Global Sourcing of Complex Production Processes

Transcription

1 Global Sourcing of Complex Production Processes December 2013 Cristian Scwarz Jens Suedekum Abstract We develop a teory of a firm in an incomplete contracts environment wic decides on te complexity, te organization, and te global scale of its production process. Specifically, te firm decides i) ow many intermediate inputs are simultaneously combined to a final product, ii) if te supplier of eac input is an external contractor or an integrated affiliate, and iii) if tat input is offsored to a foreign country. Our model leads to a ric set of predictions on te internal structure of multinational firms. In particular, it provides an explanation wy many firms coose ybrid sourcing and ave bot outsourced and integrated suppliers. Keywords: Multinational firms, outsourcing, intra-firm trade, offsoring, vertical FDI JEL-class.: F12, D23, L23 Mercator Scool of Management, University of Duisburg-Essen, cristian.scwarz@uni-due.de corresponding autor: Mercator Scool of Management, University of Duisburg-Essen, CESifo and IZA. jens.suedekum@uni-due.de We tank Pol Antràs, Bruce Blonigen, Gregory Corcos, Fabrice Defever, Giordano Mion, Peter Neary, Gianmarco Ottaviano, Uwe Stroinski, seminar participants in Tübingen, Göttingen, Nottingam, and participants at te 2011 CESifo Summer Institute in Venice and te 2010 European Trade Study Group (ETSG) in Lausanne for elpful comments and suggestions. All errors and sortcomings are solely our responsibility. 1

2 1 Introduction Researc in international trade as revealed te existence of substantial firm-level eterogeneity even witin narrowly defined industries. Te literature was first concerned wit te comparison of firms tat only sell locally wit exporting firms wic also serve foreign markets. More recent studies ten empasized tat firms also differ markedly in te teir importing beaviors, and more generally, in teir sourcing strategies for intermediate inputs. 1 In tis paper, we igligt tree important dimensions along wic firms sourcing strategies differ. Specifically, we develop a teory of a firm were te eadquarter (te producer ) decides on i) complexity: te mass of intermediate inputs eac provided by a separate supplier tat are simultaneously combined in te production process for a final good, ii) organization: if te supplier of eac component is an external subcontractor or an integrated subsidiary, and iii) global scale: if te supplier is domestic or foreign. Our model builds on te seminal approaces by Antràs (2003), Antràs and Helpman (2004) and Acemoglu, Antràs and Helpman (2007). Te former two papers were te first to study global sourcing in a property rigts framework wit incomplete contracts. Tese models are, owever, restricted to a setting wit a eadquarter and one single supplier. Te latter paper considers an endogenous mass of suppliers. Te more inputs are combined in te production process, te more specialized is te task tat eac single supplier performs and te finer is te division of labor inside te firm. However, in Acemoglu et al. (2007) tere are only symmetric firm structures were eiter all suppliers are integrated or all are outsourced. We extend teir framework and allow for ybrid sourcing, tat is, for a firm structure were some suppliers are vertically integrated wile te oters remain independent, and were some inputs are offsored wile te oters are produced domestically. Tis, in turn, endogenously generates asymmetries across suppliers in teir bargaining powers and investment incentives. Tereby, our model leads to a ric set of predictions on te structure of multinational enterprises (MNEs) tat are consistent wit stylized facts from te recent empirical literature. It also leads to several novel testable predictions tat may motivate future empirical researc. Te recent empirical trade literature as sown tat ybrid sourcing is a igly relevant penomenon. For example, Defever and Toubal (2013) observe tat in 1999 only about 8% of all Frenc MNEs in te largely globalized motor veicle industry (e.g., Iveco and Molseim) ave imported intermediates exclusively from related parties, 47% of tem (e.g., Heuliez Bus and Smart Car) ave imported exclusively from external foreign suppliers, wile te remaining 45% ave cosen some combination of outsourcing and vertical integration. Wen it comes to te important make or buy decision, we tus observe tat tere is often a co-existence of different sourcing modes for different inputs witin te same firm. Suc a pattern is also found, among oters, by Costinot et al. (2013), Corcos et al. (2013), Koler and Smolka (2012) and 1 See Bernard et al. (2010, 2012) for recent overviews ow firms engaged in exporting and global sourcing differ from firms tat only sell and source domestically. 2

3 Tomiura (2007) for US, Frenc, Spanis, and Japanese firms, respectively. Hybrid sourcing also spans te global scale dimension. Baldwin (2009), for instance, discusses te case of te Swedis car Volvo S40. He illustrates tat Volvo cooses to offsore only some intermediate inputs wile relying on domestic manufacturing for oters, and for te offsored components te firm relies on a mix of arm s lengt outsourcing and intra-firm trade. 2 Wit respect to te complexity dimension, evidence is more scarce since current data typically only allows to observe supplier relationsips were te parent firm owns a majority sare of te input provider, wereas te number of external supplier relationsips is not observable. Given tis caveat, te available recent evidence still suggests tat firms differ vastly in teir complexity. For example, Alfaro and Carlton (2009) report tat te General Motors Corporation (GM) can be traced as te ultimate owner ( global ultimate parent ) of 2,248 firm entities, 455 of wic are subsidiaries outside te USA and 123 are in manufacturing industries. Of tose 123 affiliates, Alfaro and Carlton (2009) classify 43 to be input suppliers providing manufacturing components for GM s final products. By comparison, using similar but more compreensive data for rougly 300,000 business groups worldwide, Altomonte and Rungi (2013) report tat te average US eadquarter firm owns just 21 affiliates, only some of wic can be classified as input suppliers. 3 In addition, more tan 50 % of tose eadquarters ave less tan four affiliates, and are tus far less complex tan te GM business group. Summing up, bot witin and across industries, tere is substantial eterogeneity wit respect to te complexity, organization and global scale of firms internal structures. Understanding tose patterns in te data requires a teoretical model wit multiple suppliers wic can be asymmetric in teir organizational mode and teir country of origin. Our framework can address tose facts. It provides an economic teory on te firm- and industry-level determinants of tose firm structure decisions, and it provides an explanation wy firms often coose different organizational and global scale modes for some inputs tan for oters. 4 Importantly, ybrid sourcing can arise in our model even toug all inputs are symmetric along all exogenous dimensions. Tat is, our model does not rely on supplier eterogeneity, but our key results are driven by te fact tat te eadquarter can use te firm structure 2 Furter examples for MNEs sourcing strategies are discussed in Antràs and Rossi-Hansberg (2009) and Antràs (2013). Partial offsoring can also arise in te model by Grossman and Rossi-Hansberg (2008). Tey do, owever, not analyze different organizational modes for supplier relationsips. 3 Even if it is not directly observable in te data, big corporations like GM are likely to ave not only more affiliates tan te average US firm in te same sector, but also more unrelated suppliers wit wom tey contract via market transactions. 4 A different extension of te Antràs and Helpman (2004) framework wit more tan one supplier is due to Du, Lu and Tao (2009). In teir model, te same input can be provided by two suppliers, and bi-sourcing (one supplier integrated and te oter outsourced) can arise out of a strategic motive, because it systematically improves te eadquarter s outside option. In our model tere is an endogenous mass of suppliers wo provide differentiated inputs, and our ybrid sourcing result relies on a different motive. Van Biesebroeck and Zang (2011) also study an incomplete contracts model wit a eadquarter and multiple suppliers. However, tey do not consider an endogenous complexity coice and focus on te organizational form of outsourcing. Last, Nowak et al. (2012) study a global sourcing model wit two asymmetric, discrete suppliers and tus also disregard te endogenous complexity decision. 3

