Bi-Sourcing in the Global Economy

Transcription

1 Bi-Sourcing in te Global Economy Julan Du, Yi Lu and Zigang Tao Tis revision: January 2009 Fortcoming at Journal of International Economics Abstract In organizing production, many rms conduct bi-sourcing, i.e., acquiring te same set of inputs by bot buying from external suppliers (outsourcing) and carrying out in-ouse production (insourcing). We sow tat, by adopting te bi-sourcing strategy, rms can use te payo from one supplier as a backup option in negotiating wit te oter supplier (te cross-treat e ect). Wen rms conduct bisourcing in te global economy consisting of te ig-waged Nort and low-waged Sout, tey need to make te location coice for bot insourcing and outsourcing. We nd tat te low wage in te Sout can encourage investment by component suppliers (te cost e ect). However, rms may acieve a better cross-treat e ect by relocating overly strong component supplier from te cost-advantageous Sout to te cost-disadvantageous Nort (te balancing e ect). Te optimal bi-sourcing strategy is determined by te interplay of te cost e ect and te balancing e ect. Corresponding autor: Zigang Tao, Faculty of Business and Economics, Te University of Hong Kong, Pokfulam Road, Hong Kong. Tel: ; Fax: ; ztao@ku.k. Julan Du and Yi Lu are from Department of Economics, Cinese University of Hong Kong and Scool of Business, Te University of Hong Kong respectively. We would like to tank Tom Hout, Ivan Png, Larry Qiu, Micael Riordan, Tomas Ross, editor Jonatan Eaton, two anonymous referees, and participants in te 2005 Econometric Society World Congress, te 2005 Summer Worksop on Industrial Organization and Management Strategy at Tsingua University, te 2005 International Conference on Trade and Investment in East Asia at Fudan University, and 2006 Midwest International Trade Conference for teir useful comments and suggestions. Financial support from HIEBS and Hong Kong Researc Grants Council is greatly acknowledged. 1

2 1 Introduction In organizing production, a rm needs to decide weter to produce intermediate inputs internally (insourcing) or purcase tem from external suppliers (outsourcing). Wile muc empasis as been placed on te growt of outsourcing in business magazines and newspapers, an emerging interesting arrangement is wort investigating. Many rms are acquiring te same set of inputs by bot purcasing from external suppliers and carrying out in-ouse production. We call it bi-sourcing as it contains bot outsourcing and insourcing. Mattel provides an example of bi-sourcing. Mattel made most of its own die-casting molds at a facility in Malaysia, but also outsourced tem to rms in Hong Kong (Jonson, 2007). Anoter example is te long-term maintenance of U.S. airlines. It is reported tat alf of U.S. airlines eavyoveraul work is conducted by in-ouse mecanics, wile te oter alf is now performed by outside vendors in te U.S. and overseas, wic is a big surge from less tan a tird in 1990 (Carey and Frangos, 2005). In recent years, wit IT services gaining importance, business corporations ave increasingly adopted a set of internal and external service providers in te global economy (Coen and Young, 2006). For example, DuPont as created wat it calls a global IT alliance tat blends services from more tan ten service providers and DuPont s own internal resources to meet te demands of te business. Similarly, te accounts-payable process of GMS, a global manufacturing and service rm, as in fteen years moved from being igly centralized and internal, to globally decentralized and internal, to globally decentralized wit a mix of internal and external resources. Wy do companies conduct bi-sourcing in te global economy? To answer tis question, we rst look at ow bi-sourcing may perform better tan bot insourcing and outsourcing in a closed-economy model. By conducting te bi-sourcing strategy, te rm deals wit bot an internal supplier and an external supplier. In negotiating wit one supplier, te rm can use its payo from te oter supplier as a backup option (called te cross-treat), tereby aving a iger incentive to invest tan in te case of eiter insourcing or outsourcing. Meanwile, wen negotiating sequentially wit te two suppliers, it is optimal for te rm to bargain rst wit te internal supplier and ten te external supplier. As te external supplier makes component investment later tan te internal supplier, te incentive to invest under bi-sourcing is as strong as tat under outsourcing, wic in turn is stronger tan tat under insourcing according to te property rigts teory of te rm (Grossman and Hart, 1986). Consequently, a bi-sourcing strategy induces iger levels of investment and tus production e ciency 2

