Input suppliers, differential pricing and information sharing agreements

Transcription

1 nput suppliers, differentil pricing nd informtion shring greements Anthony rene Deprtment of Economics Michign tte University Est Lnsing, Michign t is common for firms to systemticlly shre informtion with their input suppliers. Although such greements with horizontl rivls hve een thoroughly nlyzed, there hs een little work exmining verticl shring, nd tht nlysis hs focused on suppliers tht set uniform prices. However, there hs een systemtic chnge in the U policy towrds verticl reltionships in the pst decdes: oth FT inction nd courts rulings hve curtiled the effect of Roinson-Ptmn, lw ment to prevent differentil pricing. Furthermore, it is not cler if differentil pricing reflects the suppliers or the uyers power. The interction of these effects is exmined in wide rnge of environments. JEL: D83, L13 Key words: informtion shring, verticl reltionships thnk Bruce Allen, Jy Pil hoi, Keith rocker, Esther Gl-Or, teven Hider, teve Woodury nd in prticulr Jennifer Reingnum nd rl Dvidson for their useful comments s well s seminr prticipnts t Michign tte University, Emory University nd the Midwest Theory (Wshington University 2004) nd O Meetings (Atlnt 2005). Oviously, none cn e held responsile in ny wy for ny errors or the qulity of this pper.

2 1 t is well known tht some firms systemticlly shre informtion with their rivls. The motives for this shring hve een extensively explored oth theoreticlly nd empiriclly. 1 However, some firms lso systemticlly shre informtion with their input suppliers. For exmple, there is mple evidence tht firms shre informtion with their workers or the unions tht represent them. Fuess nd Mille (2002) report tht two-thirds of mnufcturing estlishments in Jpn, nd fifty-six percent of ll estlishments, shre informtion. The impct of this type of shring hs een studied empiriclly either y itself (e.g., Kleiner nd Bouillon 1988, nd Morishim 1991, 1991 who find positive effect on lor productivity) or with other vriles (e.g., chniowski, et l. 1997). Firms lso systemticlly shre informtion with their input suppliers (for exmples 2 see Lee nd Whng 2000 nd Li 2002) s well s their nks, the effects of which hve een studied empiriclly (see exmples in, respectively, hen 2003 nd Herrer nd Minetti 2006). Finlly, even when firm is not directly shring informtion with its input suppliers, it my e doing so indirectly when it shres informtion with its rivls through trde ssocitions or outside gencies. 3 Even though firms often shre informtion with their input suppliers, there hs een little theoreticl work exmining why firms do this. A notle exception is Li (2002) who ws the first to exmine whether downstrem firms would wnt to shre informtion with ech other nd their monopoly supplier. 4 Though Li s introduction of monopoly supplier is innovtive, the firm s incentives to shre firm-specific informtion re found to e inline with previous work such s Vives (1984) nd hpiro (1986). n ddition, it is ssumed tht the upstrem supplier chrges uniform 1 For n overview of the theoreticl work see Vives (1990) nd Rith (1996). Recent empiricl work includes Armntier nd Richrd (2003), Doyle nd nyder (1999), nd Genesove nd Mullin (1999). 2 Among their exmples, Proctor & Gmle, Wl-Mrt nd others shre informtion out inventories through ontinuous Replenishment Progrm: the input uyer provides inventory dt to the supplier who mnges the inventory under specified guidelines. Other times, inventory dt is shred y outsourcing it to third prty (e.g., some Apple omputer s plnts in the U.. shre informtion with some of their suppliers, using Fritz ompnies s the third prty). 3 For exmple, The Hrour Report ( pulishes, mong other informtion, lor hours per vehicle y ssemly plnt, which is otined from ech mnufcturer. 4 Zhng (2002) extends Li (2002) for the cse of uncertinty regrding common prmeter to include price competition nd differentited goods. rene (2006) exmines how productivity informtion ffects the outcomes.

3 2 price to ll downstrem firms, reflecting the Roinson-Ptmn Act which circumscries differentil pricing. However, since the 70 s oth inction y the FT nd chnges in the wy tht the ourts hve interpreted this Act hs incresingly limited Roinson-Ptmn s importnce. 5 Moreover, unions re not covered y Roinson-Ptmn so tht differentil wge greements re llowed. f input prices cn vry cross downstrem firms, new strtegic effects rise when there is firm specific (tht is, privte-vlued) informtion. To egin with, note when there is insted either uniform pricing or common-vlued informtion, firm s informtion normlly hs the sme effect on its own input price tht it hs on its rivl s input price. For exmple, low cost oservtion from the firm leds to n input price increse for ll firms. n contrst, with differentil pricing nd firm specific informtion, the effect on the own input price not only will e lrger thn on the rivl s input price, ut the sign my differ. For exmple, the sme low cost oservtion now leds to lrger input price increse for the firm nd n input price decrese for the rivl. Thus, this informtion will lso hve different effect on the rivl s choice vrile thn it would hve hd with uniform pricing (or common vlued informtion), which of course will hve other strtegic implictions. A different question is the impetus ehind the differentil pricing. For exmple, Wl-Mrt is well known for its ility to otin price concessions from suppliers nd in A&P v. FT (1979) it ws A&P (the retiler) tht otin the price concession from Borden (the supplier) nd not vice vers. The extent to which the differentil pricing reflects the firms power over the price rther thn the suppliers power (s ssumed in Li 2002) could lter the ove strtegic effects, nd hence whether informtion is shred nd its welfre consequences. To exmine the effect differentil pricing nd pricing power hve on the incentives to shre 5 ince the 70 s, the numer of cses rought y the FT hve declined to zero nd the courts hve mde it incresing difficult for plintiffs to succeed so tht it is now n exmple of progressive contrction (Kovcic 2003). n prticulr, since the upreme ourt ruling in Brooke (1993) (rought under Roinson-Ptmn, which requires price discrimintion etween different uyers) no predtory pricing plintiff hs previled on the merits in the federl courts (Bolton, et l 2000). ome hve rgued (toll nd Goldfein 2005) tht Roinson-Ptmn will e further restricted in the current Volvo Truck cse efore the upreme ourt.

