Pontifícia Universidade Católica do Rio Grande do Sul FACULDADE DE ADMINISTRAÇÃO, CONTABILIDADE E ECONOMIA PÓS-GRADUAÇÃO

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1 Potifícia Uiversiae Católica o Rio Grae o Sul FACULDADE DE ADMINISTRAÇÃO, CONTABILIDADE E ECONOMIA PÓS-GRADUAÇÃO TEXTO PARA DISCUSSÃO Nº02/2008 LOCATION, COMMUNICATION, AND CONTROL WITHIN A VERTICALLY INTEGRATED FIRM Carlos Euaro Lobo e Silva Geoffrey J. D. Hewigs Porto Alegre 2008 Campus Cetral Av. Ipiraga, 6681 P. 50 CEP: Foe: (51) Fax (51) ppge@pucrs.br

2 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm Carlos Euaro Lobo e Silva Regioal Ecoomics Applicatios Laboratory (REAL), Uiversity of Illiois at Urbaa-Champaig Geoffrey J. D. Hewigs Regioal Ecoomics Applicatios Laboratory (REAL), Uiversity of Illiois at Urbaa-Champaig Abstract: The mai purpose of the paper is to provie a lik betwee the locatio ecisio a the iteral orgaizatio of firms. I the moel that focuses o the relatioship amog agets withi the firms, the ower of the firm makes two ecisios: who will have the formal authority (the ower or the cotroller) a where the maufacturig plat will be locate (ear or far from the ower). The results show that those two ecisios are iterepeet. More tha that, for certai parameters, the corporatio goes from the seco best to the first best oly if it chages the ecisio about both aspects; chagig just either the elegatio scheme or locatio may rive it to a iferior outcome. I these cases, a flexible maagerial structure turs out to be a ecessary coitio for firms to beefit from locatioal avatages. The positive correlatio betwee the ecetralizatio of ecisio-makig a geographic ecetralizatio preicte by the moel is supporte by empirical research. Fially the recet heaquarter locatio ecisio by the Boeig compay is use to illustrate the results obtaie. 1. Itrouctio Vertical itegratio ca be efie as a process i which more tha oe lik of the prouctio chai takes place withi the bouaries of a corporatio. I the iteratioal trae literature, may papers o vertically itegrate multiatioals cosier the prouctio of fial goos as a two-phase process; iputs prouce i the maufacturig plat are combie with the heaquarter services to prouce the fial goo. The prouctio of iputs may or may ot be place ear the heaquarters. I the iteratioal trae termiology, whe iputs a fial goos are prouce i ifferet places we have a vertical multiatioal sice each coutry is see as a sigle poit. I a semial paper, Helpma (1984) costructs a moel of moopolistic competitio with two coutries, two factors, a two sectors oe prouces homogeeous goos a the other prouces ifferetiate goos. He assumes that the ifferetiate goo is prouce by two processes: oe uses oly uskille labor (maufacturig plat) a the other uses oly skille labor (heaquarter). Moreover, they ca be place i ifferet coutries. Oe of the iterestig fiigs is that, aalogous to the results i Heckscher-Ohli moels, the regio of factor price

3 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 2 equalizatio is elarge. It happes because the worl ca ow be see as a ecoomy that prouces three proucts: homogeeous goos, parts of ifferetiate goos with uskille labor, a parts of ifferetiate goos with skille labor. Thus, the specializatio ca be eve more itesive whe the heaquarters are cocetrate i the coutry with a abuace of skille labor. 1 I Helpma s moel, the firms ecisios are rive by iffereces i wages. Recet papers have show eviece that the trae of iputs has substatially icrease arou the worl over the last few ecaes, a result of the icrease of trae withi a betwee firms. Therefore outsourcig a itra-firm trae seem to have ha their relevace expae i the global ecoomy as a cosequece of the fact that the prouctio process has become multi-locatioal. Grossma a Helpma (2004), Atras a Helpma (2004), a Atras (2003) amog others have use icomplete cotractig to moel the ecisio of firms about ot oly their locatio but also the owership structure. Therefore, those papers, with the exceptio of Helpma (1984), go beyo what we propose here. The preset paper takes as give the fact that the whole prouctio process takes place withi the bouaries of a sigle firm. At first sight, this restrictio coul be see as a weakess of the moel; however what is claime here is exactly the cotrary. Eve whe the owership structure is ot uer iscussio (as i the case of Boeig s recet ecisio), icomplete cotracts establishe amog iiviuals of a give firm remai importat i etermiig the optimal locatio strategy. Icomplete cotractig provies a appropriate framework to moel owership structures. The iea here is to go oe step back a, by usig the methoology of recet papers, icomplete cotractig, aress the issue stuie by Helpma (1984): how o vertically itegrate firms ecie their maufacturig plat locatio? Of course, the aim of this paper is to a oe more elemet (iteral orgaizatio of firms) to the ebate about vertical multiatioals, rather tha substitutig ay aspect previously ietifie. While Helpma s moel focuses o iffereces i factor prices, i this work the variable labele locatioal avatage will sta for ay ehacig feature of a give regio (istace from iputs a markets, wages, etc). The moel, rawig o Aghio a Tirole (1997), is base o a iformatio structure amog iiviuals of a firm. The iformatio is essetial for them a the spatial aspects, which are the focus here, ca itrouce iefficiecy ito the chaels of commuicatio. Grossma a Helpma (2004), Atras a Helpma (2004), a Atras (2003) o ot take the cost of 1 See Feestra (2004) for refereces o papers that poit out other locatioal avatages besies wage iffereces.

