted: June 5, 007. Aepted: January 18, 008. URL:

2 Introduton There has been a long debate on merger proftablty n Cournot settngs sne the semnal paper by Salant et al. (1983). They show n a symmetr lnear Cournot model that mergers that do not nlude 80% of the atve frms are unproftable. They explan ther result by pontng out that mergers have the negatve strateg effet of nreasng produton of non-partpatng frms. Several extensons have tred to nrease merger proftablty by redung the extent of the reaton of outsders to a merger. Ths an be obtaned by allowng ether more onvex demands (Faulí-Oller (1997)) or more onvex osts (Perry and Porter (1985)). Here we take another approah. We onsder that frms not only sell the fnal good, but must also buy an nput n an mperfetly ompettve market. Therefore frms not only are about market profts, but also about how these rents are shared wth nput supplers. We show that mergers nrease the share of profts that downstream frms an approprate. Ths postve effet on frms profts of mergers must be evaluated aganst the negatve strateg effet of nreasng produton of non-partpatng frms. We obtan that mergers are proftable when the postve effet s mportant enough. Ths s the ase when the monopolst power of upstream frms s so hgh that they are able to extrat most of the rents of the vertal relatonshp. In ths ase, downstream frms strongly need to reate buyer power from mergers. The losest paper to ours s Lommerud et. al. (005). They study downstream mergers n the ase where eah produer has an exlusve nput suppler and supply ontrats onsst of a lnear pre. They obtan that downstream mergers are more proftable than wth fxed nput pres, beause they redue nput pres. Our model nstead onsders no exlusvty n the supply of nputs and two-part tarff supply ontrats. Capre (005) uses a model smlar to ours but he studes the nentve to enourage downstream ompetton by an nput suppler.

3 The model There s an upstream frm U that produes an ntermedate nput at margnal ost 0. There exsts also a ompettve supply of the nput at margnal ost >. In the downstream setor there are n frms that transform one unt of nput nto one unt of fnal produt wthout addtonal osts of produton. The fnal produt s homogeneous and ts demand s gven by P( Q) = α Q. Upstream and downstream frms set vertal ontrats that establsh the terms under whh nputs are transferred. We model ths vertal relatonshp followng the framework n Rey and Trole (forthomng), where ontrats are seret (or unobservable) and frms have passve onjetures. After ontrats are set, ompetton downstream s à la Cournot. We want to address how mergers of downstream frms affet the proess dsussed above. Mergers hange both the buyer power of downstream frms n the ntermedate market and ther market power n the fnal market. Salant et al (1983) showed that mergers solely to nrease market power are seldom proftable. We wll see that, when ahevng buyer power s very mportant to nrease profts, beause ompetton upstream s very low (hgh ), the results on merger proftablty are reversed. More spefally the stuaton s modelled aordng to the followng tmng: Stage 1: The effent upstream frm seretly offers eah downstream frm a two-part supply ontrat T ( q ) = w q + F ; eah downstream aepts or refuses the deal. If he refuses, he may use the alternatve supply. If he aepts, he orders a quantty of nput and pays aordngly. Stage : Downstream frms transform nput nto fnal produt and ompete n the fnal market à la Cournot. We solve the model for the ase where downstream frms have passve onjetures (Rey and Trole (forthomng)). The upstream frm offers to eah downstream frm the supply ontrat he would offer to a monopolst downstream fang (resdual) demand α Q q, where s the output sold by ompettors n equlbrum. Then the Q varable part of the supply tarff s set equal to margnal ost, * w =, whereas the fxed

4 fee wll be set to extrat all the rents from frm, exept the amount he an obtan usng the ompettve supply of the nput. Q Hene, the fxed fee s gven by {( ) } * α F Max α Q q q = q frms operate n equlbrum at margnal ost, eah frm produes q. As all α ( n) =. Then n + 1 the net profts of a downstream frm wll amount to Max{ ( α ( n 1) q ( n) q ) q } we defne θ, profts of downstream frms an be wrtten as: α q. If π ( n, θ ) = ( α ) 1 θ n f otherwse θ < n + 1 θ parametrzes the monopolst power of the upstream frm and wll play an mportant role n our analyss. Observe that θ s nreasng n and dereasng n. The smaller the ost gap, the hgher the ompetton faed by the upstream frm and lower the value of θ. Correspondngly, profts of downstream frms are dereasng n θ. We then have that, at one extreme, when θ = 0 there s perfet ompetton upstream, and we are bak to the standard Cournot model. At the other extreme, when θ, the upstream n + 1 suppler s de fato a monopolst beause the ompettve supply s so neffent that does not onsttute a vald alternatve; as a onsequene downstream frms obtan zero profts and all the rents are approprated by the upstream frm. The monopolst nature of the nput supply, however, depends not only on the level of produton osts but also on the number of frms n that ompete downstream. We wll onentrate below our analyss to the ase where θ 0,, and the results we obtan wll allow us to n + 1 address straghtforwardly what happens when θ. n + 1 3