4 decisions to fine-tune te revenue distribution inside te firm, and tereby te incentives of all involved parties to invest into te relationsip. Tis mecanism is different from te one operating in te recent framework by Antràs and Cor (2013). Tey consider a vertical value cain (a snake structure in te terminology of Baldwin and Venables, 2013), were inputs differ ex ante by teir level of downstreamness. Our model considers a spider structure, were many inputs are combined simultaneously, and puts forward an explanation wy te firm may organize some legs of tat spider differently tan oters. Tis paper is organized as follows. Section 2 presents our basic model structure. Section 3 focusses on te complexity and organizational decisions in a closed economy setup. Section 4 turns to te open economy and introduces te global scale decision. Section 5 concludes. 2 Model 2.1 Demand, tecnology and firm structure We consider a firm tat produces a final good q for wic it faces te following iso-elastic demand function: q = A p 1/(1 β). (1) Here, p denotes te price, and A > 1 is an exogenous term tat captures te market size for tis final product. Te demand elasticity is 1/(1 β), wic is increasing in β [0, 1]. Producing tis good requires eadquarter services and manufacturing components, wic are combined according to te following Cobb-Douglas production function: ( N ) 1 η α q = η x(j) α dj. (2) j=0 Headquarter services are denoted by and are provided by te producer. Te parameter η [0, 1] is te eadquarter-intensity of final goods production. 5 For te components, we assume tat tere is a continuum of inputs wit measure N R +, were eac component is provided by a separate supplier. Te supplier j [0, N] delivers x(j) units of is particular input, and te components are aggregated according to a constant elasticity of substitution (CES) function were α [0, 1] measures te degree of component substitutability. Using equations (1) and (2), total revenue can ten be written as follows: ( N ) γ R = A 1 β βη x(j) α dj were γ j=0 β(1 η). (3) α In our model, te producer decides on te structure of te firm, and tis coice involves tree aspects: complexity, organization, and global scale of production. 5 Te eadquarter services tus account for a fixed sare η of total value added and necessarily ave to be performed by te producer erself, i.e., tey cannot be unbundled, outsourced or offsored. 4

5 Te complexity coice refers to te mass of components N. From (2) it is clear tat te overall component-intensity of final goods production is exogenously given by 1 η. Tis parameter reflects te tecnology of te sector in wic te firm operates. Wen te producer cooses N, se tus essentially decides on te division of labor inside te firm. Te larger N is, te narrower is te task tat eac single supplier performs, and te more complex is te firm s production process. 6 We assume tat a greater mass of suppliers induces agency costs νn for managerial oversigt, were ν > 0 is te fixed cost per additional supplier. Turning to te organizational decision, te producer decides separately for eac of tose components if te respective supplier is integrated as a subsidiary witin te boundaries of te firm, or if tat component is outsourced to an external supplier. Following te property rigts approac of te firm à la Grossman and Hart (1986) and Hart and Moore (1990), we assume tat input investments are not contractible as teir precise caracteristics are difficult to specify ex ante and also difficult to verify ex post. 7 A old-up problem tus arises, even for affiliated suppliers witin te firm, and te producer and te suppliers end up bargaining at a time wen teir investment costs are already sunk. Te bargaining power of te involved parties depends crucially on te firm structure as will be explained below. Finally, te producer decides on te location were eac component is manufactured (global scale). Se is located in country 1 were final assembly is carried out. Te respective input suppliers may eiter also come from country 1, or from a foreign low-wage country Structure of te game We consider a game tat consists of five stages. Te timing of events is as follows: 1. Te producer simultaneously makes te following decisions: i) Se decides on te mass N of suppliers/manufacturing components. organizational form {O, V }. ii) For eac j [0, N] se cooses te Here, O denotes outsourcing and V denotes vertical integration of supplier j. We order te mass N suc tat eac supplier i [0, N O ] is outsourced, and eac supplier k (N O, N] is vertically integrated. Ten, ξ = N O /N (wit 0 ξ 1) denotes te outsourcing sare, and (1 ξ) = N V /N is te sare of vertically integrated suppliers. Finally, iii) for eac j [0, N] te producer decides on te country r = {1, 2} were tat component is manufactured. We order te mass of outsourced suppliers N O suc tat eac supplier i [0, N2 O ] is offsored to te lowwage country 2, and eac supplier k (N2 O, N O ] is located in te ig-wage country 1. Ten, l O = N O 2 /N O denotes te offsoring sare among all outsourced suppliers (wit 0 l O 1). Similarly, l V = N V 2 /N V (wit 0 l V 1) is te offsoring sare among all integrated suppliers, and te total offsoring sare is l = ξ l O + (1 ξ) l V. 6 Tis complexity coice is tus closely related to Acemoglu et al. (2007) s notion of te firm s tecnology. 7 Antràs and Helpman (2008) and Acemoglu et al. (2007) consider partial contractibility and cross-country differences in contracting institutions. We could introduce tose features as well, but tis would make te exposition considerably more complicated witout adding many novel insigts. 5