4 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 3 iteractio (those of commuicatio, cotrollig, or trasactio) ito accout as the theory of firm traitioally has oe. 2 Therefore, this become a secoary objective of the preset paper: preparig a framework that, oe ay elarge a aopte, ca be use to aswer questios relate ot oly to locatio but also to owership arragemets. Usually, moels for regioal ecoomics allow all factors to move across regios 3 that, i tur, te to reuce the locatioal avatages withi a coutry. This may explai why the literature o regioal ecoomics eglects the existece of multi-locate firms a the importace that their locatio ecisios might have i boostig the ecoomic evelopmet of a give uevelope regios. Fujita a Krugma (1995) provie exceptios; eve though they o ot iclue multi-locate firms i their aalysis about the ecoomic trasitio from a moo-cetric ecoomy to a multi-cetric ecoomy, they suggest the iclusio as a iterestig extesio of their moel. They commet: ( ) suppose that each firm cosists of multiple uits (e.g. HQs, R&D uits, a maufacturig plats) which ca be locate separately. The, sice ifferet uits will follow ifferet agglomeratio forces (e.g. availability of busiess services a coveiece of face-to-face commuicatio for HQs), we will be able to evelop a richer class of spatial moels (p.524). I the preset moel, there is oly oe firm forme by two uits: the heaquarters (HQ) a the maufacturig plat. Two iiviuals work i this firm: the ower (also calle as superior or pricipal throughout the paper) who resies i the HQ, a the cotroller (suboriate or aget) who maages the prouctio a lives at the maufacturig plat. The HQ is place at the cetral poit of the worl surroue by ifiite peripheral poits. The istace betwee ay peripheral poit a the cetral oe is costat. The maufacturig plat ca be locate either at the cetral poit ear by the HQ or at the peripheral poit where the locatioal avatage for maufacturig plat is the highest oe. The ower a the cotroller have oly oe task: they have to ecie the best project amog alteratives. This ecisio process starts after the ower of the firm ecies two thigs: who will have the formal authority (the ower or the cotroller) a where the maufacturig plat will be place (ear or far from the corporatio s heaquarters). The efiitio of formal 2 Eve though Coase (1937) argues that there is a cost of usig the price mechaism (p.390) a withi a firm they are greatly reuce, he says also that the cost of egotiatig cotracts is still preset i the firm. The aalysis of trasactio cost is the cetral part of his argumets. Regarig the ees of examiig the relatioship withi the firm, see Simo (1991). 3 See Fujita et al. (1999) a Fujita a Thisse (2002)

5 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 4 authority will be better uerstoo i the ext sectio where the ecisio-makig mechaism is explaie i more etail, but for ow it ca be uerstoo as the right to have the fial ecisio about which project will be chose. Thus, the ower eals with two trae-offs: Placig the maufacturig plat far from the ower etails, o oe ha, a high cost of cotrollig the process of prouctio a, o the other ha, gais i terms of locatioal avatages (e.g., lower wages or a costs). The elegatio of power icreases the icetive of the cotroller; however the ower has less cotrol over the outcome. The results will reveal that the ecisios about both the locatio of the maufacturig plat a the iteral elegatio scheme are iterepeet. More tha that, for certai parameters, the existece of multi-locate firms (here represete by those firms with heaquarters a maufacturig plat geographically separate) ca be justifie oly by the existece of a flexible maagerial structure. I other wors, uer those parameters, the first best is to elegate power to the cotroller a to place the maufacturig plat far from the ower, whereas the seco best is the opposite strategy: o elegatio a locatioal proximity betwee heaquarter a maufacturig plat. Therefore, if the ower ites to rive the firm from the seco best to the first best (give a ew cost of commuicatio for istace) she has to chage both aspects at oce; otherwise the firm ca experiece the worst outcome. I iscussio a coclusio, the Boeig compay s recet heaquarter locatio ecisio is aalyze a it is claime that it is a goo case stuy where elegatio a locatio ecisios work complemetarily. Moreover, the fiigs of recet empirical works, especially those preset i Arita a McCa (2002), are compare to the preictios of the moel expose i the ext sectios. I sectio 2, the moel by Aghio a Tirole is presete. Thereafter, some aaptatios a spatial aspects are itrouce to ajust the moel to the purpose of the paper. Sectio 3 itrouces the moel itself. I Sectio 4, a illustratio is provie that aticipates the geeral results that are presete i Sectio 5. Discussio a coclusios are show i sectio The Basic Moel a New Developmets Formal a real authority- Followig Aghio a Tirole (1997), the moel aalyzes the iteractio betwee a superior (pricipal) a a suboriate (aget) uer a particular circumstace: they have possible projects i ha a must ecie which oe will be