4 3 informtion, we exmine monopolist (for ese referred to s the union) tht supplies n input to two downstrem firms tht compete strtegiclly. nitilly ech downstrem firm hs n unknown firmspecific prmeter (either its costs or demnd intercept) tht it lone will lern. Before the firms oserve their prmeters, they cn enter into inding greement to shre tht verifile informtion (e.g., using n uditor) with the union nd the firm s rivl. 6 The firm then lerns its prmeter nd, if it hs greed to do so, shres this informtion. Nture then determines whether the firms or the union set the input price (for ese clled the wge), with this proility of setting the wge representing side s pricing power. 7 After the wges re set, the firms compete in prices or quntities. The introduction of differentil pricing genertes results tht run counter to the literture nd wht Li (2002) found. First, if the union hs sufficient pricing power, then the downstrem firms never enefit from unilterlly shring firm specific informtion. pecificlly, neither the type of competition nor the type uncertinty lters this result, while in the literture chnging either of these lmost lwys led to the firm enefiting from informtion shring if currently it ws eing hrmed. (For exmple, if firm ws hrmed y shring informtion when it competed in prices, then it would enefit from shring informtion if it competed in quntities.) Despite this, with close enough sustitutes, the sum of union nd firms profits in most settings increses in informtion shring. Thus, the union (upstrem supplier) would e willing to compenste the downstrem firms. 8 To help give insight to this result it is useful to deconstruct the effects of firm shring its 6 This is simplifying ssumption implicitly used in Li (2002) s well. However, it hs een noted tht in mny environments suppliers do lek firm s informtion to its rivls, including R&D (Bönte nd Wiethus 2005), supply-chin (Annd nd Goyl 2004) nd nking (von Rheinen nd Ruckes 2004). ometimes the informtion is ctully sold without permission to rivls, which cused oth Wl-Mrt nd Newury omics to stop selling their informtion to third prty (Annd nd Goyl 2004). n different setting, Ottvini nd Prt (2001) hve shown tht policy of lwys mking the informtion pulic increses supplier s expected profits. Finlly, even if the informtion is not directly leked, when the union mkes wge offer to the rivl, the offer will e signl to the rivl of the firm s privte informtion. imilrly, the firm s pulicly known wges is lso signl to the rivl. 7 The ssumption of liner contrct follows Li (2002). uch contrcts re one of the most common forms of contrcting etween firms nd their unions (see Oswld 1993) nd etween firms (for exmples, see Mills 2004). 8 ee Mills (2004) for exmples where downstrem firm pys liner price to the upstrem firm nd the upstrem firm pys fixed fee to the downstrem firm (such s slotting llownces).

5 4 informtion y holding the rivl s informtion constnt. When firm shres informtion with the union this will ffect the wge the union sets for oth the firm (own wge effect) nd its rivl (rivl wge effect). For exmple, if the firm is hit y n increse in costs (or decrese in demnd) nd the union lerns this, this d news is meliorted oth y lower wge for the firm nd higher wge for the rivl. Likewise, good news is wekened y higher wge for the firm nd lower one for its rivl. Thus, net, these two wge effects reduce the firm s expected profit s it mkes it less convex in the rndom vrile. Notice tht this intuition holds whether the firms compete in quntities or prices, or if the informtion is regrding the firm specific costs or demnd intercept. ompring our environment to Li s (2002), we cn see why our results diverge: the own wge effect is lrger here thn in Li nd the rivl wge effect here is the reverse of tht in Li (2002). For exmple, lower cost for the firm (good news) results in greter increse in its own wge with differentil pricing thn it would with uniform pricing. Thus, the own wge effect dmpens the firm s expected profits more with differentil pricing thn it does with uniform pricing. econd, with the differentil pricing, the lower cost lso results in lower wge for the rivl, further dmpening expected profits; ut with uniform pricing (s in Li 2002), the lower cost results in higher wge for the rivl, mplifying the good news, therey mking the firm s profits more convex nd hence incresing its expected profits. A second new result is tht when the firms hve some pricing power, prisoner s dilemm cn rise with firm specific informtion: it cn e dominnt strtegy for ech firm not to shre informtion out its demnd intercept lthough joint profits would increse if they oth shred informtion. This prisoner s dilemm rises oth when the firms compete in prices nd when they compete in quntities. t lso rises with cost uncertinty when the firms compete in quntities. 9 The intuition ehind this second result turns on two spects. First, y shring informtion 9 With cost uncertinty nd price competition informtion shring lwys reduces joint profits.

6 5 firm cretes positive externlity for its rivl; informtion increses the rivl s expected profits. However, this effect is dmpened when the union sets the wge. For exmple, when the firm lerns it hs high costs, this is good news for the rivl. However, in response to this news, the union sets lower wge for the firm nd higher wge for the rivl, oth which dmpen this good news to the rivl. econd, s the union hs less pricing power this dmpening effect lessens. Thus, s the pricing power wekens, the positive externlity grows, eventully ecoming greter thn the loss the rivl would incur y shring its informtion (which is shrinking for similr reson). At this point, while shring its informtion mkes the rivl worse off even if the firm is shring its informtion its expected profits re greter if oth of them shre informtion thn if neither shres informtion. Another new result is tht there exists pricing power such tht joint surplus (union nd firms profits) increses from informtion shring, ut welfre decreses; nd, in prticulr, this occurs under the conditions in Li (2002) tht hve oth joint surplus nd welfre incresing. This cn rise with demnd intercept uncertinty in oth price nd quntity competition nd with cost uncertinty in quntity competition. n contrst, previous work hs usully found tht if joint producer surplus (union nd firms surplus) increses, then welfre lso increses from shring firm specific informtion. 10 Thus, the relxtion of the Roinson-Ptmn constrint my hve n unexpected welfre cost y encourging welfre-reducing informtion shring. The cuse of this third result lso turns on the union s ctions. When the union hs the pricing power, informtion shring reduces socil welfre: the union rises the wge when firm hs lower costs. Hence, the wges shift output from the more efficient firm to the less efficient firm. On the other hnd, when the firms hve the pricing power, informtion shring rises oth producer surplus nd socil welfre with quntity competition or with price competition nd unknown demnd intercept. ince informtion shring s effect on producer surplus is greter thn on welfre, s the 10 The exception eing in Vives (1990) ut monopolist-competitive frmework is used so the numer of firm is lrge, i.e., ech firm cnnot influence ggregte mrket mgnitudes.