6 Given tese firm structure decisions {N, ξ, l O, l V }, te producer offers a contract to potential input suppliers for every component j [0, N]. Tis contract includes an upfront payment τ(j) (positive or negative), an ex post payment, and stipulates an input quantity for te prospective supplier. 2. Potential suppliers apply for te contract, and te producer cooses one supplier for eac component j [0, N]. Tere exists a large pool of potential applicant suppliers for eac manufacturing component in bot countries. Tese suppliers ave an outside opportunity equal to wr 0 in country r = {1, 2}. Tey are willing to accept te contract if teir payoff is at least equal to wr. 0 Te payoff consists of te upfront payment τ(j), te ex post payment s(j) tat supplier j anticipates to receive, minus te investment costs for te input production (wic may differ across applicants). 3. Te producer and te suppliers independently decide on teir input levels for te eadquarter services and te components x(j), respectively. Due to non-contractibility, suppliers are not obliged to supply te quantity as stipulated in te first stage. 4. Since input investments are non-contractible, all parties can treaten to witold teir inputs at tis stage. Te suppliers and te producer bargain over te division of te surplus. Supplier j receives te ex post payment s(j), wic need not correspond to te level tat was specified in te contract, and te producer receives s Output is produced, revenue is realized, and te surplus value is divided according to te bargaining agreement. We solve tis game by backward induction, successively moving from simplified setups were single aspects or decisions are faded out, to te encompassing version of te model. 3 Closed economy We start te analysis wit a closed economy setting. Tat is, we abstract from te global scale decision for te moment, and impose tat all suppliers are located in country 1. Te firm structure decision ten only consists of te complexity and te organizational coice. 3.1 Complete contracts As a bencmark, we first consider a setup wit complete contracts tat leads to te firstbest outcome from te viewpoint of te firm. In tis scenario, te producer cooses te complexity level N and er own input investment. Furtermore, se makes a contract offer {x(j), τ(j), s(j)} to eac supplier j [0, N] in te first stage of te game, and in stage 3 eac supplier must supply (and cannot witold) te input level x(j) tat is stipulated in te contract, in excange for te agreed payment τ(j) + s(j) tat is not re-negotiable. 6

7 We assume tat unit costs of input production are te same for all suppliers, and are given by c x > 0. Moreover, te outside opportunity w 0 is also te same for all domestic suppliers. Since all component inputs enter symmetrically into te production function, te producer terefore cooses a common input level x and common payments τ + s for all suppliers, and te make or buy question (outsourcing or integration) is irrelevant in tis scenario wit complete contracts. Te producer maximizes er payoff, wic is given by Π = R c N (τ + s) νn, were c > 0 denotes te unit costs of providing eadquarter services, and were revenue is given by R = A 1 β βη x β(1 η) N γ due to te symmetry of te component inputs. Tis payoff is maximized subject to te suppliers participation constraint τ + s c x x w 0. Since te producer as no reason to leave rents to te suppliers, se will adjust te payment τ + s in suc a way tat te participation constraint is satisfied wit equality. Te firm s optimization problem can ten be expressed in a simpler way as follows: max {,x,n} Π = A 1 β βη x β(1 η) N γ c c x x N w 0 N ν N. (4) In tis paper, we sall assume tat α > β, i.e., tat te elasticity of substitution across components is sufficiently large relative to demand elasticity. Tis implies γ < 1, and ensures tat te maximization problem (4) is concave in N. Te first-order conditions for tis problem are spelled out in Appendix A. Tey imply /(x N) = η/(1 η) (c x /c ). Tat is, te optimal eadquarter contribution relative to te aggregate input contribution of all suppliers is iger, te iger is te tecnological parameter η (te sectoral eadquarter-intensity) and te lower are te relative unit costs c /c x. Furtermore, we obtain te optimal input level for every single supplier (x ), and te optimal mass of suppliers (N ), wic are given by N = ( β A1 β c x (1 η) x = α(w0 + ν), and (5) c x (1 α) ( ) cx (1 α) 1 β ( ) ) α βη α β+(1 α)βη ηcx α(w 0. (6) + ν) (1 η)c It immediately follows from (6), and our assumption tat α > β, tat te firm s (first-best) optimal complexity coice depends positively on te market size term A, and negatively on te different cost terms c, c x, w 0, and ν. 8 Furtermore, we sow in Appendix A tat N depends negatively on η provided te market size A is sufficiently large or te cost terms ν and w 0 8 Notice tat, if eadquarter-intensity η were zero, expression (6) would become analogous to te optimal tecnology level in Acemoglu et al. (2007). To see tis, notice tat we do not include a Benassy term N κ+1 1/α in front of te integral in (2), and tat we ave set C (N) = ν for te specification of agency costs. Te parameter restriction α > β ten corresponds to Assumption 1 in Acemoglu et al. (2007). 7

8 are sufficiently small. Moreover, we sow tere ] tat te mass of suppliers per unit of revenue, N /R, can be written as β(1 η) and is tus unambiguously decreasing in η. In [ (1 α) α(w 0 +ν) oter words, te optimal (relative) complexity level is lower in more eadquarter-intensive industries. Finally, it is straigtforward to sow tat given tose first-best decisions N, x and te overall sare of te surplus tat goes to te mass of suppliers is given by N ( c x x + w 0) [ ] /R = β(1 η) w 0 +αν, wit te remaining sare going to te producer. α(w 0 +ν) Tat is, te optimal revenue sare for te suppliers is linearly decreasing in η, wic implies tat te producer sould receive a larger sare of te surplus in sectors were eadquarter services are more intensively used in production. 3.2 Incomplete constracts: Preliminaries and symmetric case From now on, we move to te incomplete contracts scenario in wic x(j) and s(j) need not correspond to wat as been stipulated in te contract in stage 1. Similarly, te producer also anticipates te old-up wen deciding on er investment in eadquarter services. To analyze te multilateral bargaining, we use te Sapley value concept due to Sapley (1953). In tis subsection we first provide some preliminaries, and ten solve a simplified case were it is imposed tat all N suppliers are symmetric in teir organizational form and, tus, teir equilibrium input amounts. 9 In te next subsection we ten consider te producer s decisions on complexity and te outsourcing sare, wic endogenously generates asymmetries across suppliers. Tere, we address te penomenon of ybrid sourcing in te closed economy Te Sapley value wit symmetric suppliers In te bargaining stage, te mass (number) of players and teir input amounts are given. Te Sapley value (SV) of a single supplier j is ten defined as te average of is marginal contributions to all relevant coalitions, were a coalition is a subset of players from te set of possible permutations. To fix ideas, first suppose we ad a setup wit te producer and wit M 2 discrete suppliers. Ten, supplier j s SV is defined as s(j) = 1 (M + 1)! M i=1 i(m 1)! j R (i, M) = 1 M(M + 1) M i=1 i j R (i, M) (7) Here, j R (i, M) is te marginal contribution of supplier j, tat is, te cange in revenue wen e drops out of te coalition and leaves beind a remaining coalition of size i M. Te notation in (7) assumes a discrete number, wereas in our model we ave a continuum of suppliers. In Appendix B we terefore derive te asymptotic SV assuming a very large (infinite) number of very small (infinitely small) suppliers. Here, in te main text, we adopt a simpler euristic approac based on Acemoglu et al. (2007). 9 Tis part largely draws on Acemoglu et al. (2007), but our analysis still differs from teirs because in our model te producer contributes inputs (eadquarter services ) to te production process. 8

