Information technology, organizational design, and transfer pricing*

Iformato techology, orgazatoal desg, ad trasfer prcg* Shae S Doll The Uversty of Texas at Ast McCombs School of Bsess CBA 4M0 Ast, TX 787-0 USA Igor Vaysma** INSEAD Accotg ad Cotrol Bolevard de Costace, 77305 Fotaeblea Cedex, Frace Agst, 005 Abstract We show how formato techology affects trasfer prcg Wth costraed formato techology, egotated trasfer prcg has a formatoal advatage: maagers agree to prces that approxmate the frm s cost of teral trade more precsely tha cost-based trasfer prces Wth sffcetly rapd offers, ths advatage otweghs opportty costs of maagers bargag tme, ad egotated trasfer prcg geerates hgher profts tha the cost-based method However, as formato techology mproves, the formatoal advatage dmshes; the opportty costs of maagers bargag evetally domate, ad cost-based methods geerate hgher profts Or reslts expla why frms geerally prefer cost-based methods, ad whe egotated methods are preferable Keywords: Cost-based trasfer prcg; Negotated trasfer prcg; Bargag; Decetralzato JEL Classfcato: C7; D8; L3; M4 *We tha Tm Baldes, Robert Göx, Lyda Thoma, Doa We, Jerry Zmmerma, a aoymos referee ad worshop partcpats at INSEAD, Lodo Bsess School, ad the AAA Maagemet Accotg Secto Coferece for helpfl commets ** Correspodg athor: Voce, +33 (0 6469 4399; Fax, +33 (0 64 773;Emal, gorvaysma@seaded

Itrodcto I the absece of compettve marets for terally traded prodcts ad servces, why do some frms base trasfer prces o teral costs ad others allow maagers to egotate prces? Allowg maagers to barga over trasfer prces has several drawbacs: the tme that maagers sped bargag s lost to other prodctve actvtes; f egotatos tae too log, the frm may mss some maret opporttes; ad f hagglg leads to ll-wll betwee maagers, the frm may sffer from sb-optmal decsos ad coflct (see Brcley, et al, 004; Kapla ad Atso, 998; Smos, 000 Faced wth these sses, why do frms ever let maagers barga over trasfer prces? Ad what ecoomc characterstcs predct the preferred prcg method? I ay large frm, local maagers have prvate formato speror owledge of local codtos, bsess processes, ad potetal cash flows Other partes the frm rely o local maagers reports, bt there are two mportat problems wth ths Frst, a local maager may dstort formato; f trthfl reports are desred, top maagemet mst provde approprate cetves Secod, trasferrg local owledge may be costly t may be dffclt or mpossble for the local maager to flly descrbe the precse ls betwee local formato, the mlttde of local decsos, all of the avalable alteratves, ad the potetal cash flows Ad t may be dffclt or mpossble for other partes the frm to qcly derstad ad act po the local maager s reports We show that t s the ablty to commcate owledge to top maagers ad others that s a ey factor determg the preferred trasfer-prcg method Specfcally, the more dffclt t s to trasfer the local owledge of the spplyg dvso, the more attractve s egotated prcg The costs of trasferrg local owledge to top maagers ad others vary wdely across dvsos, across frms, ad over tme A mber of factors flece these costs: the atre ad complexty of local owledge; the cltral, edcatoal, ad o-the-job trag bacgrods of dvsoal ad top maagers; the ecessty for rapd resposes to chages local codtos; the frm s sze; the techology for commcatg local formato; ad the geographc reach of the frm (Brcley, et al, 004; Chrste, et al, 003; Demsetz, 988; Jese ad Meclg, 99 Practtoers ad academcs recogze the mportace of trasfer prcg A srvey reports 73% of maagers th t mportat to prce teral trasfers to maxmze operatg performace (Erst & Yog, 999 Negotated ad cost-based methods are commo practce (Atso, 987; Prce Waterhose, 984; Tag, 993 Hrshlefer (956, Edl ad Rechelste (995, Baldes, et al (999, ad Vaysma (996; 998 aalytcally establsh the cotractg beefts of trasfer prcg varos ecoomc evromets

We se the term formato-techology (IT costrats to descrbe the lmtatos of the frm s formal ad formal formato systems whe trasferrg local dvsoal owledge to top maagers Ths descrbes a cotm: the extreme IT-costraed case, t s possble for the local maager to qcly ad costlessly report o everythg of local ecoomc relevace (top maagers mst stll provde trth-tellg cetves f they desre trthfl reports; at the other extreme, IT costrats are so severe that the local maager caot provde ay relevat reports whatsoever (reportg cetves are the ot a sse Of corse, ether extreme s realstc: all frms rely o dvsoal reports, yet o reportg techology flly commcates everythg abot local codtos I the extreme IT-costraed case, cost-based trasfer prcg wors well Dvsoal maagers are gve cotracts that provde them cetves for trthfl reportg (ths, of corse, costs the frm bt caot be avoded Top maagemet the receves all the relevat formato abot the spplyg dvso, comptes the relevat otlay ad opportty costs of teral trade, ad sets the prce eqal to the total relevat cost The byg dvso s teral-orderg decso s the optmal from the frm s pot of vew; bt sce top maagers cold smply mpose ths teral-orderg decso, t s ot clear why the frm s orgazed to proft ceters the frst place Costraed IT provdes a aswer: f t s ot possble to commcate all the relevat local formato, two proft ceters ad cost-based trasfer prcg garatee speror decsos (Vaysma, 996 Bt, f IT costrats prevet local maagers from flly ad qcly reportg o everythg of relevace to local cash flows, top maagemet mst rely o a cocse bt complete estmate of the spplyg dvso s costs to optmally set the cost-based trasfer prce Eve wth cotractal cetves for trthfl reportg, top maagemet caot get all the relevat formato ecessary to compte the relevat cost of teral trade At best, the cost-based trasfer prce s set to eqal top maagers estmate of the relevat cost (gve ther ecessarly complete formato I Secto 3 of the paper, we show that, sce ths cost estmate s by ecessty sometmes too hgh ad sometmes too low, the byg dvso s teral-orderg decso s sboptmal O the other had, whe dvsoal maagers barga over the trasfer prce (ad ths, effectvely, Low IT costrats characterze a local dvso wth low costs of trasferrg owledge to top maagemet; hgh IT costrats a dvso wth hgh owledge-trasfer costs Jese ad Meclg (99 descrbe ths cotm as geeral vs specfc owledge Demsetz (988 ad Chrste, et al (003 se the terms ospecalzed ad specalzed owledge

over whether to trade terally, top maagemet ca se dvsoal-proft-based compesato to esre that the maagers come to a prce agreemet oly f t s the frm s terest to trasfer terally The teral-trade decso ths corporates the maagers local formato better tha der cost-based prcg Ths s the formatoal advatage of the egotated method We compare ths advatage wth the orgazatoal ad opportty costs the frm faces from maagers bargag 3 To captre these costs, we se a mlt-perod offer-coteroffer bargag model We show that top maagemet ca se compesato schemes ad bargag rles to garatee that dvsoal maagers agree o a trasfer prce qcly Negotated trasfer prcg s the speror to the cost-based method whe offers ad resposes happe rapdly (ths s formalzed Theorems ad 4 We also cosder the mplcatos of mprovemets a frm s owledge-trasfer systems As IT mproves, expected profts crease der both methods Bt they crease faster wth cost-based prcg: IT mprovemets ehace the spplyg maager s ablty to commcate local owledge ad, coseqetly, top maagemet s ablty to set trasfer prces that approxmate the relevat costs of teral trade The formatoal advatage of the egotated method decreases wth IT mprovemets, ad s evetally otweghed by the opportty ad orgazatoal costs of maagers bargag Ths, wth sffcetly costraed IT, the cost-based method geerates hgher profts tha egotated trasfer prcg; we docmet ths Theorem 3 A mportat caveat s that or stdy does ot address two mportat practcal sses Frst, to smplfy the aalyss, we do ot cosder the effect of taxes o trasfer-prcg method choce Icome taxes, tarffs, ad domestc cotet laws flece a frm s trasfer-prce decsos, whle atoal tax laws ad teratoal treates costra the frm s choces 4 Or reslts apply drectly to statos where the tax effects are ot a overrdg cosderato for teral trade, ether becase the trade does ot cross tax 3 Two papers compare egotated wth cost-based prcg schemes wthot explctly cosderg opportty costs of bargag: Baldes, et al (999 stdy the settg wth symmetrc formato, ad Baldes (000 wth asymmetrc formato They represet prce egotatos by a statc srpls-sharg rle ad focs o specfc vestmets ad the hold-p problem as the ey cetve sses der complete cotractg By cotrast, we se dyamc blateral bargag to represet egotatos, allowg s to focs o bargag tme as a mportat orgazatoal varable ad to trade off the opportty costs of the tme spet bargag agast the formatoal advatage of the egotated method 4 The taxato lteratre stdes several related sses: ( the mpact of tax rates ad reglatos o prodcto, locato, ad prcg decsos (Copthore, 97; Halper ad Srdh, 987; Harrs ad Sasg, 998; Horst, 97; Samelso, 98; ( cetves to mae vestmets complete-cotract settgs (Sasg, 999; Smth, 00; ( comptatos of optmal trasfer prces as fctos of dfferet tax rates (Baldes, et al, 003; Narayaa ad Smth, 000 I cotrast, we focs o the cetve, coordato, ad performace-evalato objectves of trasfer prces 3

jrsdctos, or becase the frm matas a system of trasfer prces for performace evalato separately from tax trasfer prces (see Erst & Yog, 999; Sprgsteel, 999 Where tax effects are mportat, or model ca be exteded to clde these effects, alog the les of Baldes et al (003 Secod, whe a frm s mplemetg a cost-based prcg system, dvsoal maagers may exped tme ad effort attemptg to flece the system s desg Bt, as s typcal stadard models of mechasm desg wth prvate formato, t s optmal for the top maagemet to dsallow ay flece actvtes by proposg the cost-based system to the maagers a tae-t-or-leave-t fasho Or aalyss of optmal cotractg der cost-based prcg ths does ot admt the possblty that there are opportty costs of maageral tme from system-desg-stage flece actvtes The model Basc model wth costraed formato techology The frm cossts of headqarters (HQ ad two dvsos: prodcto ad maretg HQ represets the frm s rs-etral owers Maager s prodcto dvso mafactres a termedate prodct that serves as the pt to Maager s maretg dvso; the prodct s ot avalable ay otsde maret The maretg dvso fshes ad sells the prodct, earg revees for the frm (et of ay maretg dvso costs For smplcty, the qatty q of the termedate prodct s ether zero or oe the relatoshp betwee dvsos s oe of procremet 5 Each rs-etral maager has a wealth of local owledge relevat for the decsos that affect dvsoal cash flows Mch of each maager s relevat local owledge s prvate 6 We se a stadard techqe for represetg formatoal asymmetry frms: we codese all of maager s prvate owledge to a sgle prvate-formato varable, for { }, The set of possble realzatos of 5 We se the procremet scearo, wth q eqal to zero or oe, for smplcty The model ca be exteded to corporate mltple qatty levels, wth smlar reslts abot preferred trasfer-prcg methods The ey dffereces are: ( the optmal cost-based trasfer prce s a fcto of qatty (t s stll a margal-cost pls a marp prce; ad ( the bargag procedre der egotated prcg has two stages: the frm reqres the maagers to frst barga over the qatty, ad the to barga over the prce (as sggested by Brcley, et al, 004 Eve the procremet settg, less dvsoal maagers ca commcate all of ther local owledge to the frm s HQ freely ad stataeosly, dvsoal strctre ad delegato of decsos to maagers provde the frm hgher profts tha a sgle HQ-maaged resposblty ceter 6 Local decsos clde schedlg, procremet, qalty cotrol, hma-resorce maagemet, advertsg, ad dstrbto Some examples of relevat local owledge, for the prodcto dvso, clde pt prces; wages; the tradeoffs heret prodct desg; owledge of crret ad replacemet prodcto techologes; employee-satsfacto levels; owledge of prodct ad process egeerg; qalty ad relablty of local spplers; ad alteratve ses of varos costraed resorces For the maretg dvso, examples clde owledge of varos marets, chaels, ad cstomers; crret demad codtos; compettors prodcts ad prces; ad the compettve dyamcs of the prodct maret 4

ths maager s prvate formato s Θ = [, ], wth lower realzatos of prvate formato (eg low prodct-defect rates the prodcto dvso represetg good ews abot dvsoal evromet The prvate-formato varables are depedet The probablty dstrbto fcto of F( s commo owledge ad has a cotos desty fcto f ( Aalyses of cotractg ad orgazatoal desg wth prvate formato rely o a stadard assmpto abot the dstrbto of prvate formato: the rs rato F ( / f ( s creasg Ths codto holds for most stadard dstrbto fctos (sch as the form, ormal, ch-sqared, ad expoetal It garatees that the effcet dvsoal operatos ( ad (3 are mootoe the maager s prvate formato; ths, tr, allows the replacemet of the global cetve costrats by local cetve costrats the HQ s proft maxmzato program After learg prvate formato, each dvsoal maager maes decsos ad taes actos affectg the frm s cash flows May of these decsos are potetal sorces of coflct wth HQ (two examples are: a maager s choce of effort, valable to the frm bt costly to the maager; ad cosmpto of perqstes, valed by a maager bt costly to the frm It s stadard to covert cetve problems wth observable actos ad prvate formato to ecoomcally eqvalet pre-prvateformato represetatos by elmatg the acto varables (see footote 7 below for a llstrato of ths coverso; Dems ad Sappgto, 984 ad Gesere ad Laffot, 984 docmet the eqvalece of the two represetatos Wth the pre-prvate-formato represetato, the prodctve parameter z Z + represets maager s operatg decsos that are valable to the frm bt costly to the maager, as follows: the frm s C q z s strctly decreasg ; cost (, persoal cost fcto (, z revee (, R qz s strctly creasg z ; bt maager s V z s strctly creasg z Prodctve parameters ths captre the effects of both prvate formato ad observable actos o the frm s cash flows 7 For smplcty, we assme that 7 Ths pre-prvate-formato model wth persoal costs as fctos of prvate formato ad prodctve parameters s a coveet represetato of a ecoomc settg where maagers have prvate formato ad tae observable actos (ether mst spply persoally costly effort or cosme slac To llstrate, sppose the prodcto maager ca redce the prodcto dvso s cost wth observable effort a at a persoal cost a If the prodcto dvso s cost a fcto of prvate formato ad effort eqals [ / a], ths prvate-formato-ad-effort stato ca be coverted to the preprvate-formato oe of ths paper by elmatg the effort varable as follows Set z = [ / a ] ad treat z as the varable of aalyss, wth C(, z = [ z] ad V [ ] z, = / z The two represetatos are ecoomcally eqvalet; the pre-prvateformato oe s more coveet to aalyze 5