7 6 pricing power shifts from the firms to the union, there is level of pricing power such tht socil welfre decreses with informtion shring even though producer surplus increses. n the next section, the sic environment is descried. n section three, the quntity competition model is considered, while the penultimte section considers price competition. The finl section concludes. 2. Environment There is monopoly input supplier tht sells necessry input for downstrem duopoly tht produces differentited good. There is uncertinty out firm specific prmeters. For expositionl purposes, the input is clled lor nd the upstrem firm union; however, it should e cler tht the results hold for n upstrem firm tht produces n input. The firms mximize expected profits nd the union expected wge ill. This interction is modeled in five stges. n the initil stge ech firm, efore lerning its prmeter s vlue, simultneously nd independently chooses whether to enter n enforcele contrct to shre with the union nd its rivl ny informtion tht it my lern. To focus on the incentives to shre informtion, it is ssumed tht the informtion cn e shred in verifile wy. n the second stge, nture rndomly chooses the prmeters vlues nd revels to ech firm only its own vlue. 11 f firm entered the contrct, in stge three it discloses this informtion to the union nd its rivl. n the fourth stge, with proility B, nture chooses the union to mke wge offer to ech firm. 12 With proility (1 B) nture chooses the firms to mke offers to the union. The other side my ccept or reject. f the offer is rejected, the gme ends. n the finl stge, the firms simultneously nd independently compete in strtegic vrile. 11 Mny vritions of the informtiveness of the signl the firm receives or chooses to trnsmit hve een exmined in the informtion shring literture without ltering the sic results (see, e.g., Gl-Or 1986). 12 As noted in the introduction, the focus here on liner contrcts is for severl resons. First, simple wge rgining tht leves the employment decision to the firm is fr nd wy the most common form of union/firm negotitions (see Oswld 1993) nd is common to mny usiness reltionships, in prticulr, wholesler/retiler. econd, s the question of informtion shring in this environment hs hrdly een exmined, the simplest mechnism seems nturl. Finlly, this fcilittes comprison to Li (2002) which uses liner contrcts lso.

8 7 The demnd for the downstrem firms product is modeled with representtive consumer (Vives 1984). There is continuum of identicl consumers with seprle, liner utility in the numerire good nd preferences for the differentited goods represented y the qudrtic function U(q,q ) = α(q + q ) (½)(βq 2 + 2δq q + βq 2 ), α > 0, β δ > 0, so tht the goods re sustitutes if δ > For ese of reding nd with no effect on the results let β = 1. The representtive consumer mximizes U(q,q ) suject to prices p, p. Thus, inverse demnd is p = α q δ q. Producing one unit of the good requires one unit ech of two inputs, one of which is lor which is only supplied y the union. The other input is competitively supplied with costs c i. Let w j e the wge for the lor. Firm s cost function, then, is (c + w )q, nd its profits re π = (α q δq (w + c ))q. The union s opportunity cost of supply lor is zero. The union s wge ill then is ω = w q + w q. Hence, welfre is W(q,q ) = α (q + q ) (½)(q δ q q + q 2 ) c q c q. ince the interest here is in n ctive oligopoly, it is ssumed tht the vlues on the prmeters re such tht outputs re positive in equilirium. 3. Quntity competition With quntity competition, ut not with price competition, firm specific uncertinty regrding cost is equivlent to tht regrding the demnd intercept. For ese, then, let the uncertinty e regrding the price c. nitilly the vlues of c nd c re unknown ut re independently drwn from known distriution F j (c) on support [c j, c j ] with the mrginl density f j (c) nd c j >0. Denote E[c j ] = c je nd σ 2 j = E[c 2 j ] c 2 je. As symmetry in vrince hs no qulittive effect on the results, for 2 incresed trnsprency, let σ = σ = σ 2 nd the minor effects tht symmetry would hve will e noted. As usul, to derive the equilirium requires first tht the lst stge is chrcterized for ll possile outcomes nd then to work ck nd derive ech previous stge. 13 For discussion of dditionl restrictions on the form see Vives (1984).

9 8 3.A The fifth stge n the fifth stge ech firm simultneously sets output. A firm s profit mximizing output not only depends on its cost, ut lso its informtion nd its rivl s informtion. Thus, there re four outcomes tht need to e chrcterized: when oth firms shre informtion, when neither shres informtion nd when one shres ut the other does not. When oth firms shre informtion, the gme is stndrd ournot gme s ech firm knows the other s costs. Firm i mximizes (α q i δq j (w i + c i ))q i nd from the usul clculus the Nsh equilirium outputs nd profits cn e derived for relized c s nd w s: q = [α(2 δ) 2(w+c ) + δ(w +c )]/Δ q = [α(2 δ) 2(w+c ) + δ(w +c )]/Δ where the superscript represents complete informtion nd Δ = 4 δ 2. Profits, wge ill, producer surplus (profits nd wge ill) nd welfre in the fifth stge re likewise evluted t, e.g., = (α δ q (w + c )). q q When neither firm shres informtion, the gme is the typicl ournot gme of incomplete informtion with respect to the other s input price c. The stndrd derivtion yields the Byesin- Nsh equilirium outputs: q q with the profits = [α(2 δ) 2(w+c ) + δ(w +c e )]/Δ + δ 2 (c c e )/2Δ, = [α(2 δ) 2(w+c ) + δ(w +c e )]/Δ + δ 2 (c c e )/2Δ., etc. eing derived nlogously to when there is complete informtion. Finlly, consider the cse when only one firm shres informtion. Assume for concreteness tht firm shres informtion (firm lerns s cost) while firm does not. This is stndrd ournot gme of symmetric informtion. The Byesin-Nsh equilirium outputs nd profits re q π = [α(2 δ) 2(w+c ) + δ(w +c e )]/Δ, q π