6 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 5 uertake. Both aget a pricipal will ivest some effort to lear about the project. Each oe ca lear either everythig or othig about it. The probability of uerstaig everythig regarig the project is the amout of effort, which varies betwee zero a oe. The pricipal ca elegate the ecisio to the aget, thus trasferrig, the formal authority to the aget. Otherwise, the pricipal keeps the formal authority with her. 4 Here, it is importat to uersta i more etail what formal authority a real authority mea i this moel. The ecisio process ca be see as a game with (at most) four perios. I the first perio, as metioe above, the pricipal makes two ecisios: who will have the formal authority a where the maufacturig plat will be place. I the seco perio, each oe ecies her ow level of effort to be mae i orer to lear about the projects a, the, they lear either everythig or othig. Next, after the learig process, the iiviual who has the formal authority that is efie i perio 1 plays i the thir perio. Assume that player X has the formal authority. If player X has leart everythig i perio 2, she chooses the project a the ecisio is mae (i this case, there will ot be the fourth perio). Otherwise, player X gives player Y the real authority, i.e., the right to choose the project. Thus, i the last perio, player Y will ot choose ay project oly if he or she has ot leart aythig i perio 2. I this case, the outcome will be zero for both players. Otherwise if player Y kows everythig about the projects, player X will rubber-stamp player Y s ecisio. Note that, i this moel, both players tell the other the truth whe they lear othig. It happes because the authors assume that there is a project with a very egative expecte payoff; this will make the expecte outcome of choosig a project without kowig aythig about it egative. Fially, there is some ivergece betwee the iterests of the pricipal a the aget. If the pricipal chooses the project, her payoff is B, but whe the aget makes the fial ecisio, the pricipal s expecte payoff will be a fractio of B. The reverse is true: the aget s expecte payoff is lower for the case i which the pricipal ecies. The origial moel ca be represete by the ext four equatios. Equatios (1) a (2) represet, respectively, the utility of the pricipal a the aget uer o elegatio, i.e., whe 4 A cotract efies who ows the formal authority. The resiual rights whose efiitio ca be fou i Grossma a Hart (1986) are etermie via allocatio of formal authority. The formal authority ca be see as the assets i the relatioship. The party that has the formal authority ca ecie uer uexpecte circumstaces. Regarig the relatioship betwee owership of assets a icetives, Hart a Moore (1990) provie a very iactic example o page 1122.

7 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 6 the formal authority belogs to the pricipal. Equatios (3) a (4) preset the utilities uer elegatio. Iterpretig equatio (1) will assist i makig all the other equatios clear. E a e represet the pricipal a aget s efforts, respectively. The payoff of the pricipal is B whe the best project is chose accorig to her prefereces a α B whe the aget chooses the project. g(e) measures the cost of effort mae to uersta the project a it is a covex fuctio. The margial cost is zero whe effort is zero a it is ifiite whe the effort is oe. u = EB + (1 E) eα B g ( E) (1) p p u = Eβb + (1 E) eb g ( e) (2) a a u = eα B + (1 e) EB g ( E) (3) p p u = eb + (1 e) Eβb g ( e) (4) a a Note that i equatio (1), EB is the probability of ietifyig the best project times the payoff that this project yiels to the pricipal. The effect of elegatio o the pricipal s payoff ca be see i equatio (3). (1-e) precees EB; which meas that the choice of the pricipal will be uertake oly if the aget oes ot lear aythig. Otherwise, the aget will choose the project a it is represete by the first term of the equatio. Aaptatios a spatial aspects As metioe i the itrouctio, the ower a the suboriate form the firm. We ca thik of the suboriate as the cotroller of a maufacturig plat. The cotroller a the plat are always locate i the same place, whereas the ower is i the HQ, i.e., at the cetral poit. Aitioally, give the ecisios regarig elegatio a locatio, the ower chooses the level of effort for the task of learig about the project. The story takes place i a worl with a cetral poit where the ower of the firm is locate ecircle by ifiite poits. The istace betwee ay peripheral poit a the cetral oe is the same. Each poit might represet a particular city. I Aghio a Tirole s (1997) moel, the aget ecies the effort base ot oly o the formal authority arragemet, but also o the effort expee by the pricipal. The moel that will be presete here oes ot take the seco aspect ito accout. The assumptio behi this simplificatio is that the cotroller oes ot kow how much effort the ower is carryig out. Thus, the utility fuctio of the aget will ot be cosiere i this moel. Noetheless, although the aget s maximizatio problem is ot presete explicitly, it is assume that she

8 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 7 respos to the formal authority scheme efie. Istea of etermiig the amout of effort of the agets by solvig their maximizatio problems, it will be exogeously etermie for each formal authority scheme. Appeix A provies some argumets to justify this simplificatio. A istictio betwee the preset moel a the oe costructe by Aghio a Tirole (1997) is that, ow, the pricipal is the ower of the firm a the aalyses will be focuse o her utility fuctio. Thus, the utility fuctio of the pricipal is compose by the moetary retur of the projects a the cost of effort carrie out by her. As metioe, the choice of placig the maufacturig plat far away from the ower brigs avatages a isavatages to the firm. We assume that the cetral poit is the best locatio for the ower, but this may ot ecessarily be the case for the maufacturig plat. The oly sure avatage of havig the maufacturig plat close to the ower has to o with the efficiecy of commuicatio betwee the ower a the cotroller. Therefore, i other wors, the isavatage of placig the plat far from the ower is that commuicatio is less efficiet or oe coul cosier this to imply that the cost of implemetig a efficiet commuicatio system is higher. The creatio a use of the Iteret is a goo example of icreasig the efficiecy of log-istace commuicatio, eve though it is still less efficiet tha egotiatios betwee epartmets locate sie-by-sie. Joes a Kierzkowski (2003) poit out that some profou prouctivity improvemets i service liks have bee witesse i the last ecaes. Moreover, they say that the chages i commuicatio costs have probably bee the most sigificat i lowerig the service costs require to co-oriate spatially separate prouctio fragmets (p.16). There is a crucial aspect of the moel that shoul be uerstoo. The ower is see as a receptor of iformatio comig from the maufacturig plat. The ower lears from that iformatio a, therefore, ay problem of efficiecy of commuicatio will hurt her uerstaig. Moreover, the oly effort ivolve i this commuicatio is the ower s. The cotroller oes ot ee ay commuicatio to lear about a evaluate the projects sice the project is relate to the maufacturig plat cotrolle by him i loco. Therefore, eve whe the cotroller a the ower are far from each other, the cotroller oes ot have ay aitioal cost