9 In particular, recalling tat we assume a mass N of symmetric suppliers for te moment, let x(j) be te input contribution of supplier j and x( j) te (symmetric) individual contribution by all oter suppliers, were N, x(j) and x( j) are given in te bargaining stage. marginal contribution of j to a coalition not involving te producer is, by construction, equal to zero since te producer is essential in te production process. Te For coalitions tat do involve te producer and some measure n N from te total mass of suppliers, te marginal contribution of j can be written as m(j, n) = δ ( R/ n) were it follows from (3) tat R = A 1 β βη ( n k=0 x(k)α dk ) γ. Here we ave assumed tat, if supplier j drops out of te coalition, te fraction 0 < (1 δ) < 1 of is input remains wit te firm, wile j witolds te fraction 0 < δ < As j provides te last input, we tus ave x(k) = x(j) for k = n and x(k) = x( j) for all 0 k < n, and we can express supplier j s marginal contribution to tis coalition as [ ] x(j) α m(j, n) = γ δ A 1 β βη x( j) αγ n γ 1. (8) x( j) Finally, averaging supplier j s ( marginal contribution (8) to all relevant coalitions involving N ( te firm by calculating (1/N) n ) ) 0 N m(j, n) dn, we obtain is Sapley value as follows: s j [x(j), x( j),, N] = γ δ 1 + γ A1 β βη x( j) αγ N γ N ( ) x(j) α. (9) x( j) Due to symmetry, we will ave x(j) = x( j) = x in equilibrium, and ence it follows from (9) tat te SV of eac symmetric supplier, s, and te sare of te surplus s/r tat e anticipates to realize in te bargaining stage, are given by: s = γ δ 1 + γ 1 N A1 β βη x αγ N γ } {{ } R s/r = γ δ 1 + γ 1 N, (10) so tat te group of suppliers as a wole realizes te revenue sare N ( s/r) = γδ/(1 + γ). Notice tat s/r is increasing in γ and in δ. Tat is, eac supplier as a iger bargaining power in more component-intensive industries (lower η), te lower is te degree of component substitutability (lower α), and te iger is te demand elasticity (iger β). His bargaining power is also increasing in te input fraction δ tat e treatens to witold. Te producer as te essential player obtains te residual revenue sare, wic is s 0 /R = 1 N ( s/r) = (1 + γ(1 δ))/(1 + γ) by (10), and is respectively decreasing in γ and in δ. 10 If δ = 1, te supplier treatens to witold te entire amount, wic means tat e as full ownersip rigts over is input. It is important to bear in mind tat, for now, we assume tat δ [0, 1] is common to all suppliers in order to focus on a fully symmetric case. Below we ten consider an asymmetric firm structure were some suppliers are outsourced (δ = 1) wile oters are vertically integrated (δ < 1), wic in turn leads to asymmetries across suppliers in teir input amounts and teir marginal contributions to a coalition. 9

10 3.2.2 Input investments and firm structure wit symmetric suppliers Having solved te bargaining problem in stage 4, we continue wit te backward induction and now analyze te input investments (stage 3) and te firm structure decision (stage 1), wic for now only involves te complexity coice since we impose tat all suppliers ave te same organizational form and are tus symmetric along all dimensions. Input investments. In te investment stage, eac supplier j cooses is input contribution x(j) so as to maximize is expected ex post payment (is Sapley value) minus te costs of input provision. His equilibrium input contribution can terefore be written as x(j) = argmax x(j) {s j [x(j), x( j),, N] c x x(j)}, under te participation constraint s j [x(j), x( j),, N] + τ(j) c x x(j) w 0 and taking x( j) as given. Using (9), we ave { γ δ x(j) = argmax x(j) 1 + γ A1 β βη x( j) αγ N γ N ( ) x(j) α c x x(j)}. (11) x( j) Taking first-order conditions wit respect to x(j), and ten imposing x(j) = x( j) = x due to symmetry, we obtain te following supplier input contribution: ( ) αβ(1 η) 1 x = α + β(1 η) A1 β 1 β(1 η) 1 βη δ 1 β(1 η) 1 β(1 η) N γ 1 1 β(1 η). (12) c x Similarly, in te investment stage, te producer cooses so as to maximize er payoff: = argmax {s 0 [, x, N] c } = argmax { 1 + γ(1 δ) 1 + γ so tat te eadquarter contribution can be written as ( = αβη α + β(1 η) A1 β c ) 1 1 βη (1 + γ(1 δ)) 1 } A 1 β βη x αγ N γ c, 1 βη N γ 1 βη x β(1 η) 1 βη. (13) Plugging (12) into (13), we can express te input contributions x(n) and (N) as functions of te complexity level N (wic is given in stage 3) and of parameters only. We obtain x(n) = Ψ x x N β(1 η)(1 α) 1 and (N) = Ψ N β(1 η)(1 α), (14) were te terms Ψ x, Ψ, x, and collect te parameters of te model, and are defined as: ( 1 Ψ x = A c x ) 1 ( ) 1 1 Ψ = A c x = δ 1 βη 1 β 1 β ( cx c 1 β ( c c x ) βη ( 1 β αβ(1 η) α + β(1 η) ) β(1 η) 1 β (1 + γ(1 δ)) βη 1 β, ( αβ(1 η) α + β(1 η) ) 1 βη ( 1 β ) β(1 η) 1 β = δ β(1 η) 1 β αβη α + β(1 η) ( ) βη 1 β, αβη α + β(1 η) ) 1 β(1 η) 1 β (1 + γ(1 δ)) 1 β(1 η) 1 β., 10