the persoal-cost fctos are mltplcatvely separable strctly creasg dfferetable fctos of the prodctve parameter ad prvate formato (ths does ot affect the ma reslts: ( ( { } V z, = b z v for, ( We se x to represet maager s compesato Each maager s free to qt after learg prvate formato; compesato mst the be hgh eogh to assre that the maager s expected tlty exceeds a reservato level, ormalzed to zero We mpose eogh strctre o the cost ad revee fctos to assre that the frm s problem has a well-defed solto 8 We focs o the cremetal mpact of teral trade ad ths, ormalze to zero dvsoal cash flows whe o teral trade taes place: C( z R( z 0, = 0, = 0 for all z, z The cost fcto captres all costs cremetal wth respect to the trasfer decso The sse of fll-cost verss margal-cost prcg ths does ot arse or model fll costs ad margal costs are the same So far, ths stadard asymmetrc-formato model of the frm, there are o costrats o: ( the maagers abltes to commcate all local owledge to HQ costlessly ad stataeosly, ad ( HQ s ablty to completely derstad ad act po ths owledge costlessly ad stataeosly The Revelato Prcple the mples that there s o vale to decetralzato, dvsoal strctre, trasfer prcg, or dvsoal performace evalato HQ maxmzes the vale of the frm by asg dvsoal maagers for ther local formato, provdg them cotractal cetves to reveal that formato trthflly, ad the mag all the decsos abot the frm s operatos To covce each maager to reveal prvate formato trthflly, HQ mst pay a premm above the maager s reservato wage Ths compesato premm s ow as formatoal ret; t redces the frm s profts relatve to the frst-best settg wthot prvate formato I the secod-best settg wth prvate formato bt wthot IT costrats, HQ s expected paymet E Θ b z h, where F( h v + v ( ; ote that ths exceeds f( E Θ b z v 9 We se the term pre-trasfer cost to to each maager eqals the maager s expected persoal cost 8 For ths, t s sffcet that ( C( z V ( z 9 [, +, ] s strctly covex ; [ R, z V z, ] s strctly cocave z ES [] s the expectatos operator over the set S For detals o comptg formatoal rets ad solvg stadard prvateformato cotractg problems, see Fdeberg ad Trole (99 Note that Fdeberg ad Trole (99, amog others, refer to [ b( z h( ] (captrg the maager s persoal cost b( z v( ad formatoal ret as vrtal cost We refer to ths as maager s compesato, to clearly dstgsh ths term from the prodcto dvso s costs z ad ( 6

refer to the frm s relevat costs the prodcto dvso: the sm of prodcto costs (, prodcto maager s compesato ( dfferece betwee the maretg dvso s revees (, C z ad the b z h We se post-trasfer et revees to refer to the R z ad the maretg maager s compesato b z h To maxmze the vale of the frm, HQ maxmzes the dfferece betwee the post-trasfer et revees ad the pre-trasfer prodcto costs Whe teral trade taes place, effcet prodctodvso operatos z( mmze the pre-trasfer cost; ths optmally trades off cost redctos dvsoal cost C(, z ad creases reqred compesato b ( z h ( ( + ( z Z : z arg m C, z b z h ( Lewse, from the frm s perspectve, effcet operatos z( for the maretg dvso maxmze the post-trasfer et revee; ths optmally trades off creases revees (, creases reqred compesato b( z h( : ( ( z Z R z ad z arg max R, z b z h (3 The frm s gas from teral trade whe dvsos operate effcetly are ( ( ( R, z b z h C, z + b z h (4 If the gas (4 are postve, HQ madates teral trade Coversely, whe the gas are egatve, teral trade redces the frm s profts, ad HQ prohbts t Fgre shows a typcal effcet pre-trasfer total cost fcto The effcet et revee fcto s costat wth respect to chages the prodcto maager s prvate formato The gas from trade are ths strctly decreasg the maager s prvate formato The Frm s Cost ad Revee $ 0 ˆ Cost C (, z ( + b z h Revee R, z ˆ b z ˆ h ˆ Gas from teral trade Prodcto Maager s Prvate Iformato ( ( Fgre Effcet pre-trasfer cost of the prodcto dvso ad the cremetal mpact of teral trade for ay vale ˆ of the maretg maager s prvate formato The frm beefts from teral trade f ad oly f ˆ Fgre shows that the maagers prvate-formato spaces are parttoed to two regos: 7

teral trade whe prvate-formato realzatos are good eogh to yeld o-egatve gas from trade, ad o teral trade otherwse We assme that the teral-trade decso s o-trval: the probablty that the frm beefts from teral trade s postve bt less tha Maretg Maager s Prvate Iformato SB q = 0 SB q = SB Fgre Optmal teral-trade decso rle (, ˆ, ˆ breaeve pot ( Prodcto Maager s Prvate Iformato ˆ q the absece of ay IT costrats ad trasfer prces The from Fgre s o the bodary betwee the trade ad the o-trade regos Iformato techology costrats ad proft-sharg cotracts For the remader of the paper, we dscard the assmpto that the maagers ca freely ad stataeosly trasfer all local formato to HQ Each maager s owledge s rch, mltdmesoal, ad specfc to local operatos Trasferrg some local owledge to HQ s almost free (examples are pt prces ad qattes Other owledge s specfc ad costly to trasfer (examples clde techologcal expertse, prodct-desg tradeoffs, prodct ad process egeerg, maret codtos, compettors strateges, cstomer relatoshps, ad alteratve ses of costraed resorces To develop trasparet tto ad descrbe the mplcatos of IT costrats for trasfer prcg a tractable settg, we tally lmt oly the prodcto maager s ablty to commcate wth HQ ( Secto 6 we show that the ma reslts hold whe ether maager ca flly commcate all local owledge to HQ It s certaly too costly for the prodcto maager to flly expla to HQ the precse ls betwee local owledge, the mlttde of decsos the maager maes, ad the resltat dvsoal cash flows Istead, the maager provdes HQ wth a report, sch as a dvsoal bdget, whch cldes aggregated represetatos The facal lagage of bdgets captres the complexty of the prodcto maager s local owledge cocsely bt ot completely Frther, there s a delay betwee the tme the maager lears ew formato ad the tme HQ ca teralze t ad act po t HQ ca the ehace the vale of the frm by delegatg decso rghts to dvsoal maagers ad compesatg them based o dvsoal profts Whle we do ot explctly model commcato ad processg costs, the techqe trodced by ˆ 8

Melmad et al (99 allows s to represet them Formally, the maager s reports to HQ ca tae o at most dstct vales The restrcto does ot specfy how the maager commcates wth HQ, or what the maager reports It smply forces the sze of the reportg set M to be smaller tha the sze of the maager s local-formato set Θ ; ths maes t mpossble for the maager to expla everythg of local relevace to HQ Bt the followg mportat reslt allows s to relate the reportg restrcto to the commo practce of dvsoal bdgetg (the reslt also allows s to arrow the set of maageralcompesato cotracts HQ eeds to cosder The techcal reslt s that, wth the reportg restrcto, t s optmal for HQ to ( partto the prodcto maager s prvate-formato space to tervals; ad ( offer a cotract that covces the maager to trthflly report whch of the tervals cotas the maager s prvate formato (see Step of the proof of Theorem 0 We mber these tervals order of creasg, se Θ to refer to the th terval, ad se to refer to the pper bod of the th terval, for { } set s the M = { Θ Θ Θ},, The prodcto maager s reportg,,, ; HQ reqests that the maager report the terval Θ that cotas the local formato The maager s report s strategc the maager maxmzes expected tlty ad reports trthflly oly f gve approprate cotractal cetves Bt, sce t s optmal for HQ to se cotracts that gve cetves for trthfl reportg, for the remader of the paper we focs o these trth-dcg cotracts To llstrate the formal techqe ad the l to dvsoal bdgetg, cosder a extreme case of IT costrats: = The prodcto maager s prvate formato space s dvded to tervals: dvsoal codtos are favorable whe the maager s prvate formato s the terval favorable whe prvate formato s Θ Θ : Θ Θ ; The prodcto maager s reports have two ecoomcally eqvalet terpretatos: ( reports abot local prvate formato (eg favorable or favorable, ad ( bdgets, or cost estmates (eg low or hgh For example, whe the maager reports that local codtos are favorable, HQ caot precsely 0 The tto s smlar to (bt, becase of IT costrats, ot detcal to the Revelato Prcple Ay cotractg otcome where the maager s reportg strategy s to dstort hs formato ca be replcated by a cotract where HQ commts to apply the same dstorto to the maager s report I the replcatg cotract, the maager ths has the cetve to report trthflly Note that sce we do ot lmt the maretg maager s ablty to commcate wth HQ tl Secto 6, the Revelato Prcple mples that ths maager s reportg set M s the same as the prvate-formato set Θ 9

forecast ether how the maager wll operate the dvso or what the pre-trasfer costs wll be Bt the favorable report correspods to a qe cost bdget Cosder ay cotract that pays the prodcto α of dvsoal proft, wth dvsoal proft compted by T C(, z maager a share some teral trasfer prce ms dvsoal cash flows (we se proft-sharg cotracts the aalyss below The maager wll operate the dvso to maxmze the dfferece betwee dvsoal-proft-based compesato ad persoal cost; from the maager s pot of vew, optmal dvsoal operatos z wll deped o local α z ( α z α T C z b z v formato ad the maager s proft share :, argmax, Lacg fll owledge abot the dvso, HQ caot predct exactly what the dvsoal costs (, (, wll be Bt HQ ca compte ( the expected dvsoal cost E C z ( α C z α the prodcto maager s expected dvsoal-proft-based compesato,, ; Θ ad ( The maager s report that local codtos are favorable s ths eqvalet to the maager bdgetg ( dvsoal costs at E C z ( α,, HQ ca reqest that the maager provde ether ( drect reports abot Θ prvate formato, or ( bdgets; the two reportg systems are detcal For exposto, we wll call the prodcto maager s reports bdgets, wth the derstadg that a bdget report Θ refers to the bdget ( ( ( Θ E C, z α, It s sefl for the aalyss below to defe the typcal prvate-formato Θ realzato the terval Θ, whch ca be derved from h( = E h( Θ I smmary, the prodcto maager seds HQ bdgets (e cost estmates, bt these bdgets caot flly descrbe the prodcto dvso s ecoomc evromet HQ ca ether perfectly predct what the prodcto maager s operatg decsos wll be or exactly what prodcto costs wll be Sce t s optmal for HQ to provde cetves for trthfl bdgetg, HQ ca forecast that prodcto costs wll be a certa rage, bt there wll be varaces from the bdget Wth IT costrats o the prodcto sde, there s a beeft to delegatg local decsos to dvsoal maagers ad gdg teral trade va a system of teral prces ad dvsoal-proft-based compesato We ow tr to the aalyss of cost-based ad the egotated trasfer prcg Ths techqe also allows s to captre varatos IT costrats As gets larger, HQ s derstadg of the prodcto dvso becomes more accrate; expected varaces betwee the maager s bdget ad realzed costs decrease We se ths Secto 5 to aalyze the mplcatos of chages IT costrats for the frm s trasfer-prcg method choces 0

3 Cost-based trasfer prcg wth formato techology costrats Wth cost-based prcg, HQ sets the trasfer prce sg the prodcto maager s cost bdget If the maagers trade at some prce T ad dvsoal cash flows are C(, z ad (, T C z for prodcto ad (, R, z, dvsoal profts eqal R z T for maretg Each maager s compesato cossts of a fxed salary ad a share of dvsoal proft HQ ses bdget-based compesato plas: maager s bdget m determes that maager s fxed salary ( m CB maager decdes whether or ot to place a order; we se q β ad the proft share α ( m The maretg to represet ths decso It s optmal for HQ to mae tae-t-or-leave-t cotractal offers to each dvsoal maager; the maagers are ths ot allowed to attempt to egotate cotractal terms or to otherwse attempt to flece the desg of the cost-based trasfer-prcg system The seqece of evets s the tmele below HQ specfes: Message spaces; Cotract terms; Trasfer prcg schedle The bdgets determe: Specfc cotract terms; Cost-based trasfer prce HQ aoces: bdgets, prce Orders Each maager operates ow dvso to maxmze tlty After prodcto ad sale, each maager receves fxed salary ad dvsoalproft-based bos Maretg Maager Does Not Order Each maager: Lears prvate formato; Sbmts bdget to HQ Iteral trade teractos are over Each maager receves fxed salary Whe desgg the cost-based prcg system, HQ has three cotractg varables dvsoal-proft shares, fxed salares, ad the trasfer prce to tacle three related cetve qestos: Wll the maagers trthflly bdget costs ad revees? Wll the maagers trade terally f ad oly f t s the frm s terest? 3 Whe the maagers trade terally, wll they operate ther dvsos optmally? We aswer these qestos sg bacward dcto, startg at the rght-had-sde of the tmele Frst, we exame the maagers operatg decsos followg maretg s teral order (ad how HQ fleces these decsos Armed wth predctos abot operatg decsos, we ext cosder the maretg maager s teral-orderg decso (ad how HQ fleces ths decso Last, we descrbe how HQ covces the maagers to prodce trthfl bdgets Note the followg ey gredets of or model of cost-based trasfer prcg: the trasfer prce s based solely o the report of the prodcto maager; the prodcto maager ca ot refse to fll a order placed by maretg; ad each maager s compesato cotract s depedet of the other maager s report We commet o these modelg choces below, the dscsso followg Theorem