9 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 8 to lear about the project because the source of iformatio is always close to him. 5 As a cosequece, o effort of the ower meas there is o commuicatio betwee her a the cotroller. I that case, the cotroller will have the real authority. The questio, ow, coul be why shoul the maufacturig plat be locate far away if this oes ot seem to be esirable for the ower? As we have see i the first sectio, some reasos ca be avace to explai why firms implemet the multi-locatioal system. The iffereces i prices of factors across locatios are examples of those reasos. Here, we assume those avatages o exist; however, we o ot ivestigate which oes they are for a particular firm. Istea, i a imagiary process, we take all the possible reasos ito accout a rak the cities (ifiite cities i the cotiuous case) accorig to their appropriateess for the placemet of the maufacturig plat. 6 We ca ormalize this iex, assumig that the appropriateess of locatig the plat i the city of the ower is zero. As ote earlier, there is o special reaso to believe that the city of the ower presets more competitive avatages tha ay other i terms of those elemets aalyze here. Thus, oe shoul expect to have some cities with positive a others with egative iices. Sice the istace betwee the cetral poit where the ower is locate a ay other poit is the same, the ecisio turs out to be either keepig the maufacturig plat at the cetral poit where there will be the highest efficiecy i commuicatio but at the cost of givig up the chace of choosig the best place for the maufacturig plat, or placig it i the city that presets the highest iex at some cost i terms of the efficiecy of commuicatio. This is the basic traeoff for the ower i terms of locatio choice. Showig how this trae-off iteracts with the elegatio ecisio is the mai propose of the ext sectio a the core of the preset paper. 3 The Moel Depeig o ower s ecisio about the formal authority, her utility fuctio ca be represete as follows: 7 5 Although the ower ees iformatio that comes from the maufacturig plat, there is o correlatio betwee the learig processes of the ower a the cotroller. We ca justify this fact by assumig that, first, both ee objective iformatio to lear but they iterpret it by themselves, separately. Seco, the ower ca commuicate to ay worker a, thus, the cotroller caot limit the ower s kowlege. 6 Note that the (es)avatage i terms of iteral commuicatio is ot take ito accout here. This aspect will be treate separately followig what was sai i the paragraph above. The criterio of the rak takes i cosieratio the traitioal reasos for vertical multiatioal. 7 w oes ot epe o E sice it ca be see as, for example, the ifferece i cotrollers wages.

10 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 9 u = E B + (1 E ) e α B + σ l(1 te ) + w (5) u = e α B + (1 e ) E B + σ l(1 te ) + w (6) If the maufacturig plat is locate far from the ower, part of the effort uertake by the ower is lost i the process a, the, t is greater tha oe. Otherwise, t is equal to oe a there is o loss of efficiecy. w represets the gai of havig chose the best city to place the maufacturig plat without cosierig the effects of the loss of effort. Therefore, w will be positive if ower a cotroller are i ifferet places a zero otherwise. I Equatios (5) a (6), σ has a positive value a ca be see as a sort of fixe cost of the learig process. It is iclue i the utility fuctio so that the results ca be algebraically simpler. From (5) a (6), we erive the level of effort carrie out by the ower uer both formal authority schemes: E E B(1 eα ) tσ = B(1 e α) t B(1 e ) tσ = B(1 e ) t where t = 1 if the maufacturig plat a ower are locate at the same city a t > 1 otherwise. The ext step is to check which arragemet will be chose by the ower. There are four alteratives: 1) o elegatio a sigle locatio (s); 2) o elegatio a multi-locatio (m); 3) elegatio a sigle locatio (s); a 4) elegatio a multi-locatio (m). First, we will compare the first two. Pluggig (7) ito (5) yiels: σ us = eα B + B(1 eα ) σ + σ l B(1 eα ) (9) B(1 eα ) tσ um = eα B + σ + σ l w t + B(1 eα ) (10) Therefore, the coitio that the ower prefers (s) to (m), wheever the efforts are positive, 8 is: ( t 1) us um = B(1 eα ) + σ l(1/ t) w > 0 (11) t From (7), it is possible to see that: 9 8 If t is high eough, the effort of the ower of a multi-locate firm is goig to be zero. As a cosequece, the ecisio turs out to be iepeet o t. (7) (8)