10 9 N q = [α(2 δ) 2(w+c ) + δ(w + c )]/Δ + δ 2 (c c e )/2Δ, where indictes shre nd N not shre. Note tht in the first stge tht for given w nd w, expected outputs re the sme for ll informtion structures: q i [α(2 δ) 2(w i +c ie ) + δ(w j +c je )]/Δ. This implies tht profits, wge ill nd welfre, evluted t the men, re the sme. Tht is, letting c e denote the expected vlue of ech N cost, {c e,c e }, π (ce) = π (ce) = π (ce) = π (ce), etc., which will e useful lter. i i i i 3.B The fourth stge n the penultimte stge the wge is determined. There re now eight possiilities sed on which side nture chooses to mke the wge offer (union or firm) nd on the four possiilities s to whether informtion ws shred in the third stge. onsider first the four possile environments when nture chooses the union to mke the offer. To egin with, if informtion ws shred y oth firms in the third stge, then the union knows tht the stge five equilirium outputs will e q nd q nd so it chooses w nd w to mximize the wge ill ω = q w + w q. From the first order conditions, the optiml wges re w = (α c)/2 w = (α c)/2. This implies tht in the lst stge, the resulting outputs re q = (α(2 δ) 2c + δc )/2Δ q = (α(2 δ) 2c + δc )/2Δ,U where the suscripts {i,u} indicte which firm nd tht the union set the wge. These outputs cn e π i sustituted into the definitions for profit ( ) to otin equilirium profits, denoted, wge ill,u π U,i ω U W U ( ) nd welfre ( ). f neither firm shres informtion, then the union s expects the fifth stge outputs to e E[ q i ]

11 10 = q i. Hence the union mximizes ω = qw + q w. U Mximizing ωu with respect to w nd w otins w = (α ce)/2 w = (α c e )/2 nd so the fifth stge outputs re q,u q,u = [α(2 δ) 2(2c c e ) + δc e )]/2Δ + δ 2 (c c e )/2Δ, = [α(2 δ) 2(2c c e ) + δc e )]/2Δ + δ 2 (c c e )/2Δ. The corresponding profits, wge ill nd welfre re denoted, nd. Finlly, if firm shres its cost oservtion ut firm does not, then the union knows tht firm will set output q π U,i s the union hs the sme informtion tht firm does. However, the union N does not know the vlue of c so like firm only hs n expecttion of firm s output: E [ ] = [α(2 δ) 2(w+c e ) + δ(w +c )]/Δ. Hence, the wge ill is N ω U N = q w + E [ q ]w where the N superscript indictes tht firm shres, ut firm does not. Optiml wges, then, re ω U W U q N w = (α c) /2 w = (α ce) /2. N The fifth stge outputs then re N q = (α(2 δ) 2c + δc e )/2Δ, q = [α(2 δ) 2(2c c e ) + δc e )]/2Δ + δ 2 (c c e )/2Δ,U,U N N N with the corresponding profits, wge ill nd welfre denoted, nd. The cse when firm shres ut firm does not follows symmetriclly. Even though the wges my vry, when they do, they re liner in the cost oservtion nd, so in the first stge, the expected fourth stge wge re equl for ech informtion structure. As π,u π,u ω U W U

12 11 result, in the first stge the expected output re equl cross informtion structures: E[ ] = q,u q,u q,u q,u N E[ ] = E[ ] = E[ ]. For this reson, the profit, wge ill nd welfre evluted t the expected cost re equl. Thus, it is useful to define this: πi,u π (ce) = π (ce) = π (ce) = N N N π (ce); ωu ωu (ce) = ω U (ce) = ωu (ce); WU WU (c e ) = WU (c e ) = WU (c e ). i,u Turning to the cse when nture selects the firms to set the wge, it is immedite tht ech firm would offer the union wge equl to the workers opportunity cost. Tht is, the wge is for ll informtion structure lwys w F = 0. As result, the firms outputs re esy to clculte: q = [α(2 δ) 2c + δc ]/Δ q = [α(2 δ) 2c + δc ]/Δ,F q = [α(2 δ) 2c + δc e ]/Δ + δ 2 (c c e ) 2Δ, q = [α(2 δ) 2c + δc e ]/Δ + δ 2 (c c e )/2Δ.,F N q = [α(2 δ) 2c + δc e ]/Δ, q = [α(2 δ) 2c + δc ]/Δ + δ 2 (c c e )/2Δ.,F ( ) ( ) Profits, wge ill nd welfre re defined nlogously nd denoted π,,, with the superscripts indicting the informtion structure. Note tht, nlogous to when the union sets the N wge, in the first stge E[ ] = E[ ] = E[ ] = E[ q ]. As result, profits, wge ill nd q,f q,f q,f N welfre evluted t the expected costs re the sme, e.g., π (ce) = π (ce) = π (ce) = π (ce).,f,f,f, F i,f i,u i,f i,f i,u ω ( ) F W F Following previous nottion, denote these men vlues s π i,f, ω F, nd W. With the equilirium profits for the eight possile outcomes chrcterized, the conditions for firm to shre informtion nd its welfre effects cn e derived. F i,f i,u i,f 3. The first stge n the first stge the firms chose whether to enter contrct to shre informtion. f trnsfers etween gents re possile, then there re severl resons why firm might enter the contrct. First, it might e dominnt strtegy for firm to unilterlly shre informtion (i.e., regrdless of wht