Dvsoal operatos If the maretg maager orders the prodct, each maager operates hs dvso to maxmze persoal tlty, ad, followg prodcto ad sale, receves both a fxed salary ad a share of hs CB dvso s proft We se (, z m to represet maager s dvsoal operatg decso (to mae the decso, each maager trades off creases persoal costs ad compesato 3 By ow, each maager has set dvsoal bdgets to HQ, ad HQ has aoced the cost-bdget-based trasfer prce T Cojectrg for the momet that HQ ca provde cetves for trthfl reportg, the maretg maager s operatg decso maxmzes the dfferece betwee dvsoal-proft-based compesato α ( ( R(, z T ad persoal cost b ( z v ( : ( = α ( ( z, argmax R, z b z v (5 CB z Z The prodcto maager s operatg decso maxmzes the dfferece betwee proft-sharg paymet α( Θ ( T C(, z ad persoal cost b ( z v ( : ( Θ = α ( Θ + ( z, argm C, z b z v CB z Z (6 Dvsoal-proft shares are HQ s oly meas of gdg the maagers dvsoal operatg decsos; the cost-based trasfer prce does ot affect them, becase the prce s set before the maagers mae these decsos Frther, dvsoal operatos do ot deped o how the frm prces trasfers: based o cost or o maagers egotatos Dfferet prces, ad dfferet prcg methods, determe oly whether there s teral trade Ths smplfes the later comparso of the two methods Dvsoal operatg decsos z (, CB Θ ad (, CB z that are optmal der the cost-based method are avalable wth egotated prcg HQ smply ses the same dvsoal-proft shares The proft shares that covce the maagers to operate ther dvsos effcetly are 4 3 After HQ ad maager agree o the maager s compesato cotract α (, β, the ey varables that flece the maager s operatg decsos are ( local formato ad ( the maager s report m To smplfy the otato, we ca CB the wrte the maager s operatg decso z ( m, as jst a fcto of these two varables Below, we frther smplfy the otato: sce t s optmal for HQ to provde the maagers cotractal cetves for trthfl reportg, der effcet costbased trasfer prcg the maretg maager reports trthflly, e m = 4 The optmal proft shares are ot cetral to the aalyss below; we state them here to descrbe the optmal trasfer prce For the maretg maager, comparso of the operatg decso (5 wth the secod-best decso (3 pots to the optmal proft share (7; the prodcto maager s proft share taes a smlar form, bt sbject to IT costrats The dervatos of the optmal operatg decsos (ad ths the optmal proft shares are steps ad 3 of the proof of Theorem Note that each maager s proft share ca be wrtte as the rato of persoal cost ( ( strctly postve terms Accordgly, the proft shares cost, the proft shares are the terval (0,] b z v ad expected compesato b( z h(, whch are both α are strctly postve I fact, becase compesato exceeds persoal

( ( ( ( v v α Θ = ad α = (7 h h Iteral trade Havg set the proft shares to garatee effcet dvsoal operatos, HQ gdes teral trade sg the cost-based trasfer prce 5 The maretg maager orders the prodct f ad oly f, gve the trasfer prce, hs dvsoal proft share exceeds hs persoal cost: CB CB ( Θ ( α R, z, T b z, v Dvdg both sdes of ths eqalty by the proft-sharg parameter α( from (7 ad rearragg, from the maretg maager s pot of vew, teral trade s attractve f ad oly f ( R, z, b z, h T Θ (8 CB CB The frm, o the other had, beefts from teral trade as log as the maretg dvso s posttrasfer et revees (wth effcet maretg operatos exceed the prodcto dvso s pre-trasfer costs (wth effcet prodcto operatos The left-had-sde of the maretg maager s teral-order decso rle (8 eqals the maretg dvso s post-trasfer et revees Ca HQ se the cost-based trasfer prce o the rght-had-sde of (8 to covce the maager to teralze the prodcto dvso s pre-trasfer costs? Becase of IT costrats, the aswer s o the prodcto maager s bdget caot reveal everythg abot the prodcto dvso; ad lacg complete owledge abot the prodcto dvso, HQ caot desg a cost-based prcg rle that commcates the relevat otlay ad opportty costs of teral trade to the maretg maager At best, HQ ses the cost-based trasfer prce to commcate HQ s estmate of the total relevat cost, gve HQ s ecessarly complete formato Ths estmate eqals the prodcto maager s bdget, CB E (, C z Θ Θ maager s expected compesato: CB CB v( T( Θ = E C(, z (, b( z (, h( Θ Θ + Θ v( pls a mar-p for the The, sg (8, the maretg maager orders f ad oly f there are expected gas from trade the reportg terval Θ The formal reslt s Theorem below; we llstrate t Fgres 3 ad 4 for extreme (9 5 A commo crtcsm of cost-based trasfer prces s that they allow prodcers to export cost effceces Here, however, the proft shares prevet cost effceces from beg passed o to maretg becase ( the proft shares dce effcet dvsoal operatos, ad ( the trasfer prce s based o a cost bdget, wth ay effceces bore by prodcto (althogh or oeperod model does ot address the possblty of prodcto overestmatg the crret perod s bdget to pad ftre bdgets 3

( = IT costrats Here the prodcto maager s bdget ca tae o oly two vales: low or hgh The trasfer prce s based o ths bdget Ths, HQ ca set at most two dfferet trasfer prces: oe whe the maager s local formato s favorable ( Θ, ad a lower prce whe the formato s favorable ( Θ Ths trggers two types of effceces for the frm: the o-trade effcecy whe the maretg maager does ot order, eve thogh the frm wold beeft from teral trade; ad the trade effcecy whe the maretg maager does order, eve thogh teral trade destroys profts We llstrate the o-trade effcecy Fgre 3 for a gve vale of the maretg maager s prvate formato The frm beefts from teral trade as log as the prodcto maager s local formato s below the breaeve vale ˆ ; bt sce the sgle trasfer prce the reportg terval Θ s hgher tha the post-trasfer revee (left-had sde of eqalty (8, the maretg maager does ot order whe the prodcto maager s prvate formato s aywhere Θ The shaded area Fgre 3 shows the extet of the frm s loss; Fgre 4, the shaded tragles betwee the cost-based tradg bodary ad the gasfrom-trade bodary the maretg maager does ot order eve thogh the frm wold beeft Coversely, for a sbset of prvate-formato realzatos the maretg maager orders the prodct eve thogh teral trade redces the frm s profts Ths taes place whe the post-trasfer et revees are greater the the trasfer prce bt less tha the prodcto dvso s pre-trasfer cost The trade effceces are the shaded tragles betwee the two bodares Fgre 4 $ Gas frm Iteralzed gas maretg Gas From Iteral Trade 0 ˆ Θ Θ Prodcto Maager s Prvate Iformato Fgre 3 Cost-based trasfer prcg ad IT costrats for a fxed vale ˆ of the maretg maager s formato The frm beefts from teral trade as log as ˆ, bt maretg does ot order the prodct whe > 4

Maretg Maager s Prvate Iformato No-trade effceces ˆ CB q = CB q = 0 Trade effceces ˆ Prodcto Maager s Prvate Iformato CB Fgre 4 The optmal teral-trade decso rle q ( wth cost-based trasfer prcg ad IT costrats; the maagers trade the shaded rego The dowward slopg step le s the bodary betwee the regos where the frm s gas from teral trade are postve (below the le ad egatve (above the le Trthfl bdgetg HQ ses the maagers proft shares to garatee effcet dvsoal operatos ad the cost-based trasfer prce to maage teral trade That leaves oe cotractg varable for each maager the fxed salary to covce the maager to trthflly bdget dvsoal cash flows Ths s eogh HQ sets each fxed salary so that the maager faces a forecastg trade-off: a less ambtos bdget allows the maager to exert less effort (or to cosme slac, at the expese of lower total compesato; a more ambtos bdget reqres harder wor, at a hgher total compesato It s the possble to jdcosly set the fxed-salary compoet of compesato to garatee that each maager, whe mag ths trade-off, sses a based bdget 6 We formalze these reslts Theorem (see Appedx B for all proofs Theorem Uder cost-based trasfer prcg, the frm maxmzes ts expected proft wth the tae-t or leave-t offer of the trasfer-prcg rle (9 ad dvsoal proft-sharg cotracts (7 The maagers operate ther dvsos effcetly The maretg maager orders the termedate prodct f ad oly f post-trasfer et revees (, CB CB R z (, b( z (, h( exceed the trasfer prce (9 At ths pot, three ey modelg gredets leadg to Theorem deserve addtoal atteto: the trasfer prce s based solely o the prodcto maager s report; each maager s compesato cotract s depedet of the other maager s report; ad the prodcto maager caot refse to fll a order The frst gredet the trasfer prce s a fcto oly of the prodcto maager s report reflects that a cost-based trasfer prce s typcally based o the actal or estmated costs crred by the 6 Trth-dcg bdgets allow s to compte the pper bod o the frm s proft der cost-based prcg (Go, 979 ad Krby, et al, 99 provde examples of cetves eeded to elct trthfl forecasts I practce, trth-dcg bdgetg systems are rare, for several reasos Frst, whe ftre targets are adjsted based o crret forecasts ad performace, maagers have cetves to redce crret performace (ths s ow as the ratchet effect Secod, the vast majorty of frms se bdgets both to commcate local owledge ad to evalate performace; practcal trade-offs betwee the two objectves may ecesstate allowg local maagers some bdgetary slac Fally, mplemetg trth-dcg systems may be too expesve 5

frm p to the pot of teral trasfer (we dscss the coseqeces of settg the trasfer prce based o both maagers messages below, the last paragraph of ths secto I or model, the prodcto maager s report commcates the cost bdget, ad the maretg maager taes the bdget-based prce as a gve whe mag the teral-orderg decso Wth ths represetato of cost-based prcg, the secod ey modelg gredet dvsoal proft sharg s optmal, becase the cetve problem that HQ faces ca be separated to three objectves: ( gde operatos each dvso toward effcet oes; ( maage teral trade gve effcet dvsoal operatos; ad ( garatee trthfl reportg HQ ses dvsoal proft shares to acheve (, the cost-based trasfer prce to acheve (, ad the fxed-salary compesato to acheve ( Nether allowg oe maager s compesato to deped o the other maager s report or cldg the frm s proft compesato plas affects the reslts Wth cost-based trasfer prcg, allowg the prodcto maager the rght to refse maretg s order s geerally detrmetal Gve that rght ad the proft shares (7 eeded for optmal dvsoal operatos, the prodcto maager wll reject orders wheever the maager s pre-trasfer cost exceeds the trasfer prce, o matter how postve the maretg maager s formato Ths wll elmate the trade effcecy of cost-based prcg bt create addtoal losses (sg the = example of Fgre 4, there wll be o teral trade the regos mmedately below each trade effcecy tragle Ths cold be beefcal for the frm whe the rage of maretg s post-trasfer et revees s arrow 7 The o-trade effceces, however, wold stll rema ad, wth the foresght of Theorems ad 4, or ma reslts rag the two prcg methods wold be chaged As we ote below at the begg of Secto 6, less the maretg maager s ablty to commcate s also restrcted, the frm s profts are the hghest der a revee-based trasfer-prcg system where HQ: ( sets the trasfer prce based o the maretg maager s report, ad ( allows the prodcto maager to psh the prodct to the maretg dvso Ths hgher level of profts ca also be attaed wth the maretg maager placg the order, the trasfer prce set by HQ based o both maagers reports, ad the prodcto maager havg the rght to refse ay order However, whe ether maager ca flly commcate all local owledge to HQ, egotated trasfer prcg s speror to both cost-based ad revee-based prcg methods (see Secto 6 below 7 To see ths, ote that f the maretg maager s prvate formato set s a sgleto, gvg the prodcto maager the rght of refsal elmates the trade effcecy wthot creatg addtoal losses (bt the o-trade effcecy stll remas 6

4 Negotated trasfer prcg wth formato techology costrats Wth egotated prcg, dvsoal maagers barga over whether there s teral trade ad, f so, at what prce Compared wth cost-based prcg, ths method offers the frm a mber of beefts: ( the frm s cetral maagemet does ot have to be volved settg the prce, allowg dvsoal maagers to operate der greater atoomy (Vaysma, 998; ( the maagers may better explot specfc owledge abot local opporttes, whch HQ may otherwse be able to access (Kapla ad Atso, 998; ad ( the agreed trasfer prce may better approxmate the relevat cost of the teral prodct (Brcley, et al, 004 However, bargag s tme-cosmg ad ca lead to coflct ad ll-wll (Brcley, et al, 004; Kapla ad Atso, 998; Smos, 000 The tme spet egotatg prces or dealg wth orgazatoal coflct s lost to other vale-geeratg actvtes The frm ths crs opportty ad orgazatoal costs creasg bargag delays We formally represet maageral egotatos ad captre these costs sg the followg mlt-stage bargag strctre Oe of the maagers maes a prce offer at the begg of a bargag tme perod {,, }, ad the other maager accepts or rejects ths offer at the ed of the tme perod The legth of a tme perod (ths the legth of tme betwee offers s > 0 The tme the maagers sped bargag s ot spet o other vale-geeratg actvtes; there are ths opportty costs for the frm ad for the maagers Prce bargag for oe perod dsplaces the ext-best actvty If each maager has may possble vale-geeratg actvtes, t s the atral to captre these opportty costs wth a per-perod dscot factor δ ( 0, (decreasg, the sprt of opportty-cost-of-captal techqes 8 We ow aswer the followg ey qestos: How shold the top maagemet set p the egotated prcg system? What prces do maagers reach ther egotatos? Do the prces approxmate the relevat costs of teral trade better or worse tha the dctated prce der the cost-based method? 3 How log wll maageral egotatos geerally last? How ca HQ ecorage dvsoal maagers to reach agreemet qcly (ad ths to mmze the bargag-tme dsadvatages? 4 Whe ca we ra the two trasfer-prcg methods? 8 All reslts are smlar as log as there are some opportty ad orgazatoal bargag costs The dscot factor represetato has a secod atral ecoomc terpretato: there s some postve probablty r that the maagers opportty to geerate gas dsappears whe they cote bargag for aother perod (becase of compettor resposes, maret chages, a maager s expected separato from the frm, or radom factors Or aalyss captres ths settg wth δ = [ r] 7