11 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 10 te E E m s s B(1 eα ) tσ = B(1 e α) B(1 eα ) σ = B(1 e α) Equatios (12) a (13) yiel to: m (12) (13) > te (14) Therefore, because of the imperfect commuicatio i (m), the ower carries out less effort tha she oes uer perfect commuicatio. Thus, the probability of learig about the project is smaller i (m) for two reasos: the commuicatio is imperfect a, as a cosequece of that, she carries out less effort. Now, we ca aalyze the coitio escribe i (11). The first term is positive a represets the greater probability of learig uer (s) tha uer (m). The seco term, the ifferece i cost, is egative, sice t is greater tha oe. The reaso was alreay metioe; the real effort uer (s) is greater tha uer (m). Fially, w is positive a, give the sig, the gai of choosig the best place to locate the maufacturig plat favors alterative (m). It is worth examiig closely how the coitio (11) respos to variatios i t a α. The aalysis about α is straightforwar. A high α meas that the iterest of the cotroller is similar to the ower s iterest. Therefore, as α icreases, the icetive of the ower to make a effort ecreases i both cases sigle a multi-locatio. Thus, the ifferece i terms of efficiecy of commuicatio becomes less importat, favorig the multi-locate firm. The effect of t o the coitio (11) shoul be compute takig ito accout the restrictio that oes ot allow the effort of ower to be egative. The partial erivative show i (15) is true whe the coitio (15 / ) is satisfie. Otherwise, the effort of the ower is zero a a icrease i t oes ot affect the firm s outcome. ( ) u ( 1 α ) us um B e m tσ = = > 0 2 t t t if ( α ) 1 (15) B e > tσ (15 / ) a 9 Note first that uer o elegatio a multi-locatio (equatio 12), te m is the real effort mae by the ower. Moreover, uer o elegatio a sigle locatio (equatio 13), t =1.

12 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 11 ( u u ) s m t otherwise. = 0 As shoul be expecte, a larger t favors the sigle-locate firm. 10 Agai, if the iefficiecy of commuicatio is alreay high eough, the effort of the ower of the multilocate firm is goig to be zero. As a result, the icrease i t will ot have ay effect o the locatioal ecisio. The ituitio is that whe the iefficiecy of commuicatio is high eough, i a multi-locate firm the real authority always belogs to the cotroller who aalyzes the project i loco. Sice there is o commuicatio betwee the cotroller a the ower, the value of t oes ot matter. The compariso above oes ot take ito cosieratio the possibility of elegatig formal authority. Now, the iea is the reverse. O the oe ha, this assumptio will be relaxe, allowig firms to ecie their iteral structure a, o the other ha, the possibility of locatig the maufacturig plat i a ifferet city from the ower s is elimiate. I other wors, the iea is to compare the situatio (s) where there is o elegatio a a sigle-locate firm a (s) where there is elegatio a a sigle-locate firm. This ew compariso is similar to the oe i Aghio a Tirole s (1997) moel sice the spatial aspect is ot take ito accout i either case. Noetheless, i their paper, the cost fuctio is ifferet a, more importatly, they assume that the effort of the cotroller epes ot oly o the formal authority scheme, as is the case here, but also o the effort of the ower. They o ot show explicitly the solutio of the problem a these two iffereces metioe make the moel algebraically solvable. Usig Equatio (8), cosierig t = 1 a w = 0, effort uer (s) will be: E s B = ( 1 e ) B( 1 e ) σ Pluggig (17) i (8): (16) (17) 10 I more etails, iitially keepig everythig else costat - as the efficiecy of the log-istace commuicatio goes ow, the expecte pay-off of the project for the ower of a multi-locate firm reuces, say, i k uits. The, the ower imiishes her effort, which, i tur, has two cosequeces: (1) aother reuctio i her expecte pay-off of the project a (2) a reuctio i the total cost of effort. The seco cosequece reuctio i total cost overcompesate the first. Fially, the et result for the ower of a multi-locate firm will be egative, but the loss will be less tha k.

13 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 12 σ us = eα B + ( 1 e ) B σ + σ l B ( 1 e ) (18) So, the last step is to check the ifferece i terms of utility betwee the two arragemets, usig to that e equatios (9) a (18). The compariso yiels the coitio for the ower to prefer (s) to (s): 1 e us us = ( 1 α ) Be + σ l > 0 1 eα (19) The, it follows: ( ) us us σ e = e B + < 0 α 1 e α ( ) us us us σ = = ( 1 α ) B e e 1 e (20) (21) As coul be expecte, equatio (20) iicates that wheα icreases, the iterest of the cotroller is more similar to the ower s a the elegatio of formal authority is more likely to be implemete. 11 Equatio (21) has a ambiguous result. The icrease of effort of the cotroller has two effects: (1) the ower has less cotrol over the ecisio; a (2) the ower makes less effort a that, i tur, saves costs. We ca see that equatio (21) may be positive for high e a egative for low e. 12 Basically, the ituitio is that the respose of the ower to the chages i e takes ito accout the absolute value of e, sice they are uer elegatio. The, the higher the e the less relevat the ower s effort. As a cosequece, for large e, ay icrease i e geerates a strog ower s reactio, a large reuctio of effort, which saves costs. 4. Itroucig the Results: a Illustratio Followig the sequece presete above, imagie a worl where the iteral structure of the firm is give. I other wors, the ower caot elegate formal authority. The oly ecisio will be about locatio. The, the iverse will be explore: the ower ca ecie about elegatio, but there is o possibility of placig the maufacturig plat i ay other city. Fially, the thir step 11 The proof that the erivative is always egative ca be fou i Appeix B. 12 It is clear that if (1 α)b < σ, the icrease of e always favors the situatio with elegatio of formal authority.