11 It follows from (14) tat, for a given N, te input contributions x(n) and (N) depend negatively on c x and c and positively on A and α. Furtermore, x(n) depends positively on δ: te iger is te input fraction tat eac supplier treatens to witold, te iger is te (symmetric) input amount as te suppliers investment incentives are strengtened. Firm structure. Finally, in te first stage of te game, te producer decides on te complexity level N. Given te freely adjustable participation fees τ(j), wic dissipate all rents from te suppliers, te firm s problem can be expressed in te following way: max {N} Π = A 1 β (N) βη x(n) β(1 η) N β(1 η) α c (N) cx x(n) N (w 0 + ν)n, (15) were x(n) and (N) are te investment levels from (14). Substituting tis into (15), and solving for N ten yields te following complexity coice in te incomplete contracts scenario wit symmetric suppliers (see Appendix C for details): Ñ s = ( Γ A1 β c x (1 η) ( ) cx (1 α) 1 β ( ) ) α βη α β+(1 α)βη ηcx α(w 0, (16) + ν) (1 η)c were Γ is defined in Appendix C. Tis complexity coice differs from its first-best counterpart given in (6) only wit respect to te first term, wic now reads as Γ instead of β. We sow in Appendix C tat Γ < β olds, wic implies tat Ñs < N. In oter words, te firm cooses a lower complexity level under incomplete contracts tan in te first-best world. Furtermore, te comparative statics of Ñ s are analogous to tose for N. Tat is, Ñ s is increasing in A, decreasing in c x, c, ν and w 0, and decreasing in η if A is large enoug. Importantly, Ñ s is increasing in δ, as is also sown in Appendix C. We tus ave Ñs(δ = 1) > Ñs(δ < 1), so tat te producer cooses more complexity if all suppliers maintain full ownersip rigts over teir inputs. Te intuition is tat lower bargaining power δ dilutes te (symmetric) suppliers investment incentives. To countervail tis, te producer cooses a lower complexity level N, wic per se raises te incentives for eac single supplier wose individual input now accounts for a more important part of te final product Asymmetric suppliers: Outsourcing versus vertical integration After aving analyzed te simplified case wit an endogenous mass of symmetric suppliers, we now move to te asymmetric case and allow for differences across suppliers in terms of teir organizational form. More specifically, suppliers are still assumed to be symmetric along all exogenous dimensions (unit costs, outside opportunities, and input intensity of te individual component for te final product). Yet, te producer now also decides on te outsourcing sare 11 Last, using (16) in (14), it can also be verified tat x < x and < as given in (5). Tis illustrates te two-sided underinvestment problem resulting from contract incompleteness and te old-up problem. 11

12 ξ in te first stage of te game, wic endogenously generates asymmetries across suppliers in teir ownersip rigts, bargaining powers, and investment incentives in turn. Still, we encounter a scenario were te suppliers of te same ownersip form are symmetric and will, tus, contribute te same input amount in equilibrium. Tat is, we ave x O (i) = x O i [0, N O ] and x V (k) = x V k (N O, N]. Revenue from (3) becomes R = A 1 β βη N γ [ξ (x O ) α + (1 ξ) (x V ) α ] γ were ξ = N O /N is te firm s outsourcing sare. Letting ˆx α ξ (x O ) α + (1 ξ) (x V ) α, we may also write revenue as R = A 1 β βη N γ ˆx αγ, were ˆx can be understood as te input contribution of te representative (average) supplier of te firm Bargaining and Sapley values wit asymmetric suppliers We start wit te analysis of te multilateral bargaining in stage 4. issues compared to te symmetric case analyzed above. Tere are two main First, from te perspective of a single supplier j, is own organizational form {O, V } will affect is marginal contribution to any coalition, as e may (under V ) or may not (under O) leave beind parts of is input contribution wen leaving te coalition. Second, more subtly, te ownersip structure of te oter suppliers also matter for te marginal contribution of player j to a specific coalition. 12 Wit a continuum of suppliers, we can make use of a similar euristic approac as before wile leaving te more formal derivation to Appendix D. Specifically, similar as in (8), te marginal contribution of a single supplier j to a coalition wit te producer and a measure n N of oter suppliers can now be written as were ˆx( j, n) α [ ] x(j) α m(j, n) = γ δ A 1 β βη ˆx( j, n) αγ n γ 1, (17) ˆx( j, n) = ξ( j, n) (x O ( j)) α + (1 ξ( j, n)) (x V ( j)) α is te average input contribution of all oter suppliers in tat coalition, wic depends on te outsourcing sare ξ( j, n) among tose oter suppliers. Now, for specific remaining coalitions, tere are of course many different ownersip structures tat player j may encounter. But recall tat we eventually average over all feasible coalitions. Supplier j will, tus, on average face te ownersip structure ξ( j) wic corresponds to te outsourcing sare among all oter suppliers, except j imself. Finally, wit a continuum of inputs, tis supplier-specific sare ξ( j) converges to te firm s overall outsourcing sare ξ tat is te same for all suppliers. Wit tese considerations, we can obtain supplier j s Sapley value from (17) as follows: 12 For te second point, consider a simple example wit tree discrete suppliers, {1, 2, 3}. Suppose supplier 2 is outsourced wile supplier 3 is integrated, so tat teir input amounts differ, x(2) x(3). Ten, te contribution of supplier 1 to te coalition [0, 2, 1] is, in general, different from is contribution to [0, 3, 1]. 12

13 s j [x(j), ˆx( j),, ξ, N] = γ δ(j) (1 + γ) 1 ( ) x(j) α N A 1 β βη ˆx( j) αγ N γ, (18) ˆx( j) } {{ } =R were ˆx( j) α = ξ x O ( j) α + (1 ξ) x V ( j) α is te average input contribution among all oter suppliers in tis firm. It follows from (18) tat te Sapley value of a single supplier j is iger if e is outsourced tan if e is vertically integrated. Tis is for two reasons: First, external suppliers ave δ(j) = 1 wereas internal suppliers ave δ(j) = δ < 1. Second, te term x(j)/ˆx( j) captures te contribution of supplier j relative to te average supplier contribution. In equilibrium, we will ave x O ( j) = x O (j) = x O > x V ( j) = x V (j) = x V, so tat x(j) ˆx( j) if player j is outsourced, and x(j) ˆx( j) if e is integrated. Finally, notice tat if all suppliers were symmetric, so tat x(j) = ˆx( j) = x, te Sapley value from (18) boils down to te same expression as given in (10). Headquarter revenue sare producer is given by N s 0 = R j=0 Using (18), te Sapley value of te essential player te ( ) γ δ(j) x(j) α ( (1 + γ)n R dj = R 1 ˆx( j) γ N ( ) x(j) α (1 + γ)n δ(j) dj) j=0 ˆx( j) Recalling tat all outsourced suppliers are symmetric and contribute te same x O, and tat all integrated suppliers contribute te same x V, we can rewrite tis expression as [ s 0 = R 1 ( γ ξn (1 + γ)n j=0 (x O ) α N ξ (x O ) α + (1 ξ)(x V ) α dj + k=ξn Solving te integrals, and manipulating terms, yields s 0 R = 1 γ 1 + γ ( ξ (xo ) α + δ(1 ξ) (x V ) α ξ (x O ) α + (1 ξ) (x V ) α and by using (19), we can establis our first main result: δ (x V ) α )] ξ (x O ) α + (1 ξ)(x V ) α dk. ), (19) Lemma 1: Te eadquarter revenue sare (s 0 /R) is monotonically decreasing in ξ. It ranges between (s 0 /R) max = 1+γ(1 δ) 1+γ if ξ = 0 and (s 0 /R) min = 1 1+γ if ξ = 1, wit d(s 0/R) dξ < 0. For te polar cases of complete vertical integration (ξ = 0) and complete outsourcing (ξ = 1), te proof follows immediately from (19), and te respective eadquarter revenue sares correspond to tose from Section 3.2. For te intermediate cases, we need to differentiate (19) wit respect to ξ. Importantly, wen doing tis, we ave to take into account tat te suppliers input amounts x O (ξ) and x V (ξ) are also affected by ξ, since te organizational decision occurs before te investment decisions take place. Terefore, we ave 13