There are two mportat desg sses for HQ to resolve whe settg p the egotated prcg system: ( whch bargag procedre shold the maagers se; ad ( how to compesate the maagers Itally, we cosder the bargag procedre where the prodcto maager maes all prce offers, ad the maretg maager accepts or rejects them We commet o the alteratve procedre, wth the maretg maager mag offers, the paragraph followg Theorem ad se the alteratve procedre Secto 6 The secod desg sse maageral compesato s sgfcat for two reasos Frst, as der costbased prcg, dvsoal proft shares drectly affect local decsos Secod, compesato cotracts flece the rage of trasfer prces acceptable to each maager As der cost-based trasfer prcg, HQ ses bdgetbased compesato plas: HQ specfes these compesato plas; reqests a bdget from each maager; ad each maager s bdget determes that maager s fxed salary ad proft share To gde the maagers trasfer-prce bargag, HQ maes the bdgets avalable to both maagers 9 The precse seqece of evets s depcted the followg tmele ad descrbed frther below HQ specfes: The bdgets Message determe specfc spaces; cotract terms; Cotract terms; HQ aoces the Bargag rles bdgets Each maager: Lears prvate formato; Sbmts bdget to HQ Prodcto Maager Offers NO TRADE Rejects: Negotatos Cote Offers PRICE Maretg Maager Maretg Maager Rejects: Negotatos Cote Accepts Accepts Each maager operates ow dvso to maxmze tlty Iteral trade teractos are over Each maager receves fxed salary Each maager receves fxed salary ad dvsoal-proft-based bos Not depcted the tmele s HQ s threat to tervee f the maagers fal to reach agreemet by some tme chose to mae rresolvable dsptes attractve The maagers, at tme perods {,,, }, smltaeosly egotate the prce ad whether or ot the prodct s prodced ad trasferred The prodcto maager ether ( offers a trasfer prce, or ( proposes that teral trade ot tae place The maretg maager accepts or rejects the offer If the maagers agree ot to egage NEG teral trade (we se q ( = 0 to represet ths, each maager s pad a fxed salary If the maagers agree to prodce ad trasfer perod at trasfer prce p, maager operates hs ow dvso; we se NEG NEG q ( = to represet the maager s agreemet to trade, ad (, dvsoal operatos z m to represet maager 's 9 Wthot bdget-based compesato, egotated trasfer prcg performs poorly compared wth the optmal cost-based prcg of Secto 3: dvsoal decsos are strctly worse, ad maageral bargag leads to feror teral-trade decsos 8

We aalyze perfect Bayesa eqlbra of maageral teractos A formal defto ad addtoal otato descrbg maagers actos, strateges ad belefs are Appedx A As der cost-based prcg, HQ ses each maager s fxed-salary compesato compoet to provde cetves for trthfl reportg (ote that here dcg trth-tellg may ot be wthot loss of geeralty, becase the prodcto maager caot commt to how he wll se the maretg maager s message; however, wth the foresght of Theorems ad 4, trth-tellg cotracts are sffcet for the frm to ejoy the advatages of egotated prcg Or dscsso below reles o HQ s ablty to elct accrate reports Whe maagers egotate the trasfer prce, the frm ad the maagers cr costs becase of bargag tme ad teral coflcts Why the shold HQ ever se egotated trasfer prces for teral trade? Effcecy losses der cost-based trasfer prcg Fgres 3 ad 4 sggest a possblty: becase of IT costrats, HQ mposes a sgle trasfer prce that apples whe the prodcto maager s local formato s, for example, favorable (e Θ ; the trasfer prce caot be talored to jst how favorable the local formato s The cost-based trasfer prce s the HQ s expectato of the pre-trasfer cost cosstet wth a favorable bdget; the prce caot flly commcate the prodcto dvso s local owledge ad the relevat otlay ad opportty costs of teral trade Bt wth egotated prcg the prodcto maager, who derstads the local owledge, maes the prce offers; HQ provdes cetves to covce hm to se ths owledge the frm s terest to mae prce offers that, compared wth the cost-based trasfer prce, are more closely talored to jst how favorable the local formato s Despte the prodcto maager s speror owledge whe mag trasfer-prce offers, the frm does ot ecessarly beeft from egotated prcg the prodcto maager maes the offers to maxmze dvdal tlty ad ot overall frm profts; ad the maretg maager respods to the offers also to maxmze dvdal tlty To evalate the performace of the two prcg methods, we ext cosder the rage of prces egotated by the maagers, the drato of egotatos, ad, most mportatly, the performace rag of the two prcg methods Negotated prces If HQ ses the same dvsoal proft-sharg rles as der cost-based trasfer prcg v( v( α( Θ = ; α(, h = h (0 ad the maagers agree to teral trade after bargag perods at some prce p, the maagers wll 9

operate ther dvsos exactly as der optmal cost-based trasfer prcg: z NEG ( Θ = z CB ( Θ NEG CB ad z ( = z (,, 0,,, Cosder the prodcto maager s prce-offer strategy The maager, whe mag a prce offer ses maretg s bdget to predct the chage the maretg maager s tlty from acceptg the offer Ths cremetal tlty s the dfferece betwee maretg s proft share ad persoal cost: v( NEG NEG R(, z (, p b( z (, v( h The maretg maager wll deftely ot accept a prce offer that decreases hs tlty; rearragg (, the maxmm acceptable trasfer prce eqals maretg s bdgeted post-trasfer revee et of compesato costs (for otatoal clarty, we sppress the depedece of ( MAX NEG NEG MAX p o p = R, z, b z, h ( Flly aware of ths, what offers wll the prodcto maager mae? The specfc bargag procedre reqred by HQ prce offers by the prodcto maager, ad acceptace or rejecto by the maretg maager allows s to aswer ths qesto The maretg maager s bargag power s lmted to acceptg or rejectg offers If teral trade mproves the prodcto maager s tlty, the best prce-offer strategy s the smply to mae a tae-t-or-leave-t proposal: offer the maxmm prce MAX that the maretg maager wold ever accept That prce s p What s the maretg maager s best respose to ths prce offer? The maager ca ether accept the prce or reject t expectato of a better prce offer a ftre bargag perod Uder what codtos cold the maretg maager reasoably expect a better offer? Ths cold happe oly f the maretg maager, by rejectg a prce offer, chaged the prodcto maager s belefs ( all other elemets, all the bargag perods are detcal Bt ths caot happe eqlbrm, sce ( the prodcto maager oly forms belefs abot the maretg maager s prvate formato; ad ( HQ s cotract wth the maagers assres that all eqlbra volve the maretg maager ssg trthfl bdgets (ad, ths, effectvely revealg local prvate formato Ths, the prodcto maager wll ever mae a better prce offer, ad the maretg maager s best MAX respose s to qcly (after oe bargag perod accept prodcto s prce offer p To smmarze, p, ( 0 Ths s ot srprsg, sce dvsoal operatos are depedet of the agreed trasfer prce ad the bargag perod; the operatos oly deped o each maager s formato ad the proft-sharg rles 0

f the maagers ever agree o a trasfer prce, ths agreemet taes place after oe bargag perod; the prce eqals maretg s bdgeted post-trasfer et revees Iteral trade Predctable egotated trasfer prces allow precse forecasts of the codtos leadg to teral trade The prodcto maager oly tates prce egotatos f trade at MAX p creases hs tlty: prodcto s proft-sharg paymet mst exceed the maager s persoal cost: v h ( ( ( MAX NEG NEG p C, z Θ, b z Θ, v Sbstttg the maxmm acceptable trasfer prce from ( ad rearragg, teral trade taes place f ad oly f NEG NEG NEG NEG v( R(, z (, b( z (, h( C(, z ( Θ, + b( z ( Θ, h( v( The left-had sde of ths eqalty s the frm s post-trasfer et revee; the rght-had sde s the frm s pre-trasfer cost Ths, the maagers agree to teral trade f ad oly f there are gas from ths trade from the frm s pot of vew Negotated trasfer prcg elmates effcet trade der costbased prcg ( the rego ( ˆ, of Fgre 3 Ths happes becase prodcto s trasfer-prce offer s the maretg dvso s post-trasfer effcet revee Becase of the bargag power grated by HQ, the prodcto maager captres, ad ths teralzes, the etre gas from teral trade We llstrate ths Fgre 5 Maretg Maager s Prvate Iformato ˆ NEG q = 0 NEG q = ˆ Prodcto Maager s Prvate Iformato NEG Fgre 5 The teral-trade decso rle q wth egotated trasfer prcg ad IT costrats I Fgre 5, the heavy sold le s the bodary betwee the shaded trade rego ad the shaded o-trade rego der egotated trasfer prcg The th step-fcto le s the trade/o-trade bodary der optmal cost-based prcg (see Fgre 4 Note the breaeve pot ( ˆ, ˆ from Fgres

3 ad 4 Uder optmal cost-based trasfer prcg, the maretg maager made hs teral-orderg decso based o the trasfer prce mposed by HQ; the cost-based prce cold ot flly commcate all of the prodcto maager s relevat owledge; ad, ths, some effcet trade was evtable (here llstrated by the shaded rego below ad to the left of ( ˆ, ˆ ad above the th step-fcto trade/otrade bodary der cost-based prcg Wth egotated prcg, the prodcto maager, prvately aware of local owledge, captres all the gas from trade ad, wth proper cetves, oly maes reasoable prce offers whe the frm beefts from trade The breaeve pot ( ˆ, ˆ s ths o the tradg bodary; teral trade der egotated prcg s effcet Ad, whe compared wth cost-based trasfer prcg, the tradg bodary der egotated prcg s formly closer to the IT-costraed effcet tradg bodary (smooth dashed crve Fgre 5 We ca ow ra the frm s profts der the two methods, by comparg the formatoal advatage of the egotated method wth the opportty ad orgazatoal costs of maagers bargag Sce prce egotatos coclde after oe perod, the ey determat of the bargag costs s the legth of each bargag perod If the maagers ca be covced to provde prce offers ad resposes qcly, the formatoal advatage of egotated trasfer prcg exceeds the bargag costs We formalze the precedg dscsso Theorem Theorem Wth prodcto-sde IT costrats ad prodcto-maager-offer egotated trasfer prcg, the frm ca provde dvsoal-proft-based cetve cotracts that garatee: Trthfl reportg by dvsoal maagers; Effcet dvsoal operatos; 3 Trasfer-prce agreemet after oe bargag perod; 4 Iteral trade f ad oly f the frm gas from ths trade; If the legth of each bargag perod s below a threshold vale, the frm s expected proft der egotated trasfer prcg s strctly hgher tha der cost-based trasfer prcg The rapd coclso ad the effcecy of trasfer-prce egotatos hge o the prodcto maager mag the frst prce offer based o the maretg maager s restrcted report (we cosder reportg restrctos for both maagers Secto 6 If, stead, HQ reqres that maretg maes offers ad prodcto accepts or rejects them, there wll be delays pror to prce agreemet: the maretg

maager wll tally offer a low prce ad the crease prces over tme Wth the foresght of Theorem 4, the frm ca stll ejoy hgher profts wth maretg-maager-offer bargag tha wth cost-based prcg (thogh wth prodcto-sde-oly IT costrats, prodcto-maager-offer bargag s the preferred bargag procedre We ext exame the effect of mprovemets formato techology o or aalyss 5 Negotated verss cost-based trasfer prcg wth mprovg formato techology Frms cotosly pgrade the qatty ad qalty of formato avalable to maagers IT mproves becase of decreasg IT costs, the prolferato of eterprse-resorce-plag systems, ad mproved commcato techologes (Srcar, et al, 000 The ey mplcatos of IT mprovemets for or aalyss are the ehaced abltes of mproved databases ad commcato techologes to captre, aalyze, ad commcate throghot the orgazato the prodcto maager s local owledge ad the ls betwee ths owledge, bsess processes, decsos, ad resltat cash flows As IT mproves, ceters parbs, HQ ca expect creased proftablty der ether trasfer-prcg method (see, for coterexamples, Arya, et al, 000; Mshra ad Vaysma, 00; Sappgto, 986 Bt what are the mplcatos of mproved IT for the rag of the two prcg methods? To formally aswer ths qesto, we represet the IT-mprovemet dea wth a crease the mber of reportg tervals Specfcally, gve a exstg formato system that parttos the prodcto dvso s prvate-formato set to tervals Θ, Θ,, Θ, we represet a IT mprovemet by dvdg each of the tervals to two ew oes The mproved formato system splts the prodcto maager s formato set to tervals: Θ Θ Orgal formato system Θ Θ 3 Θ 4 Θ Improved formato system 3 Frther IT mprovemets tr sbdvde each of the reportg tervals Each mprovemet creases the mber of reportg tervals ad redces the sze of each of the prodcto maager s reportg tervals Coseqetly, the maager s bdget report represetg that the prvate formato s Other represetatos of IT system mprovemets provde detcal reslts For example, a mproved system ca be oe wth a greater mber of reportg tervals tha the orgal oe, as log as ether: ( HQ decdes how to partto the prodcto dvso s prvate formato space, or ( IT mprovemets happe a reglar fasho, over the etre rage of the maager s prvate formato Or represetato of IT mprovemets s the smplest, yet sffcet to obta ad llstrate the reslts 3

some terval volves less ad less certaty for HQ ad for the maretg maager; ad the varaces betwee the cost bdget ad realzed costs decrease For example, a IT mprovemet from two reportg tervals ( = to for tervals ( = 4 meas that the prodcto maager ca report codtos as hghly favorable, moderately favorable, moderately favorable ad hghly favorable, rather tha smply favorable or favorable There are for possble bdget reports wth the mproved system, compared wth two possble reports wth the orgal system; the prodcto maager s cost estmates are ths more precse Cost-based trasfer prcg wth IT costrats does ot acheve goal cogrece However, IT mprovemets dmsh ths problem As a reportg terval shrs, relyg o average pre-trasfer cost each of the smaller-szed tervals to set the prce trggers correspodgly smaller dstortos teral trade decsos ad ths creases the gas from trades I Fgres 3 ad 4, the goal-cogrece problem s the proft-destroyg teral trade the ( ˆ, rego; as the terval srrodg ˆ shrs, the mpact of the goal-cogrece problem wth cost-based prcg decreases The two paels of Fgre 6 llstrate how IT mprovemets dmsh the goal-cogrece problem Pael A shows the egotated method s formatoal advatage wth severe IT costrats: the prodcto maager s bdget ca tae o at most two vales The frm mproves ts IT Pael B: the maager s bdget ca ow tae o for vales As IT mproves, the area where the cost-based method s goalcogrece problem cases tradg effceces shrs Fgre 6 Pael A Maretg Maager s Prvate Iformato TRADING BOUNDARIES: UNDER NEGOTIATED UNDER COST-BASED Prodcto Maager s Prvate Iformato Alteratvely, IT mprovemets ca represet a IT system s ehaced abltes to captre, categorze, ad report relevat formato ot prevosly cotaed dvsoal bdgets For example, a IT mprovemet ca allow the prodcto maager to explctly corporate dfferet qalty levels to dvsoal reports; stead of creatg a bdget wthot specfcally cosderg prodct qalty, followg ths mprovemet, the maager ca provde dfferet bdgets for dfferet qalty levels A specfc example from practce s Hershey s recet formato system mprovemet that allows maagers to access formato sorted o the bass of brad type rather tha o the bass of mafactrg data (PR-Newswre, 00 Ths llstrates a fer parttog of the formato set that we represet wth mproved IT, e stead of creatg a bdget for specfc mafactrg actvtes, the mproved system maagers ca create bdgets by each brad type 4