3 tan does eiter insourcing or outsourcing. Te coice of organizational forms depends on te organizational xed costs as well as production e ciency. Bot insourcing and outsourcing involve signi cant xed costs. As bi-sourcing contains bot insourcing and outsourcing, it is expected to ave te igest xed costs among te tree organizational forms. Our analysis tus predicts tat only tose rms wit te igest productivity will adopt bi-sourcing because teir revenues are large enoug to cover te extra organizational xed costs. Our model is ten extended to te global-economy setting tat consists of te ig-waged Nort and te low-waged Sout. In addition to deciding on te organizational form, te rm also cooses te location of component suppliers. A rm wit its eadquarters in te Nort can locate bot te internal and external component suppliers in te Nort or in te Sout. Alternatively, te rm can coose to locate internal and external suppliers separately wit one in te Nort and te oter in te Sout. Wat drives te location coice of te internal and external component suppliers? We identify two factors. One is te cost e ect. Wit te lower wage in te Sout as compared wit te Nort, te suppliers (bot external and internal) ave iger incentives to invest, wic enances production e ciency. Te oter factor is te balancing e ect. Te beauty of bi-sourcing lies in tat te rm can use te cross-treat to increase its own incentive to invest. To maximize te e ectiveness of te cross-treat, owever, te rm does not want eiter component maker to be too strong relative to te oter one. In particular, it could be optimal for te rm to locate te overly strong (or weak) supplier in te cost-disadvantageous Nort (or te costadvantageous Sout) to acieve a better balancing e ect between te two suppliers. Te optimal bi-sourcing strategy is determined by te interplay of te cost e ect and te balancing e ect. In many cases we ave considered, locating bot internal and external suppliers in te Sout yields te igest production e ciency among all possible patterns of te bi-sourcing strategy. Wen one supplier is too strong relative to te oter, te balancing e ect dominates te cost e ect, and it is ten optimal to ave te stronger supplier in te Nort and te weaker supplier in te Sout. Our paper is related to a growing literature on te coice between insourcing and outsourcing in te global economy. Tese studies make use of recent advances in te economic teory of organizations suc as transaction costs economics (TCE) and property-rigts teory (PRT) 1 to explain te 1 See Williamson (1975, 1985) for te TCE, and Grossman and Hart (1986), Hart and Moore (1990) and Hart (1995) for te PRT. 3

4 growing vertical disintegration of production in te global economy. 2 Our paper is most closely related to Antràs and Helpman (2004). Tey integrate te property-rigts teory of rm and te eterogeneity of rm productivity (Melitz (2003)) into a general equilibrium model of international trade to study te coice between insourcing and outsourcing in te global economy. However, in teir paper as well as related papers in tis strand of literature, outsourcing and insourcing are two distinct and separate modes of acquiring intermediate inputs. In contrast, we focus on te emerging pattern of bi-sourcing and its strategies in te global economy. Our paper is also associated wit te industrial organization literature on second sourcing or dual sourcing. 3 Some of tese papers study te bene ts for a buyer to use multiple outside or inside sellers wen tere is uncertainty about production costs. Oters investigate te incentives for a seller to license its tecnology to its rivals as a credible commitment to ig-quality/low-price supply in face of uncertain market demand. Wit a few exceptions, 4 owever, te industrial organization literature does not look into te impacts of dualsourcing on te incentives for R&D or investment, wic is te focus of our paper. We use an incomplete-contracts framework to study ow various sourcing strategies a ect te incentives to invest. Te rest of te paper is organized as follows. Section 2 lays out te basic model. Te bencmark case of a closed economy model is analyzed in Section 3, and it is ten extended to te case of global economy in Section 4. Section 5 concludes te paper. 2 Basic Model We extend te framework of Antràs and Helpman (2004) to study bi-sourcing. Consider an economy consisting of two sectors: a omogeneous good (X) produced wit te constant returns to scale tecnology and a continuum of di erentiated goods (Y ) produced wit te increasing returns to scale tecnology. Tere is a unit measure of consumers wit te preference of te representative consumer given by 2 Te papers include McLaren (1999), Grossman and Helpman (2002, 2004, 2005), Puga and Tre er (2002), Antràs (2003), Marin and Verdier (2003), Antràs and Helpman (2004), Antràs et al. (2005), Grossman et al. (2005), etc. See Antràs (2005), Spencer (2005), and Helpman (2006) for literature review. 3 See, for example, Anton and Yao (1987), Separd (1987), Farrell and Gallini (1988), and Kerscbamer and Tournas (2003). 4 See Riordan and Sappington (1989) and Dick (1992). 4