14 d(s 0 /R) = dξ γ(1 δ) (x O x V ) (1 α) (1 + γ) (ξ (x O ) α + (1 ξ)(x V ) α ) 2 [αξ(1 ξ)x V x O + x O (x V αξ(1 ξ)x V ) ] wit x O = x O/ ξ and x V = x V / ξ. Te term in front of te squared parenteses is negative and captures te direct effect of an increase in ξ on te eadquarter revenue sare for given supplier contributions. Te term in squared parenteses captures te indirect effect of an increase in ξ on te supplier incentives. We sow below tat x V = δ 1/(1 α) x O, so tat x V = δ1/(1 α) x O. Using tis, te term in squared parenteses becomes δ1/(1 α) x 2 O > 0, and ence we ave d(s 0/R ) dξ < 0. Tis completes te proof of Lemma 1. Economically, Lemma 1 implies tat te producer is able to continuously decrease er revenue sare by increasing te outsourcing sare. Te logic beind tis insigt is similar as in Antràs and Helpman (2004): a transfer of ownersip rigts to te suppliers raises teir investment incentives, but tis comes at te expense tat te producer as to suffice wit a smaller sare of te overall surplus. Yet, te important difference to teir model is tat te firm can gradually adjust te firm structure in our framework by using ybrid sourcing, and it is not bound to coosing only between extreme organizational structures. Hence, te producer can also gradually affect te sare of te surplus tat se leaves to te suppliers (in between an upper and a lower bound), by adjusting te outsourcing sare accordingly. 13 Via te organizational decision ξ, se can terefore also gradually affect te suppliers and er own incentives to invest into te relationsip, as we sow next Input investments and firm structure wit asymmetric suppliers Input investments. We now move to te analysis of te input investment coices in stage 3. Using (18), an outsourced supplier j cooses is input contribution as { γ x O (j) = argmax x(j) 1 + γ A1 β βη ˆx( j) αγ N γ N ( ) x(j) α c x x(j)}, (20) ˆx( j) were we recall tat ˆx( j) α = ξ x O ( j) α + (1 ξ) x V ( j) α is te average investment level of all oter suppliers except j. Similarly, an integrated supplier k maximizes { γ δ x V (k) = argmax x(k) 1 + γ A1 β βη ˆx( k) αγ N γ N ( ) x(k) α c x x(k)}, (21) ˆx( k) wit ˆx( k) α = ˆx( j) α = ˆx α since tere is a continuum of suppliers. Analogously, using (19), te producer cooses er contribution as 13 Anoter difference to Antràs and Helpman (2004) is tat we do not ave to assume exogenously given bargaining powers (denoted β O and β V in teir model) for te constellations of full outsourcing or integration, respectively. In our setup, te sares (s 0/R) min and (s 0/R) max are fully determined by te model parameters α, β, η and δ, and te producer can obtain any revenue sare witin tose bounds via te coice of ξ. 14

15 [ = argmax {A 1 β βη x αγ N γ 1 γ 1 + γ ( ξ(xo ) α + δ(1 ξ)(x V ) α ξ(x O ) α + (1 ξ)(x V ) α )] } c (22) In Appendix D we derive te equilibrium supplier investments x O (N, ξ) and x V (N, ξ) as functions of N and ξ only, wic sow tat x V (N, ξ) = δ 1/(1 α) x O (N, ξ). Integrated suppliers tus contribute less tan outsourced ones, ceteris paribus, because of teir inferior ownersip rigts. Tose solutions, in turn, yield te average supplier investment x(n, ξ) and te producer s investment coice (N, ξ) wic are given by x(n, ξ) = Ψ x Φ x (ξ) N β(1 η)(1 α) 1 and (N, ξ) = Ψ Φ (ξ) N β(1 η)(1 α). (23) Te investment amounts for te asymmetric case in (23) are similar to teir counterparts from (14) for te symmetric case. In fact, te exogenous terms Ψ x and Ψ are tose given above. Yet, te oter exogenous terms x and from above are now replaced by te endogenous terms Φ x (ξ) and Φ (ξ) were te firm s organizational decision ξ enters. Tose terms read as (1 α)(1 βη) Φ x (ξ) = Ξx βη 1 β Ξ, Φ (ξ) = Ξ (1 α)β(1 η) x ξ + (1 ξ) δ 1/α wit Ξ x = ξ + (1 ξ) δ and Ξ = 1 + γ γ ξ + (1 ξ) δ 1 β(1 η) 1 β Ξ, (24), were δ δ α 1 α. Notice tat wit ξ = 1 we ave Ξ x = Ξ = 1 and tus Φ x = Φ = 1, wile for ξ = 0 we ave Ξ x = x and Ξ =. Tat is, under full outsourcing or full integration te only two firm structures were all suppliers are symmetric te input amounts (23) are te same as in (14). For te intermediate constellations of ybrid sourcing (0 < ξ < 1), te producer s input relative to te input of all suppliers is given by N x = η c x (1 η) c Ξ (ξ) Ξ x (ξ) 1 α α Since Ξ (ξ) > 1 and 0 < Ξ x (ξ) < 1, te second term on te RHS is larger tan one if 0 < ξ < 1. Moreover, tat term is larger te smaller ξ is, as Ξ x is increasing and Ξ is decreasing in ξ. Hence, wen te producer cooses a iger sare of vertically integrated suppliers (for a given mass N), se ends up contributing relatively more to te production process, because te underinvestment problems for te aggregate of suppliers is aggravated. Firm structure. Finally, in stage 1, te producer now decides on te complexity and te organization of te production process. Formally, er decision problem is given by max {N,ξ} Π = A 1 β (N, ξ) βη x(n, ξ) β(1 η) N β(1 η) α. c (N, ξ) cx x(n, ξ) N (w 0 +ν)n, 15