Fgre 6 Pael B Maretg Maager s Prvate Iformato TRADING BOUNDARIES: UNDER NEGOTIATED UNDER COST-BASED 3 Prodcto Maager s Prvate Iformato Fgre 6 I both paels, the thc le s the bodary betwee the trade ad o-trade regos der the egotated prcg method The th step-fcto le s the bodary der the cost-based method The hatched areas betwee the two bodares are the areas wth effcet trade der the cost-based method Note that the IT mprovemet from to 4 reportg tervals decreases the sze of the effcet-trade areas Whle the egotated method s formatoal advatage decreases wth each IT mprovemet, bargag ecessarly geerates opportty ad orgazatoal costs for the frm Ths, for sffcetly costraed IT, the cost-based method geerates hgher profts We formalze ths Theorem 3 Theorem 3 As the formato system mproves, the frm s expected proft creases strctly faster der cost-based trasfer prcg tha der egotated prcg Wth a sffcetly costraed formato system, the frm s expected proft der cost-based prcg strctly exceeds expected proft der egotated prcg Note that Theorem 3 reles o partal-eqlbrm aalyss: we hold fxed the opportty cost of delay per t of tme If compettors also experece lower IT costs ad start to react faster, the opportty cost per t of tme may go p The dsadvatages of delays der egotated prcg are the eve greater, favorg cost-based prcg systems 6 Maretg ad prodcto IT costrats The aalyss of sectos 3-5 descrbed the mplcatos of IT costrats for trasfer prcg a settg wth oly prodcto-sde IT costrats Ths allowed s to descrbe the ecoomc tto derlyg the advatage of egotated prcg whe commcato betwee a dvso ad HQ s restrcted However, becase of oe-sded IT costrats, the precedg aalyss sffers alog two dmesos 3 Frst, HQ s delegato of the teral-trade decso der cost-based trasfer prcg s sperfcal (HQ cold mae the decso tself, relyg o the maagers reports Secod, cost-based ad 3 We are gratefl to the aoymos referee for detfyg these caveats ad ecoragg s to stdy the settg where IT costrats affect both maagers ablty to commcate ther prvate formato 5

egotated prcg are both domated by a revee-based system, where HQ: ( sets the trasfer prce based o the maretg maager s report, ad ( allows the prodcto maager to psh the prodct to the maretg dvso Uder the revee-based system, the prodcto maager, whose commcato s restrcted, maes the resorce allocato decso possesso of all the formato relevat for maagg teral trade We ow exted or aalyss to corporate IT costrats for both dvsos The formal aalyss s the proof of Theorem 4 the appedx The tto s as follows As the aalyss of Sectos 3 ad 4, HQ ses detcal proft shares der cost-based ad egotated prcg to covce the maagers to operate ther dvsos effcetly Maretg-sde IT costrats do ot chage the optmal cost-based trasfer prce; HQ stll sets the prce as (9, at the expected cost the prodcto dvso pls a marp for the prodcto maager s expected compesato Coseqetly, the maretg maager teralzes the average gas from trade each reportg terval of the prodcto maager The cost-based method ths sffers the effceces detfed Secto 3 (see Fgres 3 ad 4: the otrade effcecy whe there are gas from trade bt the trasfer prce exceeds the maretg maager s cremetal tlty from trade; ad the trade effcecy where the maretg maager orders the prodct eve thogh teral trade redces the frm s profts Negotated trasfer prcg allows the frm to dmsh these effceces I Theorem 4, we show that the o-trade effcecy s redced wth the egotated prcg system where the frm grats the maretg maager the rght to mae prce offers (the prodcto maager accepts or rejects the offers The eqlbrm aalyss s smplfed by the fact that the prodcto maager s acceptace strategy taes the followg smple form: accept a trasfer-prce offer as log as the maager s prvate formato s below a ct-off vale (the ct-off s a fcto of the offered prce The maretg maager s strategy s to start wth low trasfer-prce offers ad crease the prce every bargag perod HQ threates to mpose the optmal cost-based trasfer prce f the maagers fal to agree by the termal bargag perod I the rego wth the o-trade effcecy der cost-based prcg, the prodcto maager s the wllg to accept prce offers lower tha the cost-based trasfer prce becase f the threateed cost-based-prce terveto s mposed, the maretg maager wll ot place the order, ad the prodcto maager wll forego ay avalable gas from trade Ths assres that teral trade ths rego taes place wth strctly postve probablty der egotated prcg, creasg the frm s proft beyod that avalable der cost-based prcg 6

Of corse, wth IT costrats o the maretg sde, ether maager ows the other maager s prvate formato, eve f HQ s able to dce trthfl reportg Ths, the earler reslt abot mmedate resolto of maagers bargag does ot apply here the maretg maager caot garatee that prodcto wll accept the frst trasfer-prce offer I geeral, maagers egotatos coclde a gve bargag perod wth some postve probablty; ad wth postve probablty the maagers egotatos last for mltple perods, as late as the peltmate bargag perod However, the specfcato of maxmm bargag tme s p to HQ Ths, to show that the frm s proft s hgher der egotated trasfer prcg tha the der the cost-based system, t s sffcet to show that the egotated system s the preferred oe for some (HQ wll se ay other maxmmbargag-perod polcy oly f t offers stll hgher proft We do ths below, Theorem 4, for = I ths case, the delay der egotated prcg s at most two perods Ad, as Theorem, f the maagers ca be covced to provde offers ad resposes qcly, the advatage of egotated prcg exceeds the bargag cost Theorem 4 Wth IT costrats lmtg commcato betwee both maagers ad HQ, the pper bod o the frm s expected proft der egotated trasfer prcg s strctly hgher tha der costbased prcg whe the legth of each bargag perod s below a threshold vale To coclde the aalyss, we ote that by symmetry, egotated trasfer prcg also allows the frm to ear hgher expected proft tha a revee-based trasfer-prcg system Also ote that the Theorem 3 reslt cocerg formato mprovemets apples to the aalyss of ths secto as well: holdg the legth of a bargag perod costat, wth a sffcetly costraed IT, cost-based trasfer prcg allows the frm to ear hgher expected proft tha does egotated prcg 7 Coclso A challege for mlt-dvsoal, vertcally-tegrated frms s to delegate operatg decsos a way that ecorages dvsoal maagers to se ther prvate formato the best terests of the frm as a whole Ths s complcated by costrats o the flow ad avalablty of formato wth the frm That better ad cheaper formato leads to mproved profts s recogzed; less obvos are the mplcatos of IT mprovemets for orgazatoal desg Or reslts show that a frm s formatoal evromet s a ey factor determg ts trasfer-prcg method 7

Whe IT costrats prevet dvsoal maagers from trasferrg local owledge abot the frm s prodcto process, we show that properly strctred egotated trasfer prcg has a formatoal advatage over the cost-based method: wth the rght cetves, maagers agree o trasfer prces that approxmate the costs of teral trasfer more accrately Coseqetly, whe opportty ad orgazatoal costs of bargag are sffcetly small, the formatoal advatage of the egotated method geerates hgher frm profts Coversely, mprovemets IT lead to faster creases proft der cost-based trasfer prcg tha der the egotated method, becase the vale-destroyg teral trade der cost-based prcg dmshes Wth sffcetly costraed IT, the cost-based method provdes hgher profts tha egotated trasfer prcg becase, all else eqal, the remag opportty ad orgazatoal costs of maageral bargag otwegh the proft destroyed by effcet teral trade der IT-costraed cost-based trasfer prcg Or reslts have several emprcal mplcatos Frst, the reslts help expla srvey evdece Vacl (978 who fod that: ( frms comprsg related bsesses se egotated trasfer-prcg sgfcatly more tha cost-based trasfer prcg (34% verss 5% ad ( vertcally-tegrated frms operatg wth a sgle prodct maret se cost-based trasfer prcg sgfcatly more tha egotated trasfer prcg (49% verss % Maagers frms comprsg related bsesses are more lely to have dverse edcatoal, fctoal, ad trag bacgrods; the cost of trasferrg dvsoal owledge to top maagers s ths hgher (e hgher IT costrats tha vertcally-tegrated frms a sgle prodct maret Vacl s evdece s ths cosstet wth Theorems ad 4 4 Secod, or reslts mply that frms wth the followg characterstcs are more lely to prefer egotated trasfer prcg: ( derstadg dvsoal operatos reqres specalzed edcato or trag; ( dvsoal operatos are physcally located far from the headqarters; ( dvsoal operatos are qcly-chagg evromets reqrg rapd resposes; (v lac of sophstcated eterprse-resorce-plag (ERP systems; ad (v large frm sze 5 4 Or dscsso of emprcal mplcatos, cosstet wth the modelg the paper, addresses frms where the tax effect of trasfer prcg s ot a overrdg cosderato, prmarly becase the trade does ot cross tax jrsdctos Eve whe t does cross tax jrsdctos, emprcal evdece sggests that at least some frms mata two trasfer-prcg systems: oe to maage teral trade, ad a separate oe for taxes (Erst ad Yog 999 However, matag separate systems ca be extremely costly becase the taxato athortes ca arge that the tax-based trasfer prcg system has o legtmate bsess prpose ad tae legal acto to se the teral system for taxato prposes (Sprgsteel, 999 5 The frm-sze factor may expla why 5 Caada frms, Atso (987 fds 60% se cost-based methods, ad 7% se 8

Thrd, Theorem 3 offers a mber of testable predctos The most drect predcto s that the rato of frms wth cost-based trasfer prcg to those wth egotated prcg s hgher after the 990s IT boom tha before 6 Drg the 990s, may frms vested heavly teral formato systems ad beefted from creased comptg power per maager (Srcar, et al, 000 Frther, ERP systems streamled commcatos betwee dfferet fctoal les large orgazatos, mprovg frms abltes to pla ad to coordate decsos that prevosly had to be made wth complete formato abot teral processes (Carcross, 000 The vestmets commcato ad reportg systems lowered the barrers to teral commcato Theorem 3 predcts that ths redcto owledge-trasfer costs creases the attractveess of cost-based trasfer prcg Forth, the reslts ca predct preferred prcg methods moder bsess-to-bsess retal allaces 7 Ay ls betwee two compaes formato systems are lely to be costraed becase the beefts of costraed sharg of formato wll be otweghed by assocated propretary costs If so, a testable predcto of Theorems ad 4 s that the trasfer prces these allaces are more lely to be egotated tha to be based o the sppler s cost Fally, or reslts have practcal mplcatos All else beg eqal, frms wth low costs of trasferrg dvsoal owledge ear hgher profts wth cost-based tha wth egotated trasfer prcg Frms wth hgh owledge-trasfer costs ear hgher profts wth the egotated method, bt mst strve to mmze orgazatoal coflct ad the opportty cost of maagers tme devoted to bargag; these mportat mplcatos for job desg mst be explored ftre research Gve the wdespread se of trasfer prcg practce, srprsgly lttle evdece exsts that detfes preferred methods Moreover, o emprcal wor o trasfer prcg has bee gded by hypotheses geerated from the reslts ad ecoomc tto of theoretcal modelg Or reslts, as well as those of Baldes et al (999 ad Baldes (000, ca form a framewor of testable hypotheses that ca be sed to gde emprcal tests of the theory egotated oes statstcs that dffer sgfcatly from the Tag (993 ad Vacl (978 srveys that docmet sgfcatly hgher se of egotated prcg If the Caada frms are smaller tha the US frms the latter srveys, trasferrg local owledge s less costly, ad or reslts predct greater se of cost-based trasfer prcg for the Atso frms 6 As a pre-it-boom bechmar, Tag (993 detfes a 7: rato of cost-based to egotated trasfer-prce sage 7 For example, Crct Cty has a agreemet wth Amazocom to spply pcp servces to Amazo cstomers 9