5 Z 1= U = X 1 Y ; Y = y(!) d! ; (1)!2 were represents te weigt tat te consumers put on te di erentiated goods, X is te consumption of te omogeneous good, y(!) is te consumption of variety! of te di erentiated goods Y, Y is te index of aggregate consumption of di erentiated goods and te set represents te mass of tose goods. Te elasticity of substitution between any two di erentiated goods is 1=(1 ) > 1. Te consumer preference of equation (1) leads to an inverse demand function for eac variety! of te di erentiated goods: p(!) = I Y 1 y(!) (2) Y were p(!) is te price of variety! and I denotes te consumers total expenditure. To produce any variety of te di erentiated goods, two variety-speci c inputs, (!) and m(!), are jointly required, wic are referred to as eadquarters service and manufactured component respectively. Correspondingly tere are two kinds of producers: nal good producers (denoted by H), wo provide te variety-speci c eadquarters services ((!)), and component makers (denoted by M), wo supply te variety-speci c manufactured components (m(!)). Eac unit of (!) and m(!) requires one unit of labor, te wage rate of wic is assumed to be a constant w in te closed-economy setting (Section 3) and will be relaxed in te global-economy setting (Section 4). Every nal good producer organizes te production process, combining te eadquarters service and te manufactured component in te fasion of te Cobb-Douglas function to make te di erentiated good 1 (!) m(!) y(!) = ; 0 < < 1; (3) 1 were is a rm-speci c productivity parameter, and is a sector-speci c parameter regarding te intensity of eadquarters service in te production of di erentiated good! wit a larger indicating a iger intensity of eadquarters service. Combined wit (2), it yields te revenue R = IY (1 ) m (4) 1 were te variety parameter! is left out ereon as all te cases are symmetric. 5

6 For simplicity, it is assumed tat te nal good producer owns te assets for te production of eadquarters service (encefort, te nal good producer and te eadquarters are used intercangeably). 5 But it needs to make an organizational coice for te supply of te manufactured component. Te nal good producer can set up a subsidiary making te component in-ouse (called insourcing and denoted by I), or contract wit an external supplier for te manufactured component (called outsourcing and denoted by O), or bot (called bi-sourcing and denoted by B). In te global-economy setting (Section 4), tere is an additional location-coice decision between te igwaged Nort and te low-waged Sout for te component manufacturing. Te time line of te model is as follows. At time 0, te nal good producer makes te organizational and location coices. Ex ante investments in input production, including manufactured component (m) and eadquarters service (), are made at date 1. At date 2, m is supplied and combined wit to make te nal product. As in Antràs and Helpman (2004), we consider a setting of incomplete contracts. It is assumed tat te precise nature of te required inputs is di cult to specify ex ante, and tat, once revealed ex post, te nature of te required inputs is still not veri able by a tird party. It is furter assumed tat te ex ante investments for input production are not contractible and neiter is te sales revenue. As a result, te nal good producer H and component supplier M bargain over te surplus value from trade at date 2 after tey make teir own investments at date 1. Following te property-rigts teory of te rm (Grossman and Hart (1986), Hart and Moore (1990), and Hart (1995)), we assume tat te bargaining takes place in bot outsourcing and insourcing and tus in all te tree organizational forms we examine. Neverteless, as ownersip over te assets for component manufacturing confers te residual rigts of control, te e ective bargaining powers between H and M vary from outsourcing to insourcing and bi-sourcing, wic will be elaborated furter in Section 3. 5 In a more general setting, it could be optimal for te component manufacturer to own te assets for te production of eadquarters services, especially wen component manufacturing is very important relative to eadquarters service. We would like to tank an anonymous referee for pointing out tis type of insourcing, wic is alternative to te oter type of insourcing te nal good producer owning te assets for component manufacturing. In tis paper, as in Antras and Helpman (2004), we implicitly assume tat te eadquarters service is su ciently important so tat it is optimal (or not optimal) for te nal good producers (or te component manufacturers) to own te assets for te production of eadquarters services. Wat remains to be investigated is weter te nal good producers sould own te assets for component manufacturing or not. 6