16 were x(n, ξ) and (N, ξ) are te investment levels from (23). In Appendix E we sow tat tis maximization program is equivalent to te following simpler problem: max {N,ξ} Π = Θ(ξ) N β(1 α)(1 η) (w 0 + ν)n, (25) subject to Θ(ξ) = A 1 β (Ψ Φ (ξ)) βη (Ψ x Φ x (ξ)) β(1 η) c Ψ Φ (ξ) c x Ψ x Φ x (ξ). (26) Te outsourcing sare tus enters te payoff Π only via te term Θ(ξ), wic does not depend on N. Te first-order conditions (FOCs) for problem (25) can be expressed as follows: dπ dξ dπ dn = η Ξ x Ξ [ Ξ Ξ x (α + β(1 η) α (1 β(1 η))ξ ) αβ(1 η)ξ 1/α (1 α)(1 η)ξ x α = β(1 α)(1 η) α(1 β) [ Ξ x (α + β(1 η) αβηξ ) α(1 βη)ξ 1/α x x ] + ] = 0, (27) Θ(ξ) N β(1 α)(1 η) 1 (w 0 + ν) = 0, (28) and we can proceed in two separate steps: First, te FOC (27) tat does not depend on N is solved for te payoff-maximizing outsourcing sare ξ. Second, using tis solution in (28), we ten solve te oter FOC for te complexity level Ñ. As for te first step, we derive te second-order condition (SOC) in Appendix E and sow tat α + β < 1 is sufficient (toug not necessary) to ensure tat d 2 Π(ξ)/dξ 2 < 0. We assume tat tis parameter restriction is satisfied, wic rules out cases were demand is igly elastic and at te same time components are close substitutes. Te function dπ(ξ)/dξ is ten monotonically decreasing in ξ, wic implies tat ξ (wit 0 ξ 1) is uniquely determined. In te second step, Ñ is also unique. In particular, plugging ξ into Θ(ξ) from (26), and using tis in (28) we obtain Ñ = ( ( ) ) α β(1 α)(1 η) 1 β α β+(1 α)βη α(1 β)(w 0 Θ( ξ) 1 β. (29) + ν) Caracterization and discussion of te firm structure decisions We now caracterize and illustrate te firm s complexity and organization decisions in more detail, and discuss te economic intuition. Proposition 1 summarizes te main insigts Proposition 1 In te closed economy, were te producer decides on te firm s complexity and organization, our model predicts tat: 1. Firms from igly component-intensive industries (η < η 1 ) coose full outsourcing of all suppliers. In more eadquarter-intensive industries, η > η 1, we ave an optimal outsourcing sare 0 ξ < 1. Te tresold level η 1 is given below in eq. (30). 16

17 2. Firms from more eadquarter-intensive industries coose a lower complexity level Ñ and a lower outsourcing sare ξ. 3. Firms wit a larger market size (iger A) coose a iger complexity Ñ, wereas iger unit costs c x and c, iger agency costs ν, and a iger outside opportunity w 0 lead to a lower complexity level Ñ; te outsourcing sare ξ is unaffected by tose parameters. Result 1 sows tat firms from igly component-intensive industries coose full outsourcing of all suppliers, and te corresponding complexity level follows directly as ÑO by using ξ = 1 in (29). To derive te tresold level η 1, notice tat te FOC (27) implies tat dπ(ξ)/dξ > 0 for all values ξ [0, 1] if η is below η 1 = [ ] 1 α α 2 (1 β) 1 δ1/α 1 1 δ [0, 1] (30) 1 α To see tis, evaluate (27) at ξ = 1. Tis yields te following function tat is decreasing in η: dπ(ξ) dξ ξ=1 = β(1 η) α [ 1 η α(1 η α δ 1/α (1 β)) δ(1 ] α α 2 (1 β) η(1 α)) Setting tis expression equal to zero, and solving for η, we obtain η 1 as given in (30). Te tresold level η 1 is decreasing in α and increasing in β. In words, full outsourcing is less likely to occur te better te single components are substitutable (te iger α is) and te less elastic final goods demand is (te lower β is). Importantly, if η > η 1, full outsourcing is no longer te optimal organizational structure, and firms in tose industries turn to a ybrid sourcing strategy (0 ξ < 1) wit some (or all) suppliers vertically integrated. Result 2 decribes te comparative statics of te firm structure wit respect to te sectoral eadquarter-intensity. Starting wit te complexity coice, Ñ from (29) depends on η bot directly and indirectly via te outsourcing sare ξ. Te direct effect is negative, for essentially te same reason as explained for Ñs above, assuming tat market size A is large: Supplier incentives are weaker in more eadquarter-intensive industries, and te producer countervails tis by coosing fewer suppliers. As for te indirect effect, more outsourcing is per se endogenously associated wit more complexity, since te producer countervails te adverse impact of vertical integration on te suppliers incentives by aving fewer suppliers. As ξ depends negatively on η (as we sow next), te indirect effect of η on Ñ is tus also negative. Turning to te comparative statics of ξ wit respect to η, we can adopt an indirect approac to illustrate te economic intuition. First, recall our Lemma 1 wic states tat te producer is able to obtain every revenue sare (Sapley value) in te range between (s 0 /R) min = 1 1+γ and (s 0 /R) max = 1+γ(1 δ) 1+γ by adjusting te outsourcing sare appropriately. Tis available range is illustrated in Figure 1, were te dased curve depicts (s 0 /R) min and te dotted curve depicts (s 0 /R) max, respectively. Notice tat bot curves are monotonically increasing 17

18 in η, tat is, te producer as iger bargaining power in more eadquarter-intensive sectors under any organizational structure. Second, recall from te analysis in Section 3.1. tat te optimal revenue sare 0tat ite producer would obtain in a first-best world is given by w +αν (s0 /R) = 1 β(1 η) α(w 0 +ν). Tis sare, wic is linearly increasing in η, is depicted as te solid curve in Figure 1. Te left (rigt) panel in tat figure assumes a ig (low) value of δ, wic sifts up te (s0 /R)max curve wile te oter curves are te same in bot panels. s0 R s0 R Η Η Figure 1: Organizational decision optimal and realized eadquarter revenue sare Solid: optimal sare (s0 /R). Dased: sare under full outsourcing sare, (s0 /R)min. Dotted: sare under full integration, (s0 /R)max. Parameters: α = 0.5, β = 0.4, ν = 1, w0 = 0.5. Left panel: δ = 0.9, rigt panel: δ = 0.4. Intuitively, te producer s organizational decision can be tougt of as coosing ξ in suc a way tat er realized revenue sare is realigned as closely as possible wit te optimal one. For low eadquarter-intensity, tis means tat te producer cooses full outsourcing since (s0 /R) < (s0 /R)min. Moreover, in te left panel, se cooses full vertical integration for ig values of η since (s0 /R) > (s0 /R)max. Finally, in te range (s0 /R)min < (s0 /R) < (s0 /R)max te producer can freely coose ξ so as to matc (s0 /R), and since tat revenue sare is increasing in η, tis implies tat se cooses a lower outsourcing sare in more eadquarter-intensive industries. In te left panel te organizational structure across industries tus canges from full outsourcing to ybrid sourcing to full vertical integration over te range of η. In te rigt panel, for low values of δ, integrated suppliers ave too little investment incentives, and ence tere is no fully integrated firm structure even in igly eadquarter-intensive sectors.14 Finally, result 3 of Proposition 1 sows tat N is affected by te oter parameters similarly as N s and N. For instance, te firm s complexity level is lower te iger te suppliers unit costs cx are. Yet, te organizational structure is unaffected since two effects exactly offset eac oter: Lower unit costs cx raise te bargaining power of eac single supplier, as e ten tends to contribute more. Yet, since te firm also cooses more suppliers te lower cx is, and Te prediction tat ξ and η are negatively correlated is similar as in te seminal model by Antràs and Helpman (2004). Yet, since tere are multiple suppliers in our framework, te firm can engage in ybrid sourcing and tereby adjust te firm structure gradually