Appedx A Maagers belefs ad reportg ad bargag strateges I each perod { 0,,, } maager {, } maageral reports: { } A 0 taes a observable acto a A Perod-0 actos are = M Wth prodcto-maager-offer extesve form, perods,,,, the prodcto maager ether ( offers a trasfer prce p, or ( offers that prodcto ad trasfer ot tae place At the ed of each tme perod, the maretg maager ether ( accepts the offer, or ( rejects the offer The A = "No Prodcto" ad A = {"Accept","Reject"} for {,,, } Wth maretg-maager-offer extesve form, { } "No Prodcto" A = for { } Let a ( a, a 0 ( a, a,, a,,, If the game cotes throgh ay perod, A = "Accept","Reject" ad ϒ s the hstory for all pror perods, wth 0 ϒ If 0, = or f the maagers cote prce egotatos perod, the bargag hstory ϒ s o-termal Otherwse, the hstory s termal Followg a o-termal hstory ϒ, maager s strategy s a probablty dstrbto maager wth formato taes the acto 0 (,,,, {, } σ over the set A For every a A, σ ad σ ( σ σ ( a, a followg the hstory ϒ Let ϒ s the probablty that σ σ σ σ, Maager s belefs abot the prvate formato of maager j are descrbed by the probablty desty fcto µ ( j, ϒ after ay game hstory ϒ Let µ ( µ, µ A perfect Bayesa eqlbrm s the a set of strateges ad belefs (, Followg every game hstory the cotato game gve the belefs µ ( j ϒ σ µ sch that: ϒ, the cotato strateges form a Bayesa-Nash eqlbrm for, Bayes rle s sed to pdate belefs wheever possble 3 Maager s belefs abot maager j s prvate formato are depedet of maager s prvate formato ad maager s actos,,, :, µ ϒ = µ, ϒ ad (,(,,( a, aˆ µ ϒ = µ ϒ f a = aˆ j j Appedx B Proofs j ϒ ( j ( j j Theorem We prove ths reslt for steps Frst, we show that the maretg maager s operatos ad compesato eqal the optmal secod-best oes Secod, we show that the performace of ay cotract wth the prodcto maager ca be replcated by oe where HQ provdes hm cetves for trthflly j 30

reportg the terval cotag prvate formato Thrd, we derve ( the optmal dvsoal operatos ad compesato of the prodcto maager; ad ( the teral-orderg decso optmal for the frm Forth, we show that the prodcto maager does fact operate hs dvso optmally, ad that the maretg maager orders the prodct f ad oly f t s beefcal for the frm Step The maretg maager Gve the trasfer-prcg rle (9 ad proft shares (7, we show that HQ dces the maager to operate the maretg dvso optmally at the lowest possble compesato The frm s gas from trade are the ( CB CB v ΓΘ (,, R(, z( b( z( h( C, z ( Θ, + b z Θ, h( (A- v( If the maagers report trthflly: ( wth teral trade, maretg dvso s operatos are detcal to CB the secod-best oes (3: z z ad oly f E ΓΘ ( Θ fxed-salary as follows:,, 0 (, = for all Θ ; ad ( the maager orders the prodct f { } ΓΘ ˆ,, max 0, ΓΘ,, HQ sets the maager s Let ( ( ( ( SB ˆ SB {,,,, ( } m β m = b z m v m α m Γ Θ m + b z t v t dt f d = The maretg maager s expected compesato s the SB SB ( (( ( + ( ( E b z, v b z, t v t dt Θ, (A- whch s the mmm secod-best compesato (Fdeberg ad Trole, 99 The maretg dvso s effcet revee (et of compesato s R( R( z( b( z( h(, We ext show that the maager reports trthflly sg the followg from Mrrlees (986 for ay postve-valed fcto :, ( W Θ Θ W (, W (, m for all, m Θ f: W, = W, W t, t dt Θ; for all, m ad ( W (, m Θ To se these sffcet codtos, let W (, m s wealy creasg represet the expected tlty, der cost-based trasfer prcg, of the maager wth prvate formato who reports m We the have W, = 0 ad, sg (A-, sffcet codto ( holds Usg the evelope theorem, m 3

CB W(, m = E Θ b z m, v α s decreasg, z m, s Sce ( m m CB lewse decreasg m Ths, sce b s creasg z ad v ( > W (, m 0, s creasg m, ad sffcet codto ( holds Step Usg trth-dcg cotracts wth prodcto maager s wthot loss of geeralty Cosder ay fte message set of sze ˆ for the prodcto maager: M { ˆ m m} ˆ =,, Ay mplemetable dvsoal-operatos rle z: M ˆ Θ sed by ths maager mst satsfy seqetal ratoalty: t mst maxmze hs tlty at the stage of the game where the maager decdes o dvsoal operatos: ( α ( z m, argm m C, z + b z v (A-3 z Z The Revelato Prcple does ot apply here, bt we ow prove that a argmet alog the les of the Prcple apples to the followg relaxed cotract-desg problem for the HQ abstract for ow from the maretg maager s teral-trade decso, ad maxmze the frm s profts wth followg strmets: the trasfer-prcg rle T( m compesato pla ( m ( m ; α, β ; ad HQ s teral-trade decso q m, Ths modfed program s a relaxed oe, sce the real problem cldes a addtoal costrat: the maretg maager s teral-trade decso mst be seqetally ratoal Whe the prodcto maager s prvate formato s, expected tlty from reportg m s { } ( ( W, m E Θ α m T m C, z m, b z m, v q m, + β m (A-4 ( W / z the partal dervatve of the maager s expected tlty (A-4 wth respect to z( m, eqals E Θ α( m Cz (, z( m, b ( z( m, v( q m,, ad { } W = E Θ b ( z m, v q m, < 0 z (A-5 Note that (A-5 s the stadard Spece-Mrrlees sgle-crossg codto (Fdeberg ad Trole, 99: 59 The codto meas that, whe vewed as fctos of, ay two expected tltes W (, m ad W(, mˆ ether ( are eqal for all, ; or ( cross at most oce o, Now cosder ay perfect Bayesa eqlbrm (PBE of the modfed problem; the prodcto maager s eqlbrm reportg strategy λ : Θ ˆ M mst maxmze the maager s expected tlty: 3

arg max W(, m λ (for smplcty, we cosder pre strateges; detcal aalyss apples to mxed m ˆ M strateges Sce M ˆ <Θ, the prodcto maager s reportg strategy mst se detcal reports for dfferet realzatos of prvate formato: for some, λ λ = Ths meas ether that the maager s reportg strategy s costat (e, λ ( λ( < or the reportg strategy has a =,, mber of dscottes We ext show that f λ ( has more tha ˆ dscottes, the there s a PBE of the modfed problem all respects detcal to the PBE wth λ ( maager s reportg strategy ˆλ ( has at most ˆ dscottes Cosder ay par, [, ], e that for some [ ], < wth λ ( = λ( Sppose that s ot possble that W W ˆ,, λ ˆ λ wth oe excepto: the prodcto λ s ot costat o the terval Ths meas that W ( ˆ λ ˆ W ˆ λ( ( ˆ, λ( ˆ > W( ˆ, λ( W some ope terval (, ( ˆ λ ˆ W ˆ λ(,, Bt t, >,, as we ow show by cotradcto Sppose that cotas ˆ ( ˆ, ˆ ad W ˆ, λ λ are both cotos Ths, there exsts ad s tself a sbset of (, sch that W(, λ > W(, λ ad W(, λ > W(, λ (ad, fact, for every (,, the maager strctly prefers reportg ( ˆ (A-6 λ over that the maager at least wealy prefers λ ( at the bodares of [, ] : W λ W (, λ( W, λ( ˆ Together wth (A-6 ths mples that (, twce o (, λ Recall that (, W, λ ( ˆ W λ ad W, λ ( ˆ ad a cotradcto of sgle crossg Ths, the maager wth prvate formato ˆ s dfferet betwee reportg ( ˆ (A-4 s cotos E q λ ( for z Θ λ ad λ : W ˆ λ( ˆ W ˆ λ ad, some ope terval cotag ˆ, ( z ( λ ˆ, = λ, for that terval cross, =, Also, sce expected tlty z f the maager s dfferet betwee reportg λ ( ˆ the Θ = Θ ( E ˆ q λ, E q λ,, ad ad 33

We are ow ready to costrct the eqvalet reportg strategy ˆ λ : Θ ˆ M that has at most ˆ dscottes Beg wth It s possble that that mltple messages ˆ m { ˆ M m,, m} = maxmze the prodcto maager s expected tlty whe the maager s prvate formato s We fd the message Mˆ m that also maxmzes the maager s expected tlty for the frthest, Defe Mˆ as the set of messages amog these that also maxmze the maager s expected tlty some ope set (,, For each m M ( ( m for whch ˆ, fd the maxmm prvate formato realzato m maxmzes the expected tlty of the maager wth ths prvate { } formato: ( m sp, m arg max W ˆ ( ˆ ˆ, m m M Fd the largest ( m : ˆ max ˆ m m M If there s a qe message m Mˆ ( that maxmzes the expected tlty of the maager wth prvate formato ˆ (, defe m as that qe message; f there are several messages, defe m( as the oe amog these wth the lowest sperscrpt dex (jst to mpose a selecto rle Note that, sce the message m( maxmzes the maager s expected tlty at ad at ˆ (, t s also a best-respose message for all ˆ, ( Defe ˆ λ ( = m( for all, ˆ Note that Next, proceed to ( ˆ m caot maxmze the maager s expected tlty for ay > ( ˆ I the same maer, fd the message m( that maxmzes the maager s expected tlty at ad at the frthest, (se ˆ ( to represet ths frthest pot Defe ˆ λ ( m( = for all ˆ process tl fdg a message ( Defe ˆ ( λ m at, Proceed to ˆ ( Cote ths teratve m that maxmzes the maager s tlty at some, ad also = for all, By costrcto, ˆλ ( s a optmal reportg strategy; t s almost everywhere cotos, wth at most ˆ dscottes, ad where ˆλ ( s cotos, t s costat Frther, ( ˆλ parttos Θ to 34

ˆ tervals Nmber these tervals order of creasg : { Θ } M Θ, Θ,, Θ Θ, Θ,, ; let We ow costrct a trth-dcg cotract that replcates the performace of the PBE eqlbrm (ths follows the sprt of the proof of the Revelato Prcple - for example, see Fdeberg ad Trole, 99: 55-56 Defe : M ˆ M wth α α λ; β β λ; T T λ ; ( Θ λ by λ λ E [ ] Θ = ˆ Cosder α, β, T, q, ad q( m q ( m Θ If, λ, for all λ s the maager s reportg strategy the orgal PBE, the trthfl reportg s the maager s reportg strategy der T q α, β,, The eqlbrm otcomes are detcal Ths, the otcomes of every PBE ca be obtaed as otcomes of a PBE wth trth-tellg, ad there s o loss for the HQ cosderg oly trth-dcg cotracts Step 3 Optmal cotractg wth the prodcto maager Becase of IT costrats, secod-best prodcto decsos ad compesato are ot attaable We ext determe the optmal trth-dcg cotract the modfed problem We ow se W(, Θ prodcto maager wth prvate formato who reports z (, to represet the expected tlty of the Θ, { } Θ that satsfes (A-3 (sppressg the depedece of W ( o,,,, ad selects ay α ad β ( : ( Θ β ( Θ + Θ ( Θ α ( Θ ( Θ ( ( Θ ( ( Θ ( W, E q, T C, z, b z, v The frm s modfed problem s the Program A: z(, α(, β (, T(, q( Θ Θ = { ( } max E E q Θ, R C, z Θ, + α Θ T Θ C, z Θ, + β Θ,,,,, Θ : sbject to: for all { } (A-7 z Θ, argm α Θ C q Θ,, z + b z v z Z for all Θ ; (A-8 W v (, W (, Θ Θ for all v { },,, ; (A-9 W, Θ 0 (A-0 (A-8 s the prodcto maager s seqetal ratoalty costrat; (A-9 garatees that the maager trthflly reports the terval cotag ; ad (A-0 s the stadard partcpato, or dvdal 35

ratoalty, costrat, whch assres that the maager does ot qt W For every Θ, HQ eeds to garatee that the maager prefers reportg Θ to + ( W ( + ˆ +, +, Θ e, Θ, Θ For every Θ HQ eeds to garatee that the maager prefers reportg Θ to, Θ e ( ˆ + ( ˆ W W Θ Θ By cotty of (,,, meas that ( ( + W W, Θ =, Θ, or, sbstttg (A-7: ( Θ ( W Θ for all { },,,, ths ( ( E q, α T C, z, b z, v Θ Θ Θ Θ Θ Θ + β Θ = E q, α T C, z, b z, v Θ Θ Θ Θ Θ + β Θ + + + + + + for all { },,, We the set the fxed salary for the worst report Θ as low as possble to satsfy the partcpato costrat (A-0 for every : Θ ( Θ E Θ q( Θ, T( Θ C(, z ( Θ, + ( Θ = E q(, b ( z (, v Θ Θ Θ (A- α β By dcto, (A- gves the followg ecessary codto o prodcto maager s compesato: ( ( EΘ q(, T C, z (, Θ α Θ Θ Θ Θ + β Θ j j j j j = E q Θ, b z Θ, v + q Θ, b z Θ, v v j= + Tag expectato over each, compesato over the etre set Θ gves Θ {,, }, ad the smmg over {,, } to fd expected j j j j j ( Θ, ( ( Θ, ( + ( Θ, ( ( Θ, ( ( ( E E q b z v q b z v v Θ Θ = j= + = ( ( ( ( = E E Θ q Θ, b z Θ, h Θ Sbsttte (A- ad (A-3 to the objectve of program A ad rearrage to obta Program A: v F max E E q( Θ, R( ( α( Θ C(, z( Θ, b( z( Θ, v( α(, q( Θ Θ = v ( F( α( Θ C(, z( Θ, b( z( Θ, v( v( f ( sbject to z (, argm α ( C( q(,, z b( z v( Θ Θ Θ + z Z From (A-4, z( Θ, argm α( Θ C( q( Θ,, z + b( z v( ( ( ( ( v f (A- (A-3 ; Θ; Θ (A-4 z Z Program A s the jst: 36