7 3 Bi-sourcing in te Closed Economy In tis section, we analyze te equilibrium in a closed-economy setting were te production of bot components and nal goods is carried out in one country. Te decision to be made concerns only wit te organizational coice tat te eadquarters coose to ave insourcing, or outsourcing, or bi-sourcing for te supply of components. Te tree organizational forms di er in teir xed organizational costs. We assume tat te xed organizational costs of insourcing (denoted by f I ) are iger tan tose of outsourcing (denoted by f O ) (for rationales please read Antràs and Helpman (2004)), and tat bi-sourcing as te igest xed organizational costs (denoted by f B ) for te xed costs associated wit bot insourcing and outsourcing are involved. Tat is: 6 f B > f I > f O : (5) Te main di erence among te tree organizational forms, owever, lies in teir impacts on te incentives for investment in input production and consequently te size of te trading surplus, wic we turn to in te following subsections. 3.1 Single Sourcing In single sourcing, te nal good producer H eiter signs a contract wit M to purcase te variety-speci c component (i.e., outsourcing) or integrates wit M to produce te component in-ouse (i.e., insourcing). As sown by Grossman and Hart (1986) and Antràs and Helpman (2004), even if te nal good producer H as te same bargaining power wit te internal and external suppliers, it can obtain greater e ective bargaining power vis-a-vis te internal supplier as compared wit te external supplier. Tis is because under insourcing te nal good producer owns te assets for component manufacturing and as better outside options. For simplicity, we assume tat te ex post bargaining process follows a generalized Nas bargaining game were H as iger e ective bargaining power in insourcing (denoted by I 2 (0; 1)) tan in outsourcing (denoted by O 2 (0; 1)), i.e., I > O. 7 Assume furter tat te ex post bargaining is e cient. Ten H and M will reac an agreement on te division of surplus R at date 2. H gets k R 6 For convenience, te xed costs (f I ; f O and f B ) are expressed in terms of units of labor. We can obtain te monetary value of xed costs by multiplying tem by wage rate w. 7 Hencefort, e ective bargaining power is simply referred to as bargaining power. 7