19 since te revenue level increases, tere is no need for te producer to adjust te distribution of revenue witin te firm via a cange in te organizational structure. 4 Global sourcing We now incorporate te global scale dimension into te producer s problem. Se may now also decide on te country r {1, 2} were eac component i [0, N] is manufactured, and tus se can effectively coose from four different sourcing modes for eac supplier: domestic integration, domestic outsourcing, foreign integration (intra-firm trade) or foreign outsourcing. We assume tat unit costs of foreign suppliers are lower tan for domestic suppliers, c 2 < c 1, were we ave dropped te subscript x for convenience. owever, not depend on te ownersip form of te foreign supplier. 15 Tose unit costs do, Furtermore, for te moment we abstract from any oter cross-country differences, suc as different fixed costs for domestic or foreign component manufacturing, but we will return to tose issues below. It is important to notice tat, altoug suppliers can now be asymmetric along two dimensions, it is still te case tat all suppliers wo sare te same organizational form and te same unit costs (country of origin) are symmetric in teir investment incentives, and tus in teir equilibrium input contributions. Revenue in te open economy can be written as R = A 1 β βη ˆx αγ N γ, were te average supplier contribution is now given by: ˆx α = ξ [(1 l O ) (x O1 ) α + l O (x O2 ) α ] + (1 ξ) [(1 l V ) (x V 1 ) α + l V (x V 2 ) α ]. (31) Here, x kr is te input contribution of a supplier from country r {1, 2} wit ownersip form k = {O, V }, and l k [0, 1] is te offsoring sare among te suppliers of ownersip form k. 4.1 Bargaining and input investments Starting wit te multilateral bargaining in stage 4 of te game, to compute te asymptotic Sapley value for a single supplier j, notice tat a relationsip as in (18) still olds, s r (j) = γ δ(j) (1 + γ)n ( ) xr (j) α R. (32) In oter words, te revenue sare realized by supplier j reflects is ownersip rigts via δ(j), and is own input contribution x r (j) relative to te average supplier contribution ˆx, wic is te same for all j since we ave a continuum of suppliers. Turning to te producer, se realizes te residual revenue sare in te bargaining stage, tat is ˆx s 0 R = 1 γ N ( ) (1 + γ)n xr (j) α δ(j) dj (33) j=0 ˆx 15 See Nowak et al. (2012) for a global sourcing model wit two asymmetric suppliers and economies of scope, were it is assumed tat external contractors ave iger unit costs tan integrated affiliates. 19

20 In stage 3, te suppliers of te four different sourcing modes coose teir input amounts wile anticipating (32), as described in Appendix F. From tose contributions, it is straigtforward to see tat x k2 = (c 1 /c 2 ) 1/(1 α) x k1 and x V r = δ 1/(1 α) x Or. Tat is, foreign suppliers contribute more tan domestic suppliers of te same ownersip form, because of teir effective cost advantage (c 1 /c 2 > 1). Furtermore, internal suppliers contribute less tan external suppliers from te same country, because of teir inferior ownersip rigts. As for te producer, we sow in Appendix F tat er realized revenue sare (33) can be rewritten as s 0 R = 1 γ 1 + γ ξ(1 + φ l O) + (1 ξ) δ 1/α (1 + φ l V ) ξ(1 + φ l O ) + (1 ξ) δ(1 + φ l V ), (34) were φ = [ (c 1 /c 2 ) α/(1 α) 1 ] > 0 captures te unit cost advantage of foreign suppliers. It follows from (34) tat te producer realizes a lower revenue sare te iger is te sare of external suppliers ξ, analogously as in te closed economy. As for te global scale dimension, it turns out tat tere is no impact on te producers s revenue sare as long as se sets te same offsoring sare for external and for internal suppliers, i.e., if l O = l V = l. Te intuition is tat two effects ten exactly offset eac oter: On te one and, foreign suppliers ave a iger bargaining power since tey contribute more. On te oter and, tese iger input contributions also raise te revenue level, so tat s 0 /R can effectively remain uncanged. Te producer s revenue sare is affected by te global scale decision, owever, wen l O and l V are not uniform. In particular, if te producer raises l O wile keeping l V fixed, se ends up wit a lower revenue sare s 0 /R, because tis boosts te incentives of already powerful (external) suppliers. Vice versa, increasing l V wile keeping l O fixed, leads to a iger s 0 /R. Te solutions for te optimal eadquarter contribution (N, ξ, l O, l V ) and for te average supplier contribution x(n, ξ, l O, l V ) in te open economy resemble teir closed economy counterparts given in (23). In particular, te optimal contributions by te average supplier and by te eadquarter can be written as (see Appendix F): x(n, ξ, l O, l V ) = Ψ x Φ open x (ξ, l O, l V ) N β(1 η)(1 α) 1 (N, ξ, l O, l V ) = Ψ Φ open (ξ, l O, l V ) N β(1 η)(1 α), (35) were te terms Ψ x and Ψ are still te same as in (14), except tat c x is replaced by te domestic c 1, and were Φ open x (ξ, l O, l V ) and Φ open (ξ, l O, l V ) are now defined as: Φ open x (ξ, l O, l V ) = (Ξ open x Φ open (ξ, l O, l V ) = (Ξ open x ) (1 α)(1 βη) ) (1 α)β(1 η) (Ξ open ) βη 1 β, (Ξ open ) 1 β(1 η) 1 β, (36) wit Ξ open x = ξ(1 + φ l O ) + (1 ξ) δ(1 + φ l V ) Ξ open = 1 + γ γ ξ(1 + φ l O) + (1 ξ) δ 1/α (1 + φ l V ) ξ(1 + φ l O ) + (1 ξ) δ(1 + φ l V ) 20