max,,,, α E E q( Θ R( ( α( Θ C( z( Θ b( z( Θ v( (, q( Θ Θ ( ( ( ( = sbject to z( Θ, argm α( Θ C( q( Θ,, z + b( z v( z Z ; Θ; Θ The frst part of the solto s the to select, for every { } v v ( F ( = ( Θ ( Θ f α α Ths gves α( ( ( v,,,, α( Θ ( 0, sch that v Θ =, whch s eqato (7 Effcet operatos are the h ( Θ + ( ( ( zˆ, argm C, z b z h v / v The secod part of the solto to the z Z relaxed program s to fd the optmal teral-trade rle q ˆ To do ths, maxmze potwse over q { 0, }; sbsttte the optmal ( α Θ ad z( Θ, qˆ ( Θ, = f ad oly f E Γ( Θ HQ the sets ( wth the mes of cotracts α, β(,, 0 Θ ; ad se (A- to coclde: v F f (A-5 (A-6 β Θ to satsfy (A- The fact that the prodcto maager reports trthflly whe faced Θ Θ ca be verfed sg the Mrrlees (986 techqe the same maer as (thogh more tedosly tha for the maretg maager Step 4 Frm s operatos der the cost-based trasfer-prcg cotract I step 3, we derved the optmal operatos of the frm der a relaxed cotract-desg program The fal step s to show that the frm s expected proft wth the addtoal costrat s the same as the modfed program CB the prodcto maager s operatg decso z (,,,, Θ, Θ, For all { } detcal to zˆ (, Θ s Θ the optmal oe the relaxed program From (8 ad (9, the maretg maager orders the prodct f ad oly f E Γ( Θ,, 0; Θ CB ths, from (A-6, q ( qˆ ( Θ, = Θ, It s easy to verfy that der ether the frm s problem or the relaxed problem the prodcto maager wth the worst prvate formato does ot receve ay formatoal rets The revee eqvalece theorem (Myerso, 98, amog others the garatees that the frm s expected proft s detcal to the oe der 37

the relaxed program NEG Theorem : { 0,} q M Θ Θ represets the teral-trade decsos wth egotated prcg Wth trthfl reportg, proft shares (0 garatee that the maagers operate ther dvsos effcetly HQ sets ( ˆ ( j j j β Θ = δe b z, v v Θ α, t, f t dt Θ Θ Γ Θ ; j= + ( ( ( m β m = δ b z, t v t dt F F Θ, = z Θ, zˆ Θ, ; z Θ, z Γ Θ,, 0; otherwse, where ( ( ( f ( ( z ( z Θ, = Θ, = 0 HQ also sets a stable terveto polcy; oe example s f, followg a 0 ( m = Θ,, tme perod s reached, HQ reqres maager to mplemet the operatg decsos z ( Θ, m, forces teral trasfer f ad oly f ( ( j= + Γ Θ,, 0, ad pays the maagers ( j j j x = b z Θ, m v + b z Θ, m v v ; ( ( x = b z Θ, m v m + b z Θ, t v t dt m Now a straghtforward adaptato of Vaysma (005 garatees that, whe maagers have prvate formato Θ, Θ, every perfect Bayesa eqlbrm of maagers teractos s a trth- 0 tellg oe ( a = ( Θ, Also, f ( the prce (8; f (,, 0, ΓΘ,, 0, maagers agree at = to prodce ad trasfer at ΓΘ < maagers agree at = ot to prodce We complete the proof of the theorem by showg that as log as the dscot factor δ s strctly decreasg the legth of each bargag perod, the frm s expected proft s hgher der egotated trasfer prcg tha der cost-based trasfer prcg We prove ths for the case where the dscot factor represets cotos dscotg at the rate r, or δ = e The proft-sharg parameters der each method are eqal Dvsoal operatos are the: CB NEG ( f q ( Θ, = ad q ( r Θ,, =, the ( Θ = ( Θ + z, z, argm C, z b z v / v h, ad (A-7 NEG CB z 38

CB ( ( ( NEG z, = z, = z ; (A-8 CB NEG ( f q ( Θ, = 0 ad q ( zero der ether trasfer-prcg system Θ,, = 0, the each maager sets the prodctvty parameter to Wth the optmal cost-based system of Theorem, the frm s expected proft s CB CB Π EΘ q Θ, E,, Θ Γ Θ (A-9 =,,,,, the frm s expected proft der these NEG NEG Wth Π E E Θ q ( Θ Γ( Θ Θ = NEG egotated trasfer-prcg eqlbra s δ Π Let every { } r CB Π ε = l + NEG Π,,,, partto the terval Θ to the followg for sets: S ( 0 { q CB ( q NEG ( } For every Θad Θ, Θ sch that Θ, = 0 ad Θ,, = 0 ; (A-0 S ( { q CB ( q NEG ( } Θ, Θ sch that Θ, = ad Θ,, = ; (A- S ( { q CB ( q NEG ( } Θ, Θ sch that Θ, = ad Θ,, = 0 ; (A- S ( 3, { sch that q CB (, 0 ad q NEG (,, } Θ ad every {,,, }, at least two ad at most three of the sets S j ( Θ, Θ ad {,,, }, the sets S ( Θ, ad S3 ( Θ, For every Θ Θ Θ = Θ = (A-3 are oempty For at least some For every Θ ad every { },,,, we se (A-7 ad (A-8 to derve the followg: NEG CB q,,,, f d Θ Γ Θ = q Θ, Γ Θ,, f d; (, S (, S0 Θ 0 Θ NEG CB ( Θ Γ( Θ = ( Θ Γ( Θ q,,,, f d q,,, f d (, S (, S Θ NEG Whe S ( Θ,, q ( Θ,, = 0 ad, ths, ( Γ Θ,, < 0 Hece, are o-empty NEG CB q Θ,, Γ Θ,, f d > q Θ,, Γ Θ,, f d (, S (, S Θ Θ NEG Whe S3 ( Θ,, q ( Θ,, = ad, ths, ( Γ Θ,, 0 Hece, 39

NEG CB q,,,, f d q,,, f d Θ Γ Θ Θ Γ Θ (, S (, S3 Θ 3 Θ Combg the above for reslts, smmg over {,,, }, ad tag expectato over Θ : NEG CB EΘ E q,,,, E q, E Θ,,, Θ Θ Γ Θ > Θ Γ Θ Θ = = NEG CB or Π >Π From (A-9, we ths have CB Π NEG + < ad ε > 0 Wth 0 < < ε, Π CB r e Π CB NEG r NEG NEG Π CB > +, NEG ad δ Π = e Π >Π + NEG >Π Π Π Theorem 3 Beg wth a formato system wth reportg tervals Let K {,,4, } the set dexg the seqece of mproved formato systems We se M,, j K, to refer to the j represet prodcto maager s message space der the system wth j reportg parttos A geerc reportg terval ths system s { j} Θ,,,,, The prvate formato wth average pre-trasfer costs the j terval Θ, j s, j We cote to se Θ, j to represet prodcto maager s report that prvate j formato s the terval Θ, We se SB ( ( ( ( SB G(, R q (,, z( C q,, z b z h (A-4 = to represet the frm s gas from trade the absece of IT costrats Let Π SB E G, Θ, Θ NEG Π j represets expected proft for the optmal egotated trasfer-prcg scheme wth a IT system wth j K tervals For ay bargag-perod legth, wth dscot factor δ, for all j K, NEG j SB Π δ Π (A-5 For optmal cost-based prcg from Theorem, wth a IT system wth j K tervals, we se the followg otato: CB j CB Π s the frm s expected proft; : { 0,} CB teral-orderg decso; z, j (, j, q M Θ s the maretg maager s j, j Θ s the prodcto maager s operatg decso: ( Θ + ( ( ( CB z,,, argm j j z Z, C z b z h, j v / v, j The gas from trade wth a IT system wth j tervals are (A-6 40

(, j,, R(, z ( b ( z ( h ( ( Θ + Θ Γ j Θ CB CB C(, z, j, j, b ( z, j (, j, ( v ( / v (, j h (, j For each formato system j K, for every, terval Θ, j to the followg for sets: Θ ad for every { j } CB SB S0, j(, j {, j qj (, j q ( } CB SB S, j(, j, {, jsch that qj (, j, ad q (, 0 }; CB SB S, j(, j, {, jsch that qj (, j, ad q (, }; CB SB S3, j(, j, {, jsch that qj (, j, 0 ad q (, } CB SB Wth q j ( Θ, j, = f ad oly f Γj( Θ, j,, 0, ad (, (A-7,,,, partto the reportg Θ, Θ sch that Θ, = 0 ad, = 0 ; (A-8 Θ Θ Θ = = (A-9 Θ Θ Θ = = (A-30 Θ Θ Θ = = (A-3 q = f ad oly f G, 0, j CB Π j = EΘ E,,,, Sm, j, j, j j Θ Γ Θ (A-3 = m= j 3 SB Π = EΘ E G, Sm, jθ, j, (A-33 = m= For every Θ, for every ε > 0, there s a j K sch that f l K, l > j, ad Θ,, the, l ε < for all {,,, l} For all j, for all { j},,, : ( (A-6 ad (3 mply that CB z, j ( Θ, j,, j = z (, j ; ad ( (A-7 ad (A- mply that (,,,, ( j j j G, j, Θ CB z, j ( Θ, j, ad Γ j( Θ, j,, are mootoe ; ths, for every, ε > 0, there s a j K sch that f l K, l > j, ad,, (,,, (, Γl Θ l G < ε for all { l} Θ Ths form covergece of j(, j,, that for all l K, l > j, ad Θ : l = = l j j l Γ Θ to (, l Γ Θ = for every Θ for every CB Θ the z (, z Θ < ε ad, l, l,,,, (A-34 G tr mples that there s a j K sch f, (, ; f S l Θ l, ad (A-35 S, j( Θ, j, = = Sce δ > 0, (A-34 ad (A-35 mply that for some j K, f l Kad l > j, the for all Θ, f( 3, (,, f S l Θ l (A-36 S3, j( Θ, j, 4

(, l G( f( l δ Γ,,,, S, l( Θ, l, l Θ ad, ths = 4 l E E,,,, S, l, l, l l G δ Θ Γ Θ Θ = 4 (A-37 From (A-34 ad (A-36, for some j K, f l K ad l > j, the for all Θ, l δ Γ (,,, (, (, S3, l(, l, l Θ l G f Θ ad, ths = 4 l E E,,,, S3, l, l, l l G δ Θ Γ Θ Θ 4 (A-38 = For some ˆ j K, f l K ad l ˆ, j { l},,,, Θ Now f l K δ Γl Θ, l G < for all 4 Θ, > the (,, (, ad l { j j ˆ j} l 3 CB SB l Θ S l l ml,, = m= CB NEG l l > max,,, the, by (A-37 ad (A-38, 3 Π Π = E E Γ ( Θ,,, G(, δ Θ l, < 4 Ths, alog wth (A-5, gves Π >Π, completg the proof Theorem 4 The maretg maager s reportg set { M = Θ, Θ,, Θ} s a partto of Θ to tervals mbered order of creasg (the reslts are ot affected f the maagers reportg sets are v v of dfferet szes We se to refer to the pper bod of Θ ; the typcal prvate-formato v v realzato = Θ For completeess, set 0 We prove the theorem three steps: ( we docmet the frm s operatos wth optmal cost-based trasfer v Θ s mplctly defed by h ( E v h ( prcg; ( we show how HQ ses mes of maageral compesato cotracts ad terveto rles to gde the maagers toward a trth-tellg perfect Bayesa bargag eqlbrm der egotated prcg; ( we show that, for a large eogh dscot factor δ, the frm ears strctly hgher expected proft der egotated prcg Step To docmet the frm s operatos der optmal cost-based trasfer prcg, we adjst the cotract from Theorem to corporate maretg s IT costrats Frst, ote that, smlar to Step of Theorem proof, there s o loss for the HQ cosderg oly trth-dcg cotracts wth each maager HQ the ses: ( α( Θ ad ( v α Θ to provde cetves for the maagers to operate effcetly; ( the trasfer-prcg rle to maage teral trade gve effcet dvsoal operatos; ad ( β( Θ ad ( v β Θ to garatee trthfl reportg gve the other cotractg compoets 4

CB Alog the les of Step 3 of Theorem proof, effcet dvsoal operatos whe q = satsfy ( Θ, argm z (, ( / Z + v v v ( Θ z ( Z z C z b z h v v z, argmax R, z b z h v / v ad (A-39 (A-40 To provde cetves for the maagers to operate ther dvsos effcetly, HQ sets proft shares 8 ( ( v ( v ( v v v α( Θ = ; α( Θ = (A-4 h h We se the followg otato to represet each dvso s effcet cash flow (cldg the dvsoal maager s expected compesato ad the frm s gas from trade: v v v v ( ( ( ( ( ( ( v R Θ, R, z Θ, b z Θ, h ; (A-4 v ( v ( v C ( Θ, C, z ( Θ, + b z Θ, h ; (A-43 v ( v R ( v C ( ( ( Γ,, Θ, Θ Θ, Θ, (A-44 Atcpatg β( Θ ad ( v β Θ specfed below, alog the les of Steps 3 ad 4 of Theorem proof, the frm s optmal teral trade decso s q v ( Θ, Θ, = f ad oly f E ( CB v The cost-based trasfer-prcg rle ( Γ,, Θ, Θ 0 Θ T Θ that mplemets ths decso s detcal to (9 (A-45 HQ garatees trthfl reportg at a mmm cost wth the followg fxed-salary compoets of maagers compesato (ths ca be checed sg the Mrrlees, 986 techqe: ( CB v ( Θ = E v q ( Θ, Θ, b ( z ( Θ, v ( Θ T( Θ C(, z ( Θ, Θ β α v= ( ( ( ( ( ( CB j v j j j j + E v q,, b z, v v ; Θ Θ Θ Θ v= j= + v CB v v v v v v ( Θ = E q ( Θ, Θ, b ( z ( Θ, v ( Θ Γ(,, Θ, Θ Θ β α = ( ( ( ( ( ( CB v j j j j + E q,, b z, v v Θ Θ Θ Θ = j= (A-46 (A-47 8 As expected, the prodcto maager s proft share s the same as (7 43