14 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 13 is to allow her to make a ecisio about both aspects. The parameters are chose i orer to provie the mai result of the paper. It might mea a loss of geerality, but it will ot be claime here that the locatio ecisio is always etermie by iteral structure; rather, as see i the itrouctio, the argumet iicates that the iteral structure may be a importat source of ispersio of a give firm. Assume the followig values for the parameters: σ = 0.5; B = 4; w = 0.8; e e = 0.4; = 0.6; α = 0.75; t = 1.8 B is equal to 4 i orer to guaratee a positive effort. Therefore, w shows that placig the maufacturig plat i aother city yiels for the firm a gai of 20% of the maximum obtaie by it. The effort of the cotroller rages from 0.4 to 0.6 whe the formal authority is trasferre to him. The choice of the cotroller provies 75% of the total to the ower. The efficiecy of commuicatio withi a multi-locate firm has a loss of arou 45% if it is compare to the face-to-face commuicatio, that is, about 45% of the ower s effort are waste through logistace commuicatio. I this worl, the formal authority is give to the ower. The ecisio is about whether or ot to place the maufacturig plat i aother city. As will be reveale below, the parameters favor the sigle-locate alterative. u 2.64 > u = 2.49 (22) s = m Sice we have several parameters, there are multiple ways to iterpret this result. The result show i (22) might happe because either t is high or w a α are low. Now compare the two sigle-locate optios: with a without elegatio of formal authority. u 2.64 > u = 2.32 (23) s = s Agai, the s alterative presets better results.

15 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 14 Therefore, at first sight, we coul coclue that, give those parameters, sigle-locate a o elegatio are more esirable tha, respectively, multi-locatio a elegatio. However, if we allow the ower to ecie about both aspects, the results are ifferet as show i (24): u 2.64 < u = 2.7 (24) s = m Hece, give these parameters, the best alterative is to place the maufacturig plat far from the ower as log as the ower is allowe to elegate the formal authority to the cotroller. Otherwise, she will locate the plat close to her. Table 1: Utilities of the four arragemets for ifferet values of t T No elegatio sigle No elegatio multi Delegatio sigle Delegatio multi Assumig that t is the oly parameter that sigificatly chages over time, table 1 shows the best optio for ifferet levels of commuicatio efficiecy; it also helps with the uerstaig of the ituitio behi the results of the illustratio. Note that sigle-locate firms have costat utility because the value of t oes ot matter. I aitio, for t = 1, the ifferece betwee utilities uer the same elegatio scheme is w sice there is o iefficiecy of commuicatio.

16 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 15 The key poit of table 1 is that u m > u m for large t. This happes because whe the formal authority belogs to the ower, she carries out more effort tha uer elegatio as reveale i equatios (7) a (8) a, thus, the loss of efficiecy has more impact o u m. Note that uer o elegatio a for t betwee 2.2 a 2.5, the gai w of movig the plat to the other city oes ot offset the loss of efficiecy i commuicatio, but the possibility of elegatig formal authority combie with the gai w oes offset. 5. Results I this sectio, the mai result will be presete a it will be see that the iteractio betwee formal authority a locatio of maufacturig plats always moves i a uique irectio as commuicatio costs chage, i.e., the possibility of elegatig power is ever a reaso to have a sigle-locate firm. This property oes ot epe o the parameters. Fially, there is a iscussio about the rage of the parameters that provies us the special trasactio: from oelegatio a sigle-locate to elegatio a multi-locate arragemet. Graphically, we ca see how each type respos to variatios of t. Note first that: 2 ( α ) σ u m B 1 e = + 2 t t t 2 ( ) σ 1 = + 2 t t t u m B e (25) (26) It easy to check that (25) a (26) will ever be positive because the coitio for havig positive effort is: ( α ) B e > tσ (25 ) 1 ( ) B e > tσ (26 ) 1 Otherwise, (25) a (26) will be zero. Sice σ is less tha oe, the erivatives will be egative for ay positive value of effort a zero otherwise. Note that (25) is greater tha (26) i absolute value (25 is more egative tha 26). This result happes because uer o elegatio, the effort is bigger tha uer elegatio a, cosequetly, a ecreasig t has a stroger impact o the o elegatio arragemet. Thus, the example presete before ca be illustrate i figure 1, where ay

17 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 16 evelopmet i commuicatio ecreases t, therefore, the teecy over time is to go through the graph from the right to the left. Utility a c U m U m b U s U s h g f e t=1 t t j t Figure 1: From s to m The horizotal axis shows the value of t. Whe t is equal to oe there is o iefficiecy of commuicatio. For t > t, E m is zero a for t > t, E m is zero. Note also that: a = bc = w (27) jg = Bα e + w (28) je = Bα e + w (29) eg = Bα ( e e ) (30) First, (27) reveals that whe there is o iefficiecy i commuicatio, multi-locate firms are always better off tha sigle-locate oes for obvious reasos. It is possible to see i (30) that whe t is high eough, elegatio is always better tha o elegatio sice the ower s effort is zero i both cases. I that case, the best the ower ca o is to provie icetives to the cotroller to work as much as possible.

18 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 17 Aitioally, it ca be see i figure 2 why the reverse ever happes. I other wors, figure 2 shows that the possibility of elegatio ever makes the ower of a multi-locate firm chage to a sigle-locate oe. I other wors, the trasitio ever goes from (m) to (s). Utility U m U m U s U s t=1 t t t Figure 2: The impossibility of goig from s to m As ca be see from figure 2, if U m > U m for ay t, implies that u s > u s for all t sice (27) a u s a u s are ot fuctios of t. Therefore, if o elegatio a multi-locate firm is the best optio for ay t, the, there are o values of t that make elegatio a sigle-locate firm the best alterative. 6. Discussio a Coclusio Puga a Trefler (2003) aalyze carefully, from the perspective of their moel, the chage i the orgaizatioal structure of the Boeig Compay aouce i March Briefly, the compay ( ) promote the three existig uit heas to chief executive officers a geographically separate the corporate heaquarters from all three busiess uits (p.23). The, they coclue that the cotrol of iovatio was give to the uit heas as they were promote to chief executive officers. It is worth otig that, i cotrast to the moel presete here, their moel aims to lik the elegatio of cotrol over the prouctio process with kowlege