13 12 the rivl decides). econd, joint profits my e greter if they oth shre thn if neither shres, nd so quid pro quo rrngement my rise when there is prisoner s dilemm. Finlly, even if the firms profits re lower with shring, producer surplus my increse; the union s gin from the firms shring my e greter thn the firms joint loss. n such cse, the union my e willing to py up front fees to one or oth firms to induce them to shre the informtion. onsider the effect on profits from informtion shring. Given pricing (or rgining) power B, there re four possiilities sed on whether ech firm entered the greement to shre informtion. f firm chooses to shre its informtion when its rivl does not, then tking the expecttion of the π,u π,f profits nd from section 3.B otins B E[ ] + (1 B) E[ π ] = B [ π, U + σ 2 /Δ 2 ] + (1 B) [ π, F + 4σ 2 /Δ 2 ]. (1) π,u,f f the firm does not shre informtion when its rivl does not, then tking the expecttion, it is B E[ ] + (1 B) E[ π ] = B [ π, U + σ 2 /4] + (1 B) [ π, F + σ 2 /4]. (2) π,u,f On the other hnd if it shres informtion when its rivl lso shres expected profits re B E[ ] + (1 B) E[ π ] = B [ π, U + σ 2 (4+d 2 )/4Δ 2 ] + (1 B) [ π, F + 4σ 2 (4+d 2 )/4Δ 2 ], (3) π,u,f while if it does not shre when its rivl shres its expected profits re B E[ π,u N N ] + (1 ) E[ π ] = B [ π, U + σ 2 (Δ 2 +d 2 )/4Δ 2 ] + (1 B) [ π, F + σ 2 (Δ 2 +4d 2 )/ 4Δ 2 ]. (4),F Notice tht in differencing either (1) nd (2) or (3) nd (4) tht the men profits ( π,( ) ) fll out. ompring equtions (1-4) the condition for firm to unilterlly shre informtion or for firms to e jointly willing to shre informtion cn e otin. pecificlly, Proposition 1: With quntity competition nd uncertin firm specific cost or demnd intercept, firm unilterlly chooses to shre informtion if nd only if B δ 2 (8 δ 2 )/12. A firm s profit is greter when oth shre informtion thn when neither shre if nd only if B δ 2 (12 δ 2 )/3(4+δ 2 ).

14 13 Proof: From (1) nd (2), firm s expected profit when they oth do not shre less its expected profit when only firm shres, is incresing in B, nd equls zero t B = δ 2 (8 δ 2 )/12. From (3) nd (4), the sme is true for firm s expected profit when only it does not shre less its expected profit when they oth shre. For the second prt, from (2) nd (3), firm s expected profit when they oth do not shre less its expected profit when they oth shre, is incresing in B nd equls t B = δ 2 (12 δ 2 )/3(4+δ 2 ).// 14 There re two effects tht rise from firm shring its informtion. On one hnd, the union cn exploit the informtion to the firm s detriment. On the other hnd, the informtion eing shred with the rivl cretes enefit. n the environment here, the gin from shring is greter thn the loss from the union lerning, if the union is sufficiently wek or the products re sufficiently undifferentited. t is interesting to contrst these results to those found in Li (2002) who ssumes tht the union hs ll of the pricing power nd the products re perfect sustitutes (equivlent to B = 1 nd δ=1). n contrst to the result here, Li (2002) finds tht the firm s dominnt strtegy is to shre informtion nd profits re greter if ll firms shre informtion. The difference rises ecuse here the union sets different wges, while in Li (2002) uniform price is considered. 15 By setting differentil wge the extent to which the union cn exploit the informtion is enhnced sufficiently to chnge the results found in Li. omprison of the pricing power (B) needed for joint profits to increse from informtion shring (δ 2 (12 δ 2 )/3(4+δ 2 )) to tht needed for n individul firm to unilterlly shre informtion (δ 2 (8 δ 2 )/12), revels tht there re levels of pricing power such tht there is prisoner s dilemm. nterestingly, this only rises if the pricing power is more evenly divided. 14 f symmetry is not imposed on vrince then the condition is for firm i when δ = 1: B (7σ i + 4σ j ) 3(4σ i + σ j ). Thus, e.g., if firm s cost were known y ll ex nte, then firm prefers complete informtion for ll B nd firm prefers complete informtion only if B 7/ lcultions showing this cn e provided on request from the uthor.

15 14 orollry: With quntity competition nd uncertin cost or demnd specific intercept, for ll δ (0,1], there exists pricing power B such tht the firm s dominnt strtegy is to not shre informtion, ut joint profits increse if oth firms shre informtion. While n informtion shring prisoner s dilemm mong downstrem firms hs een found to rise regrding uncertinty of common prmeter (Vives 1984, Kiry 1988, Rith 1996), here it is regrding privte prmeter. Furthermore, prisoner s dilemm does not rise in Li (2002). 16 Finlly, the prisoner s dilemm in previous work required either sufficiently differentited goods (Vives 1984, Rith 1996) or convex costs (Kiry 1988), while here it cn rise even with perfect sustitutes nd liner costs. Turning to the effect product differentition hs, s δ decreses, the criticl vlue for B decreses; s the products ecome more differentited, informtion shring is more likely to hrm firm, nd in the limit only if the firms hve ll the pricing power would firms unilterlly shre informtion. This is in contrst to the literture which finds tht if nything, s the products ecome more differentited, informtion shring is more likely to help firm (Vives 1984, 1990). Prt of the reson for this is tht with privte prmeter uncertinty, the gin from shring informtion with rivl decreses s products ecome more differentited. The second prt of the reson cn e found in Zhng (2002) who shows tht if there were only monopoly downstrem, then the downstrem firm is lwys hrmed. 17 The finl prt is the differentil pricing here which increses the cost to the firm from the union s lerning. Thus, s the products ecome more differentited the firm gins less from its rivl lerning nd is hrmed more from the union lerning. onsider next the effect informtion shring hs on the wge ill nd producer surplus. 16 With uncertinty regrding common prmeter in quntity competition (Zhng 2002), prisoner s dilemm rises if informtion is sufficiently imprecise nd the goods re strong enough complements (ut not if they re strong enough sustitutes). Here whether the products re sustitutes or complements hs no effect. 17 Though there is common prmeter uncertinty in Zhng (2002), with monopoly downstrem, common nd privte prmeter uncertinty re the sme.