5 Profts from a horzontal merger of k+1 downstream frms s defned 1 dfferene between post-merger and pre-merger profts of partpatng frms: as the π ( n k, θ ) ( k + 1) π ( n, θ ) (1) A merger s sad to be proftable f (1) s non-negatve. It s useful to rewrte the proftablty of mergers ondton the followng way: π ( n k, θ ) k + 1 π ( n, θ ) () We an dentfy the effet of θ on proftablty through the effet of hanges of θ on the left hand sde of (), whh s strtly nreasng n θ. Ths analyss yelds to the followng result: Proposton 1 A merger of k+1 frms s proftable for θ max{ 0, θ ( k, n) }, n k k + 1 θ ( k, n). n + 1 n + 1 k n + 1, where Salant et al. (1983) obtaned n a Cournot settng that mergers are proftable only f the number of partpatng frms s hgh enough. In proposton 1, we show that mergers of any sze are proftable, provded that θ s hgh enough. 3 The ntuton of the result s nterestng but not straghtforward. A graphal llustraton s useful to explan t. Fgure 1 llustrates the stuaton n the standard Cournot settng ( θ = 0 ). Fgure 1.a plots the pre-merger resdual demand of a frm, and fgure 1.b the post-merger resdual demand. The reduton n rvalry moves the resdual demand to the rght, even though n equlbrum non-partpatng frms expand ther produton. Salant et al. (1983) show that, unless k s hgh enough, the profts obtaned 1 Vertal mergers are addressed n the orgnal paper of Rey and Trole (forthomng). They onsder = 0 θ k, n s negatve. Ths amounts to θ. Then, a merger s proftable only f ( ) k + k + 1 > n, whh only holds f k s hgh enough. 3 Observe that θ ( k, n) <, and therefore the nterval n proposton 1 s non-empty. For θ n the n + 1 nteror of ths nterval, the merger s strtly proftable. 4

6 after the merger (area B) are lower than k+1 tmes the profts obtaned before the merger (area A). Fgure onsders what happens when nreases whle stays onstant 4. In equlbrum, downstream frms wll stll be suppled by the effent upstream frm at margnal ost. Therefore the sales of frms do not hange. Ths mples that the premerger (post-merger) resdual demand n Fgure a (b) s lke the one n Fgure 1a (1b). However, the profts downstream frms obtan hange beause they depend on the possblty to use the ompettve supply: as t has beome less effent they wll obvously obtan less profts (A>A' and B>B'). But the man pont s that a frm s more affeted n ts profts by an (absolute) nrease n osts, the lower ts (resdual) demand. In graphal terms, the rato between post-merger and pre-merger profts has nreased B B ' ( s lower than ). Therefore t s more lkely that a merger s proftable, the hgher A A' the value of (and hene ofθ ). Salant et al. (1983) showed that (gven n) mergers larger that a ertan mnmal sze were proftable. In our model, the same result s obtaned for any θ. The exstene of the mnmal sze omes from the fat that the left hand sde of () s nreasng and onvex n k. Furthermore, the mnmal sze s dereasng n θ. It omes from the fat that the left hand sde of () s nreasng n θ. Ths hghlghts the postve effet θ has on merger proftablty. Combnng the exstene of a mnmal proftable merger sze and Proposton 1, we an obtan the values of θ for whh mergers of any sze are proftable. Consder a merger of two frms (.e. a merger for whh k = 1); Proposton 1 tells us that t s θ θ 1, n, n + 1 proftable for ( ). If a two-frm merger s proftable then mergers of larger sze are also proftable, beause a mnmal proftable merger sze exsts. Hene, all mergers are proftable n ths nterval. When θ s hgh enough, the nrease n the resdual demand (through a merger) s the only way to obtan sgnfant profts. Imagne that n fgure.a we had set slghtly below the nterept of demand. Then pre-merger profts would be so lose to zero that mergers would be proftable. If any merger s proftable although frms are obtanng postve (even f small) profts before 4 It s the hange that nreases θ that an be represented more easly. 5

7 the merger, t s obvous that mergers wll also be proftable when frms do not obtan profts at all,.e. when θ. n + 1 Conludng Remarks. Rey and Trole (forthomng) showed that vertal mergers are proftable when supply ontrats are seret. In the same settng, we have shown that horzontal mergers are also proftable. Therefore, n future work, t would be nterestng to study the nteraton between both types of mergers. Referenes Capre,S., 005, Inentve to enourage downstream ompetton under blateral olgopoly, Eonoms Bulletn, pp.1-5. Faulí-Oller, R, 1997, "On merger proftablty n a Cournot settng", Eonoms Letters 54, Lommerud, K.E, O.R. Straume and L. Sorgard, 005 Downstream merger wth upstream market power European Eonom Revew. 49, Perry, M. and R. Porter, 1985, "Olgopoly and the nentves for horzontal merger" Ameran Eonom Revew 75, Rey, P. and J. Trole, "A Prmer on Forelosure", n M. Armstrong and R.H. Porter, eds, Handbook of Industral Organzaton, 3. New York: North-Holland, forthomng. Salant, S.W., S. Swtzer and R.J. Reynolds, 1983, "Losses from horzontal mergers: The effets of an exogenous hange n ndustry struture on a Cournot-Nash Equlbrum". The Quarterly Journal of Eonoms, 98 (),

8 P P P=α-(n-k-1)q (n-k)-q A P=α-(n-1)q (n)-q B = = 1.a q Fgure 1 1.b q P P A P=α-(n-1)q (n)-q B P=α-(n-k-1)q (n-k)-q.a q Fgure.b q 7