19 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 18 creatio. They are ot cocere about locatioal avatages. 13 Noetheless, the moel presete here iffers from the oe propose by Puga a Trefler (2003), eve though both moels are base o Aghio a Tirole (1997). 14 I their moel, Boeig s ecisio to relocate part of the firm is see as a way to guaratee the elegatio of power to the busiess uits. I cotrast, it is claime that i the preset moel, rawig o the commets of the presiet a vice-presiet of the compay to support the argumet, that the elegatio a the locatio ecisios are itercoecte aspects a their et effects are take joitly by the compay as the preset moel preicts. Puga a Trefler (2003) ote that the simultaeous aoucemet of these two ecisios [relocatio a promotio] a the explaatio give by Boeig s Chairma at the ews coferece mae it clear that the relocatio of Boeig s corporate heaquarters ( ) was ot just about locatig more cetrally withi the Uite States; it was maily a commitmet to elegatig cotrol over icremetal kowlege creatio (p.23). I orer to show that their iterpretatio is correct, Puga a Trefler recomme reaig the recorig of Boeig s ews coferece of 21 March 2001 i The recorig reveals the Chairma s cocers about havig a creative a iovative compay. It is worth sayig that the ivestors of the compay forme the auiece at that time. He commets: Yesteray, we took aother step ow this path of trasformatio. First, we aouce that we will operate from a ew Worl Corporate Ceter. Seco, we ame the heas of our three largest busiess uits as CEOs of those core uits. These moves, like the oes before, are aime at oly oe thig; i.e., to create value. O 18 September 2002, oe year after Boeig s corporate maagers ha move to Chicago, the Executive Vice Presiet of the compay Laurette Koeller aalyzes the future of 13 As i Muroe et al. (1999), Locatioal avatages are realize by locatig prouctio accorig to access to particular markets or by takig avatage of regioal wage ifferetials (p.17). 14 Other recet workig paper base o Aghio a Tirole (1997) has bee oe by Acemoglu et al. (2005). They costruct a very sophisticate cotiuous-time moel to aalyze the relatioship betwee techology a ecetralizatio. Geographic aspects with ifferet costs of learig are ot aresse. Besies, Maria a Verier (2002) also use Aghio a Tirole (1997) to iscuss market power i a geeral equilibrium approach.

20 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 19 Boeig i a talk etitle Boeig: Yesteray, Toay a Tomorrow. About the ew locatio, she says: Here at Worl Heaquarters we also have the office of ethics a busiess couct, the law epartmet, commuicatios, fiace, iteratioal relatios, a the office of techology. ( ) I May of 2001, whe we aouce the selectio of Chicago as the site of our ew Boeig Worl Heaquarters we marke a importat milestoe i the trasformatio of the compay. Boeig is workig towar log-term growth a value creatio. ( ) We chose Chicago i part because after the mergers of 1996 a 1997, Chicago became a locatio cetral to Boeig operatig uits as well as close to the fiacial commuity. It provie easier access to our customers all over the worl, a it provie a iverse professioal talet base i a busiess friely eviromet ( ) it was separate from existig operatios, so that leaership woul ot be ietifie with ay oe busiess uit. This was part of a strategy i which the busiess uit CEOs base i St. Louis a Washigto State - are resposible i a autoomous way to maage their busiess, while allowig Boeig Worl Heaquarters to cocetrate o strategy a the evelopmet of people. Puga a Trefler poit out that our aim is ot to explai the specific choice of Chicago (p.23). However, as is eviet from the speech above, there was a clear reaso for movig to Chicago, to where the office of techology was move as well. Therefore, it is ifficult to figure out which reaso was omiat: the ecessity of beig closer to the fiacial commuity with easier access to their customers or the ecessity of givig autoomy to the uit heas. It seems to be clear that there were two avatages of movig to Chicago a Puga a Trefler s moel icorporates just oe of them. Iee, it may be a oversimplificatio to see the ecisio of movig the HQ to Chicago oly as a commitmet to elegatig cotrol over icremetal kowlege creatio (p.23) i the busiess uits locate i Seattle. Therefore, what we ca erive from this story is that: (1) the geographic separatio betwee uit heas a maagers geerates more autoomy for the former a that, i tur,