16 15 Although the firms re less likely to enefit from shring informtion s union hs more pricing power, the union s vlue from informtion shring increses. f producer surplus increses if the union s gin is greter thn the firms comined loss then the union would e willing to py the firms n upfront fee to induce them to shre their informtion. Thus, consider the chnge in producer surplus from informtion shring. Given pricing power B, if oth firms shre their informtion then expected producer surplus is, where + + ω = P U, etc., π,u π,u π,u π,u U ω U π,f π,f ω F B E[ + + ] + (1 B) E[ + + ] = B [ P U + σ 2 (4 + d 2 )/4Δ 2 ] + (1 B) [ P F + σ 2 /Δ]. 18 (5) Expected producer surplus when oth firms do not shre informtion is B E[ + + ] + (1 B) E[ + + ω ] = B [ P U + σ 2 /2] + (1 B) [ P F + σ 2 /2]. (6) π,u π,u ω U Differencing (5) nd (6) shows tht π,f π,f F Proposition 2: With quntity competition nd uncertin cost or demnd specific intercept, producer surplus increses with informtion shring if nd only if B δ 2 (12 δ 2 )/(4+5δ 2 ). trightforwrd lger shows tht the criticl B for producer surplus is lwys greter thn the criticl B for joint profits; for ll δ > 0, there lwys exist B such tht the firms jointly do not enefit from informtion shring, ut the union is willing to induce them to shre. For exmple, with perfect sustitutes, when the firms would not shre informtion, union cn lwys profitly induce the firms to shre informtion. Not surprisingly, then, from the condition in proposition 2, there is rnge of δ such tht for ll pricing power (B), producer surplus increses with informtion shring. 18 As the informtion is firm specific nd the vrinces re identicl, only the cses of either oth shring or neither shring need e considered. The effect of symmetric vrinces is nlogous to tht in footnote 16.

17 16 pecificlly, δ 2 (12 δ 2 )/(4+5δ 2 ) is incresing in δ on δ [0,1], so solving for the δ such tht δ 2 (12 δ 2 )/(4+5δ 2 ) = 1, otins: orollry: With quntity competition nd uncertin cost or demnd specific intercept, if δ ( 11 3)/2 ( 4/5), then for ll pricing power producer surplus increses with informtion shring. tted in reverse, the corollry implies tht s the products ecome more differentited, it is more likely tht producer surplus decrese with informtion shring. n prticulr, with doulesided monopoly (δ = 0), n upstrem monopolist cn never induce the downstrem monopolist to shre informtion. This my e somewht surprising s there is superior coordintion in the union s wge setting from complete informtion. However, intuitively producer surplus decreses ecuse it is convex in costs c : smll decrese in cost increses producer surplus more thn n equivlent increse in cost reduces producer surplus. ince with complete informtion, the union s wge setting dmpens the effect the cost chnge hs (e.g., when cost c decreses, w increses), producer surplus decreses with the informtion. Turning to welfre, priori the effect of informtion shring is uncler. Without the union informtion shring increses welfre in this environment (hpiro 1984). Likewise, with union setting uniform wge informtion shring increses welfre (Li 2002). Finlly, even with union setting differentil wges, producer surplus increses with informtion shring when the products re sufficiently similr for ll pricing powers B. To determine the net effect, note tht if oth firms shre their informtion thn expected welfre is B E[ ] + (1 B) E[ W ] = B [ W + (28 5δ 2 )σ 2 /4Δ] + (1 B) [ W + (12 δ 2 )σ 2 /Δ 2 ]. (7) W U Expected welfre when oth firms do not shre informtion is F U B E[ ] + (1 ) E[ W ] = B [ W + σ 2 /2] + (1 B) [ W + σ 2 /2]. (8) W U F U Equtions (7) nd (8) cn e used to derive tht, counter to the results in the literture, welfre cn F F

18 17 decrese with informtion shring when the union hs enough pricing power: Proposition 3: With quntity competition nd uncertin cost or demnd specific intercept, welfre is greter when oth firms shre if nd only if B < δ 2 (20 3δ 2 )/(20 + δ 2 ). nspection of proposition 3 shows tht there does not exist δ such tht when the union hs ll of the pricing power (B=1), welfre increses with informtion shring: for δ (-1,1), δ 2 (20 3δ 2 )/(20 + δ 2 ) is incresing in δ, nd t δ=1, δ 2 (20 3δ 2 )/(20 + δ 2 ) = 17/21. The intuition is tht the informtion leds the union to induce output chnges tht re in the opposite direction of wht would increse welfre. A lower cost firm receives higher wge nd so produces less, while higher cost firm receives lower wge inducing it to produce more. On the other hnd, when the union hs reltively little pricing power, welfre increses from informtion shring ecuse of the interction etween the firms. Thus, s δ decreses (so tht the interction etween the firms decreses) informtion shring is less likely to rise welfre. Tht welfre decreses with informtion shring when the union hs the pricing power is the opposite of wht is found in Li (2002), pointing to the effect of differentil wges. Worse, compring proposition 2 nd 3 shows tht the criticl threshold in pricing power for producer surplus to increse is lwys greter thn tht for welfre. Thus, orollry: With quntity competition nd uncertin cost or demnd specific intercept, for ll δ (0,1), there exists pricing power B such tht the union cn profitly induce the firms to shre, ut welfre decreses. 4. Price competition 4.A Unknown demnd With price competition, in contrst to quntity competition, previous results depend on

19 18 whether the uncertinty is regrding the firm specific cost or intercept. onsider first then wht occurs when the intercept is unknown. For nlyticl symmetry, let demnd e q i = A i p i + d p j with d [0,1), which genertes utility of the form exmined in the quntity competition model). 19 Tht is, now the vlues of A nd A re initilly unknown ut re independently drwn from known distriution G j (A) on support [A j, A j ] with the mrginl density g j (A) nd g j >>0. As symmetry in the men nd vrince hs no qulittive effect on the results, the distriutions re ssumed symmetric: A e = A e = A e nd σ 2 2 = σ = σ 2. With no loss of generlity, costs c i re set to zero for the cse of unknown intercept. As the nlysis is nlogous to tht with quntity competition, the derivtions re left for the ppendix nd only the results re presented. The first result is quite surprising: the conditions for firms to shre informtion or to enefit from shring informtion with price competition nd intercept uncertinty (P) re identicl to those in quntity competition. Proposition 1(P): With price competition nd uncertin intercept, firm unilterlly chooses to shre informtion if nd only if B d 2 (8 d 2 )/12. A firm s profit is greter when oth shre informtion thn when neither shre if nd only if B d 2 (12 d 2 )/3(4+d 2 ). orollry: With price competition nd uncertin c intercept, for ll d (0,1), there exists pricing power B such tht the firm s dominnt strtegy is to not shre informtion, ut joint profits increse if oth firms shre informtion. ince the conditions on the firms profits re identicl to those in quntity competition, it might e concluded tht this cse is trivil: tht the reminder of the results would lso e identicl. However, with price competition the interction etween the union wge setting nd the firms 19 pecificlly, this type of uncertinty would e generted y utility [A (q + dq ) + A (q + dq ) (½)(q d q q + q 2 )]/(1 d 2 ).