Step We ow show how egotated trasfer prcg allows the frm to dmsh the cost-based-prcg method s effceces Itally, we mata the assmpto that HQ ca se β( Θ ad ( v β Θ to spport perod-0 trthfl reportg a perfect Bayesa eqlbrm (we wll call sch a eqlbrm a trthfl PBE wth the followg HQ-madated strmets: ( proft shares detcal to the oes (A-4 ; ( = ; ( HQ s terveto threat to mpose the optmal cost-based trasfer prce ad let the maretg maager mae the orderg decso Cosder ay game hstory a = Θ, Θ Defe ˆ v ( Θ, Θ as follows: 0 ϒ wth ( v ˆ Θ, Θ = ; v v If R ( Θ, > E C ( Θ,, Θ let v v ˆ, ; v v If R ( Θ, < E C ( Θ,, Θ let v v ( Θ Θ = Otherwse, mplctly defe ˆ (, v Θ Θ by ˆ v v ( Θ Θ Θ = ( Θ R,, E C, Θ I We se U ( to represet the terveto-stage tlty chage of maager { } ratoalty, f ˆ v > ( Θ, Θ, I (, v,, I (, v v U Θ Θ = U Θ Θ, = 0; f ( Θ Θ, By seqetal ˆ, : ( ( Θ ( E C, C, ; Θ ( ( Θ ( R, E C, Θ U Θ, Θ,, = α Θ E C Θ, C, z Θ, b z Θ, v I v = α Θ Θ Θ U Θ, Θ, = α Θ R, z Θ, E C Θ, b z Θ, v I v v v v v v = α Θ Θ Θ (A-48 (A-49 I ay trthfl PBE where maretg s perod- prce offer v tha or greater tha ( p reveals whether s (wealy less ˆ Θ, Θ, prodcto s acceptace strategy taes the form of two ct-off rles: ˆ v Θ, Θ If µ (, ϒ d =, prodcto accepts prce offer p f ad oly f * I v * α( Θ ( p C ( Θ, δu ( Θ, Θ,,, or, eqvaletly (becase C (, ad oly f ˆ ( Θ, p, wth ˆ (, p Θ defed as follows: * * If p > δe C ( Θ + ( δ C ( Θ the ( p,,, Θ,,, Θ ˆ Θ, = ; ˆ, ; * * If p δe C ( ( δ C ( < Θ + Θ the ( p Θ = Θ s creasg f 44

Otherwse, mplctly defe ˆ (, * * Θ p by ( ˆ p = δe C Θ + δ C Θ ( Θ p ˆ v Θ, Θ If µ (, ϒ d = 0, eqvaletly, f ( Θ, p, wth (, Θ p * If p > C ( Θ,, the ( p prodcto accepts prce offer defed as follows: Θ, = ;,,, Θ (A-50 * p f ad oly f p C ( * If p < C ( Θ,, the ( Θ, p = ; Otherwse, mplctly defe (, * Θ p by p = C ( Θ, ( Θ, p 0 v Now cosder the followg pre strateges by the maretg maager after a = ( Θ Θ Case : If ˆ v v ( Θ, Θ, maretg offers prce p ( Θ, Θ, that solves ( ˆ v * {( F ( p F( ( R ( E C ( p } Θ Θ δ + δ Θ Θ max,,, p 0 Θ,, or, (A-5 Case : If ˆ (, v > Θ Θ ad R ( v, C (, v Θ > Θ, maretg offers p (,, max {( F ( ( }, p F Θ R Θ v, p p 0 Case 3: If R ( v, C (,,, : (A-5 Θ Θ that solves (A-53 Θ < Θ maretg maager offers No Prodcto (A-54 We ext show that these offers ad the prodcto maager s strategy to accept maretg s No Prodcto offer ad the ct-off prce-acceptace rles ˆ (, Θ p ad ( Θ, p specfed above are eqlbrm for the cotato game startg at perod, gve a hgh eogh δ I a trthfl PBE, 0 followg ( v a = Θ, Θ, the maagers pdate ther belefs as follows: v v v (,(, f ( F F v µ Θ Θ = f ; v (,(, f F F µ Θ Θ = f ; Θ ( v µ, Θ, Θ = 0 otherwse; (A-55 Θ ( ( v µ, Θ, Θ = 0 otherwse (A-56 Gve these belefs ad the prodcto maager s strategy, f R ( v C ( Θ, < Θ,, ay prce offer by the maretg maager that has a strctly postve probablty of beg accepted mst satsfy > ( Θ,, whch, sce ths mples p R ( v p C v maretg maager Wth R ( Θ < C ( Θ < E C ( Θ > Θ,, reslts strctly egatve tlty for the,,,, Θ terveto-stage trade also 45

strctly lowers the maretg maager s tlty The maretg maager ths offers No Prodcto v We tr to Case Wth ( ˆ Θ, Θ, f prodcto rejects maretg s offer p, there wll be teral trade at = Gve prodcto s ct-off strategy, maretg s assessmet of the probablty that ˆ ( Θ, p v a prce p s accepted eqals µ (, ( Θ, Θ d; maretg s tlty chage whe ths prce s accepted s v v α( Θ ( R ( Θ p U (,, I v, If the prce s rejected, maretg ears the tlty Θ Θ oe perod later Sbstttg (A-49 ad (A-56, maretg pcs ( ˆ F ( Θ, p F( v v α( Θ R ( Θ, p F( F( ( ˆ F ( Θ, p F( v v * + δα ( Θ R ( Θ E C ( Θ Θ F( F( whch, after rearragg ad dvdg by ( v ( ( ( α F F 0, I Case, wth ˆ v > ( Θ, Θ, maretg s assessmet of the probablty that ( Θ, p v µ (, ( Θ, Θ d; wth o terveto-stage trade, maretg pcs F ( ( Θ, p F( v v α ( Θ R (, p, F( F( Θ whch s eqvalet to (A-53 p to maxmze,,, Next, we show that, for a large eogh, Θ > yelds (A-5 p s accepted eqals p to maxmze ˆ Θ, Θ We do v v δ p ( Θ, Θ, reveals whether ( ths by cotradcto: sppose for some ˆ v ( Θ, Θ <, p ( Θ Θ v = p ( Θ v Θ v Dfferetatg (A-5 ad rearragg, p (,, Θ Θ satsfes,,,, v v ( Θ, Θ, = ( Θ, ( δ + δ (, Θ Θ ( ˆ v F ( Θ, p ( Θ, Θ, F( ˆ v (, (,, ˆ v f Θ p Θ Θ ( Θ, p Θ, Θ, p R E C * From (A-53, ( v p,, p Θ Θ satsfes v v ( R ( p ( v ( Θ, ( Θ, Θ, ( F p F Θ, Θ, = Θ, f p p ˆ Θ, Θ <, v Sce ( v v ( Θ, Θ, Θ, ( Θ, ( Θ, Θ, p (A-57 (A-58 46

v * * v ( Θ ( δ + δ ( Θ ( Θ > ( Θ R, E C, E C, R, Θ Θ (A-59 From (A-50 ad (A-5, for some ( 0,, δ whe δ < δ <, we have, for all p > 0, ˆ ( Θ, p = > = ( Θ, p p ( ˆ δ C Θ, ( Θ, p C ( Θ, ( Θ, p p ˆ v v * > Θ, Θ, p ( Θ, Θ, < E C ( Θ,, Θ ad ths Sce v v v * p ( Θ, Θ, δ p ( Θ, Θ, > p ( Θ, Θ, δe C ( Θ, Θ Usg the defto of ˆ (, Θ p (A-50, of ( Θ, p ( Θ p ( Θ Θ v < ( Θ p ( Θ Θ v ( ˆ F ( Θ, p ( Θ, Θ, F F ( Θ, p ( Θ, Θ, F < ˆ v v f ( Θ, p ( Θ, Θ, f ( Θ, p ( Θ, Θ, (A-5 alog wth (A-6 gves ˆ,,,,,, ad, ths, sg the mootoe rs rato codto, v v Combg (A-59, (A-60, ad (A-6 gves p ( v p ( v Usg smlar logc, for some ( 0,, δ as log as δ δ, (A-60 (A-6 (A-6 Θ, Θ, > Θ, Θ,, provdg the cotradcto ˆ Θ, Θ <, t s ot possble that v < < f ( v p Θ, Θ, solves v * max {( F ( (, p F( ( (, ( (, } Θ R Θ δ + δe C Θ p p 0 Θ Ths, whe the maretg maager s prvate formato s ˆ v ( Θ, Θ, the maager does ot mmc the prcg strategy sed whe prvate formato s ˆ v > ( Θ, Θ Ad whe the maretg maager s prvate formato s ˆ v v > ( Θ, Θ, the maager does ot mmc by offerg p ( Θ, Θ, for some ˆ v ( Θ, Θ, sce ˆ ( ( Θ, p < Θ, p ad (A-53 mply ( ˆ v v v ( F ( Θ, p ( Θ, Θ, F( ( R ( Θ, p ( Θ, Θ, v v v < ( F( ( Θ, p ( Θ, Θ, F( ( R ( Θ, p ( Θ, Θ, v v v F ( Θ, p ( Θ, Θ, F ( R Θ, p Θ, Θ, ( Off the eqlbrm path, followg a detectable devato, belefs are pdated as follows: the maretg maager does ot revse pror belefs; the prodcto maager pdates belefs to µ, ϒ = Maretg s strategy followg a prodcto devato s to order the prodct f ad oly 47

ˆ Θ, Θ Prodcto s strategy followg a maretg-maager devato s: ( to accept a No v f ( Prodcto offer, ad ( accept a prce offer { } * v p f ad oly f p > C ( Θ R ( Θ max,,, max, < δ <, gve maretg s strategy, f offered No Prodcto, the prodcto Now, wth { δ δ } maager always accepts Otherwse, the ct-off strateges ˆ (, Θ p ad ( Θ, p are optmal Ad maretg s strateges (A-5-(A-54 are a optmal respose for the cotato game startg at NEG v perod of a trthfl PBE We se q (,,, { 0,} 0 ths PBE, whe ( v Θ Θ to represet the teral-order otcome a = Θ, Θ, ad the maagers prvate-formato realzatos are ad NEG v ( Θ Θ represets the preset vale, at tme 0, of q ( Θ Θ NEG v qˆ,,, ( δ q (,,, : NEG v NEG v qˆ Θ, Θ,, = Θ, Θ,, f there s teral trade at tme ; f there s o teral trade ( NEG v qˆ Θ, Θ,, = 0 HQ sets β ( s as follows: ( NEG j v v ( Θ = E v qˆ ( Θ, Θ,, b ( z ( Θ, v ( Θ p ( Θ, Θ, C(, z ( Θ, Θ β α v= ( ( ( ( ( ( NEG j v j j j j j + E v qˆ,,, b z, v v ; Θ Θ Θ Θ v= j= + ( v NEG j v v v v v v v v v v ( Θ = E qˆ ( Θ, Θ,, b ( z ( Θ, v ( Θ R(, z ( Θ, p ( Θ, Θ, Θ β α = ( ( ( ( ( ( NEG j v v j j j j + E qˆ,,, b z, v v Θ Θ Θ Θ = j= Wth the off-eqlbrm belefs ad strateges specfed above, these fxed-salary compoets of maagers compesato cotracts spport perod-0 trthfl reportg the eqlbrm specfed above (as before, the Mrrlees, 986 techqe mples ths as log as z (, v v z ( Θ, s decreasg v, whch tr holds by (A-39 ad (A-40 Θ s decreasg ad Step 3 The aalyss proceeds closely alog the les of Theorem proof above (thogh, of corse, here t s o loger that case that egotated trasfer prcg leads to teral trade f ad oly f there are gas from trade The ey steps the aalyss are as follows From Step ad Step above, ote that f q q v ( Θ, Θ, =, the R ( Θ, > E C ( Θ, ; Θ ths, I v U ( CB v ( Θ, Θ, > 0; ad, ths, Θ, Θ,, = for all Θ Ths, wheever there s teral trade der optmal cost-based NEG v 48

trasfer prcg, there s teral trade der egotated prcg of Step (delayed at most two perods v Cosder the regos Θ Θ where (, v Γ, Θ, Θ v > 0 ad ( v v Γ,, Θ, Θ < 0(the exstece of these regos s garateed becase the frm s teral-trade decso s o-trval Uder cost-based v trasfer prcg, the o-trade effcecy s the sbset of v Θ Θ where ( Γ,, Θ, Θ > 0 yet v E (,,, v v v Γ Θ Θ < 0 Θ The set S (, { sch that (,,, 0} ad cotos Whe ( v v S Θ, Θ, the maretg maager offers the prce p (,, v (A-53 The prodcto maager revses belefs to v accepts the prce offer f ad oly f ( Θ p ( Θ Θ * f p (, v, C (, Θ Θ Θ Cosder (A-53, reprodced below: {( F ( ( } p F Θ R Θ v p p 0 Sce ( v, Θ Θ Θ Γ Θ Θ > s o-empty Θ Θ that solves (,, v µ Θ Θ = f f t S t dt ( Θ, Θ ad,,, Usg (A-5, there wll be teral trade max,, (A-53 S Θ Θ s o-empty, for a o-empty sbset of, v * R Θ, > C Θ, Ths, for a o-empty sbset of, Θ * v v C, p (,, R (, Θ ( ( Θ Θ Θ < Θ (ths gves a strctly postve vale of the objectve (A-53; settg the prce otsde these bodares gves a zero-vale objectve Ths, wth strctly postve probablty, there s teral trade der the PBE of egotated trasfer prcg the o-trade effcecy rego The sbset of the set wth trade der egotated prcg the cost-based o-trade effcecy rego s depedet of δ (becase, at =, there s o trade at terveto stage Ths, for a hgh eogh δ { δ δ } < delay max,,, the vale of ths trade to the frm strctly exceeds the opportty cost from 49

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