21 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 20 provies greater icetives to them to achieve greater prouctivity a value for the compay; a (2) it was importat to locate the HQ close to the fiacial commuity (locatioal avatage). Both coclusios fit well i the preset moel s assumptios. 15 The fact that both ecisio were mae joitly, icreasig at the same time the autoomy of uit heas a the geographic ecetralizatio, fits well i the moel s preictios. There are some stuies that, istea of examiig a specific case, have empirically ivestigate the heaquarter-subsiiary relatios i some iustries (see, for example, Muambi 2002). Of particular importace for the propose here work by Arita a McCa (2002) that aalyzes the electroics a semicouctor iustry a tries to lik the iteral structure of the America a Japaese firms with the locatio of their assembly plats. Accorig to the authors (p. 360), the Japaese orgaizatioal arragemets are costructe withi a strict hierarchical system with very little iiviual autoomy, whereas US firms have a greater egree of ecisio-makig latitue. Therefore, it may be see that there is more elegatio i the America structure tha i the Japaese corporatios. 16 With this assumptio, the moel propose here woul expect there woul be a teecy for the Japaese plats to be locate closer to heaquarters, whereas America plats woul be more aggressive i placig their plats where the locatioal avatage appears to be higher. Arita a McCa (2002) commet that ( ) the US firms are much more spatially ifferetiate a iteratioally itegrate tha the Japaese firms, i the sese that the activities are istribute more wiely accorig to both locatio a activity types (p. 359). Stuyig the US a Japaese automobile iustry, Shear (1983) fou the same results i terms of spatial orgaizatio. The preset paper claims that the iteral orgaizatio of firms is a importat aspect to efie locatio eve whe the owership structure is ot take i cosieratio. It has bee show that the itrouctio of commuicatio iefficiecy betwee owers a cotrollers offsets a small gai of placig the maufacturig plat far from the heaquarters. Therefore, the ower will ecie to move the plat oly if the gai is greater tha a miimum value. O the other ha, the possibility of elegatig the ecisio to the cotroller reuces, for a rage of the 15 Moreover, eve though the fiacial commuity oes ot belog to the firm, it is iterestig to ote that the ees of placig the HQ i Chicago captures the iea of the importace of face-to-face commuicatio icorporate here as well. 16 If we assume that the Japaese maagers elegate less power tha the Americas because of the maagemet culture i Japa, we coul itrouce, i the moel, a aitioal cost for the Japaese maagers to elegate power. By oig so, the moel obtais the same result as we see i semicouctor iustry: the US firms will be more spatially ifferetiate a iteratioally itegrate.

22 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 21 parameter set, the miimum gai require. As has bee emostrate, the elegatio of formal authority may make multi-locate firms much more likely. From the results, oe shoul expect that (1) plats a epartmets place far from the ower have more autoomy tha those close to the heaquarters ot oly because of the iefficiecy of commuicatio per se but also because the ower carries out less effort as a respose to this iefficiecy. Moreover, (2) there is a teecy that plats place i ifferet cities tha the ower s have more ot oly real but e facto formal authority. Therefore, the framework icorporates some aspects that shoul be take i cosieratio whe multiatioals (regioal) ecie their strategies i terms of locatio. The results of the preset moel call attetio to the fact that there is a teecy for uits locate far from the HQs to have greater autoomy. It coul provie a aitioal reaso to believe that for a less evelope regio that wats to expa its iustrial sectors via attractio of maufacturig plats, ivestmet i services (e.g., uiversities to eucate the labor force a services i geeral to attract highly-eucate workers) coul prove to be more efficiet tha ivestmet either i ifrastructure or i icetives programs give irectly to iustrial corporatios (e.g. tax abatemets). Fially, as metioe, there are some stuies that have empirically ietifie the positive relatio betwee geographic ispersio a ecetralizatio of ecisio-makig. This relatio seems to be quite ituitive. I cotrast, the preset paper tries to offer a formalizatio of this pheomeo. Appeix A I Aghio a Tirole (1997), Equatios (A1) (A4) represet the utility fuctios of the pricipal a the aget. u = EB + ( 1 E) eα B g ( E) (A1) p p u = Eβb + (1 E) eb g ( e) (A2) a a

23 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 22 u = eα B + (1 e) EB g ( E) (A3) p p u = eb + (1 e) Eβb g ( e) (A4) a a The authors assume that g p (E) a g a (e) are icreasig a strictly covex. The, whe the pricipal has the formal authority, the cotroller maximizatio problem is: ' (1 E) b ga ( e) = (A5) If the cotroller has the formal authority: β E b = g e (A6) ' (1 ) a ( ) Thus: e > e (A7) Aghio a Tirole justify the result as follows: Delegatio thus icreases the aget s iitiative; because the pricipal caot overrule the aget, the aget has more icetives to become iforme (p.12). This iterpretatio is icorporate i the preset moel. The ifferece is that, i equatios (A5) a (A6), E woul be a costat. It ca be uerstoo from the perspective that the aget ha a expectatio about the effort of the ower uer those two elegatio schemes. Thus, the expectatio of E woul be icorporate i e, istea of its actual value. Note that, i their moel, E is lower whe the aget has the formal authority; therefore, i this case, ot oly ca the pricipal ot overrule the aget, but also E is low. Both cosequeces of the elegatio icrease the aget s iitiative a, cosequetly, e. I other wors, icluig the effect of the actual effort of the ower o the aget s effort woul oly itesify the ifferece betwee e a e. Hece, assumig that e > e seems to chage either the iea of the origial moel or the mai results of the preset work. Equatio (21) iicates that: ( ) us us σ e = e B + < 0 α 1 e α We have see that: Appeix B (B1)

24 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 23 E s = B(1 e ) σ B(1 e ) (B2) B(1 e ) > σ (B3) Equatio (B2) shows us that if the coitio (B3) is ot satisfie, E s will be zero. I that case, the seco term of (B1) isappears, sice it represets the gai i terms of cost from reucig effort. Therefore, whe (B3) is ot true, (B1) is clearly egative. Assumig that B(1 e ) = σ, it is eough to show that: B(1 e ) e e B + < 0 1 e α That is the same as: (B4) ( e e ) e e (1 α) < 0 (B5) e > e α 1; Sice: It is straightforwar to show that (B1) hols.

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26 Locatio, Commuicatio, a Cotrol Withi a Vertically Itegrate Firm 25 Shear, P. (1983) Auto-prouctio system i Japa: orgaizatioal a locatioal features, Australia Geographical Stuies, 21(1): Simo, Herbert. (1991) Orgaizatios a markets. The Joural of Ecoomic Perspectives, 5(2):