20 19 pricing differs, which ffects producer surplus nd welfre in different wys. First, there is etter coordintion in pricing nd so producer surplus is more likely to increse with informtion shring. However, this sme gin in coordintion is more likely to led to lower expected welfre. Define d * s the unique root of {d 6 11d d 2 4} on the intervl [0,1] (d * 0.437). Proposition 2(P): With price competition nd uncertin intercept, producer surplus increses with informtion shring if nd only if either d d * or d< d * nd B d 2 (12 d 2 )(1 d 2 )/(4 11δ 2 2d 4 ). Though how the firms compete does not ffect whether firms shre informtion, how the firms compete does effect whether producer surplus increses with informtion shring. n prticulr, producer surplus is more likely to increse with price competition (for ll B when d >.437) thn with quntity competition (δ >.8). The reson is tht when the firms compete in prices the differentil wge hs smller deleterious effect on profits. This is ecuse with sustitutes n increse in own demnd not only rises the firm s wge, ut its rivl s s well, thus mitigting the profit loss from higher wge. (With complements, it lowers the rivl s wge which mitigtes the profit loss from higher wge.) Both effects lso induce higher price from the rivl. n contrst, with quntity competition n increse in the own wge results in the rivl expnding its output. Finlly, s the products ecome less differentited, the unions profit is greter frction of the producer surplus nd so its enefit domintes. Turning to welfre, the condition gin differs from tht with quntity competition. Proposition 3(P): With price competition nd uncertin intercept, welfre is greter when oth firms shre if nd only if B d 2 (1 d 2 )(d 2 +4)/(20 7d 2 4d 4 ). As compred to quntity competition, with price competition it is much less likely tht informtion shring rises welfre even though it is more likely tht producer surplus incresess.

21 20 First, while in quntity competition the threshold pricing power increses in δ, here it is nonmonotonic: incresing nd then decresing, which is the only instnce of this. n prticulr, s δ 1 with price competition, the threshold pricing power goes to zero with price competition, while with quntity competition it reches its mximum. As the goods ecome less differentited, the firms profits go to zero nd so do the reltive gins from informtion shring. Wht remins then is union whose ffect on wges in response to the informtion is detrimentl to welfre: the lower cost firm sees higher wge. Finlly, the δ [0,1) tht mximizes B is pproximtely.79. However, this mximum B is pproximtely 1/13, which is significntly smller thn the mximum B in quntity competition (17/21). ince welfre is less likely to increse with informtion shring, ut producer surplus is more likely to increse, the finl result of the previous section is even more likely to hold: orollry: With price competition nd demnd specific intercept, for ll δ (0,1), there exists pricing power B such tht the union cn profitly induce the firms to shre, ut welfre decreses. 4.B Unknown ost Firm i s profits re now (A p i + d p j )(p i w i c i ). n the informtion shring literture (i.e., there is no union), it is well known tht in price competition, then firms re hrmed y informtion shring of costs nd welfre decreses. As the previous results here show tht the introduction of the upstrem monopoly reduces the firms enefit nd welfre from shring informtion, the impliction is tht for no B re joint profits or welfre greter with complete informtion. Wht is less cler is whether producer surplus cn increse for ny B. The equilirium prices nd expected profits re in the ppendix from which cn e derived the following. Proposition 1(P): With price competition nd uncertin cost, firm never unilterlly chooses to

22 21 shre informtion nd profits re lwys lower when oth shre informtion thn when oth do not shre informtion. Proposition 2(P): With price competition nd uncertin cost, producer surplus lwys decreses with informtion shring. Proposition 3(P): With price competition nd uncertin intercept, welfre lwys decreses with informtion shring. The most interesting result here is tht producer surplus cn never increse with informtion shring while it does with unknown intercept even when the goods re very close sustitutes nd so the firms profits re reltively smll. The reson is tht with unknown cost, chnge in the firm s cost does not chnge the rivl s wge while with unknown intercept chnge in the firm s intercept does ffect the rivl s wge. As result, producer surplus does not increse with informtion shring no mtter the pricing power. However, simply ecuse producer surplus decreses with informtion shring does not men it will not rise. f the union is le to institutionlize structure tht promotes informtion shring, then it cn still rise despite the firm s ojections. 5. onclusion Given the prevlence of informtion shring in verticl reltionships (see, e.g., Lee nd Whng 2000 nd Fuess nd Mille 2002) nd the prevlence of work exmining informtion shring etween horizontl rivls, there hs een surprisingly little nlysis of informtion shring in verticl reltionships, with the noteworthy exception of Li (2002) nd Zhng (2002). While Li (2002) nd Zhng (2002) ssume tht tht supplier sets uniform price, since the 1970 s, there hs een grdul loosening of U policy towrds differentil pricing etween input suppliers nd downstrem firms. n ddition, differentil pricing is llowed in lor greements. A second issue is tht it is not lwys cler if the differentil pricing reflects the mrket power of the supplier or of the uyer.

23 22 This pper exmined the effects of differentil pricing on firm s incentive to shre privte informtion with its rivl nd input supplier. This nlysis ws done in rnge of environments. First, pricing power etween the firm nd the union ws llowed to vry. econd, this pper exmined oth firms tht compete in quntities nd prices, s well s products tht rnge from perfect complements to (nerly) perfect sustitutes. Finlly, oth firm specific demnd nd cost uncertinty were exmined. t ws found tht the greter the pricing power of the firms, the more likely firm is to unilterlly shre informtion. Empiriclly, then, unilterl informtion shring (e.g., Hrour Assocites) should e more common, the more power the downstrem firms hve. However, prisoner s dilemm cn rise: there cn e rnge of pricing power such tht the firms would not unilterlly shre informtion, ut joint profits increse with informtion shring. Despite this, producer surplus cn still increse with informtion shring. Thus, the union could induce informtion shring y pying upfront fees while the firms py the per unit price for the input commonly oserved reltionship, e.g., in groceries with slotting fees. 20 On the other hnd, with sufficiently differentited goods, producer surplus is likely to decrese in the union s pricing power. Finlly, though welfre is lso likely to decrese in the union s pricing power, the reltionship etween pricing power, producer surplus nd welfre is not uniform: there usully exists level of pricing power such tht producer surplus increses ut welfre decreses with informtion shring. 21 Exmining the interction etween the type of competition nd pricing power, it ws found tht with price competition there is not only greter rnge of pricing power such tht producer surplus increses with demnd uncertinty, ut lso greter rnge in which welfre decreses. Thus, welfre-decresing informtion shring greements my e more likely if the downstrem 20 For dditionl exmples of downstrem firms pying suppliers per unit price, while the supplier pys fixed fee to the firm see Mills (2004). For exmples in the lor mrket see rene nd Dvidson (2006). 21 The exception is if the firms compete in prices nd the uncertinty is regrding costs (ecuse welfre lwys decreses with informtion shring in tht cse).

24 23 firms compete in prices. The reson why there is greter rnge of pricing power such tht producer surplus increses in price competition is ecuse the union s differentil pricing cuses reltively less hrm to the firms in price competition. For exmple, with sustitutes, n increse in own demnd rises the firm s wge, which in price competition leds to the rivl s price incresing (to the firm s enefit), ut in quntity competition this leds to the rivl s output incresing (to the firm s hrm). On the other hnd, informtion shring is more likely to decrese welfre when firms compete in prices ironiclly ecuse there is greter competition etween the firms, which is discussed next. As the products ecome more differentited, regrdless of whether they re sustitutes or complements, informtion shring is more likely to reduce the firms profits nd producer surplus (though the union s surplus lwys increses), which runs counter to the results in the informtion shring literture (Vives 1984, 1990). The reson for this is tht s the products ecome very differentited, ech firm-supplier reltionship essentilly ecomes independent of the other. o, first, ny producer surplus gins from the rivl s rection to the firm s informtion pproches zero. econd, in ech reltionship, producer surplus ecomes convex in the unknown cost or demnd intercept. However, the union s response to this informtion ( higher wge for lower costs), dmpens this effect mking producer surplus less convex in the unknown prmeter nd hence reducing expected producer surplus. For these resons, s the products ecome more differentited, welfre decreses if the firms compete in quntities. Things re not s simple with price competition. Though welfre decreses if the products re ecoming sufficiently differentited, it lso cn decrese if the products re ecoming sufficiently undifferentited; there is non-monotonic reltionship etween product differentition nd welfre with price competition. This is ecuse s the products ecome close sustitutes in price competition, the firms profits go to zero nd so do the gins to them from informtion shring, while the own dmpening effect of the union s pricing remins. n ddition to the effects tht product differentition nd pricing power hve on the outcomes,

25 24 there re some surprising results given previous findings in informtion shring literture regrding privte vlued informtion. First, n increse in producer surplus from n informtion shring greement does not imply tht welfre increses. Tht is, previous work in informtion shring finds tht if producer surplus increses with informtion shring, then welfre increses with oligopolistic firms. For exmple, with unknown costs nd quntity competition, informtion shring increses producer surplus nd welfre oth with (Li 2002), nd without (hpiro 1984) the informtion eing shred with n upstrem firm. However, it ws found here tht with differentil pricing producer surplus cn increse when welfre decreses. A second new result is tht if the union hs sufficient pricing power, then firms never unilterlly shre informtion. n the literture, if firms compete in quntities, or if the firms compete in prices with demnd uncertinty, then in equilirium they would unilterlly shre informtion (e.g., hpiro 1984), even if the upstrem firm otins the informtion (Li 2002). This result is lso surprising in tht it holds for ll the environments exmined demnd nd cost uncertinty; price nd quntity competition while in the informtion shring literture this type of result lmost lwys depends on the environment. For exmple, if shring informtion increses the firms profits in quntity competition, then it will decrese profits in price competition. Finlly, the finding here tht informtion shring reduces welfre when the union sets the wge is likely to e generl ecuse of how the union responds to the informtion: when firms re low cost producers, the union sets higher wge, nd so the more efficient firm produces less nd the less efficient firm responds strtegiclly y producing more. This effect overwhelms ny welfre enefit from the informtion shring etween firms. roniclly, the welfre-reducing informtion shring lso reduces output vriility, sometime policy gol. Tht is, here the reduction in output vriility is linked to the reduction in welfre.

26 25 Appendix A: Price competition with unknown intercept trting with the lst stge, profits for firm j re (A i p i + d p j )(p i w i ). First, when oth firms shre informtion, the equilirium prices re p p = [2(A + w ) + d(a + w )]/Δ = [2(A + w ) + d(a + w )]/Δ where the super nd suscripts follow the previous sections nottion nd Δ = 4 d 2. ustituting these vlues into q i = A i p i + d p j otins output ( q welfre cn e clculted, with the sme nottion s efore, e.g., ) with which profits, producer surplus nd π When neither firm shres informtion equilirium prices re p = [2(A + w ) + d(a e + w )]/2Δ d 2 (A A e )/2Δ, p = [2(A + w ) + d(a e + w )]/2Δ d 2 (A A e )/2Δ, from which, gin, outputs, profits etc. in stge five cn e derived. Finlly, when firm shres, etc. informtion while firm does not yields prices (nd symmetriclly when only firm shres) p = [2(A + w ) + d(a e + w )]/Δ, N p = [2(A + w ) + d(a e + w )]/2Δ d 2 (A A e )/2Δ. As with quntity competition, given some w nd w, in the first stge expected outputs re the sme for ll informtion structures nd so profits, wge ill nd welfre, evluted t the men, re the N sme. Tht is, π (ce) = π (ce) = π (ce) = π (ce), etc. i i i i Moving ck to the fourth stge, when the union is selected to mke the wge offer, the wge it chrges depends on its informtion. f informtion is shred y oth firms, from its mximizing the wge ill, the wges re w = (A + d A )/2(1 d 2 ) w = (A + d A )/2(1 d 2 ).