8 and M gets (1 k )R, were k = O in te case of outsourcing (i.e., k = O) and k = I in te case of insourcing (i.e., k = I). At date 1, M and H coose m and to maximize (1 k )R wm and k R w respectively. Te total payo of te two parties under single sourcing can be sown as follows: k = k (I) 1 1 Y 1 1 wf k (6) were k = 1 w 1 (k ) 1 (1 k ) 1 (1 ) [1 ( k + (1 k )(1 ))]: To save space, derivation of key equations and proof of all Lemmas and Propositions are contained in te Appendix (available upon request). 3.2 Bi-sourcing Te scenario of bi-sourcing is more complicated as te nal good producer H obtains te manufactured component from two suppliers one internal (denoted by M 1 ) and one external (denoted by M 2 ). Te investments made by te internal and external suppliers are denoted by m 1 and m 2 ; respectively. We de ne some notation as follows: R = IY [ ] [ m 1+m 2 ] (1 ) ; 1 R 1 = IY [ ] [ m 1 1 ](1 ) ; R 2 = IY [ ] [ m 2 1 ](1 ) : (7) Expressions (7) denote te respective total revenues wen bot M 1 and M 2 supply te component (R), only M 1 supplies te component (R 1 ) and only M 2 provides te component (R 2 ). In negotiations, te total revenue available to te tree parties amounts to R, from wic H needs to pay P 1 to M 1 and P 2 to M 2 respectively. We consider a sequential bargaining process among te tree parties. After deciding to adopt bi-sourcing but before all tree parties make any investment, te nal good producer H may announce weter to negotiate wit te internal supplier M 1 rst and ten te external supplier M 2 or te oter way around. 8 8 Tere is a large literature on multi-party bargaining problems, focusing on te Nas bargaining solution and te strategic bargaining approaces tat ave unique equilibrium and implement te Nas bargaining solution (Jun, 1987; Cae and Yang, 1988, 1994; Krisna and Serrano, 1996). Te tree-party bargaining problem studied by Marx and Sa er (2004) is probably te closest to te bargaining problem of bi-sourcing. Tey use strategic bargaining approac to analyze ow a buyer bargains sequentially wit two sell- 8

9 Consider te case were te eadquarters H rst bargains wit te internal supplier M 1 and ten wit te external supplier M 2. Using te backward induction approac, we rst analyze te second stage te negotiation between H and M 2 given tat H as successfully concluded its negotiation wit M 1, in wic H pays P 1 to M 1 and retains R 1 P 1 for itself. In negotiating wit M 2, H expects to get R P 1 P 2 if te transaction is carried out but obtains te disagreement option value R 1 P 1 if negotiation breaks down, wereas M 2 obtains a transfer payment P 2 from H if te transaction is conducted and zero oterwise. Given tat bargaining is e cient, H and M 2 reac an agreement wit M 2 receiving P 2 = (1 O )(R R 1 ) (8) and H aving R 1 P 1 + O (R R 1 ). Next we analyze te rst stage te negotiation between H and M 1. If tere is trade wit M 1, H secures R P 1 P2 ; oterwise, H is able to at least gain wat e can reap from te scenario of outsourcing, i.e., O R 2. 9 Similarly, M 1 gets P 1 wen te transaction is carried out, and zero oterwise. Tus te Nas bargaining yields a division of te surplus from trade: R P2 O R 2 = R 1 + O (R R 1 ) O R 2 between H and M 1, wit M 1 receiving P 1 = (1 I )(R 1 + O (R R 1 ) O R 2 ) (9) and H obtaining R P1 P2. Note tat te nal good producer as te outside option of R 1 P 1 wen bargaining wit te external supplier and te outside option of O R 2 wen bargaining wit te internal supplier. In comparison wit te zero outside option value under single sourcing, tese outside options increase te sare of payo to te nal good producer. Hencefort, te impacts of tese increased outside options are referred to as te cross-treat e ects. Under te assumption of perfect foresigt, H cooses to maximize R P1 P2 w, M 1 cooses m 1 to maximize P1 wm 1, and M 2 cooses m 2 ers, and nd tat te result is te same as tat under te Nas bargaining solution. We tus use te Nas bargaining solution to study te bargaining between te eadquarters and te two suppliers, wit te eadquarters rst bargaining wit one supplier and ten wit te oter supplier. Tis framework allows us to ave easy comparison wit te bargaining solutions of single insourcing and single outsourcing, and it also o ers a tractable way of examining ow te eadquarters bargaining wit one supplier is a ected by its bargaining wit te oter supplier. 9 R R 1 collapses into R 2 wen te internal supplier M 1 does not supply any manufactured component, i.e., m 1 = 0, and consequently R 1 P 1 + (R R 1 ) collapses into R 2. 9

10 to maximize P2 wm 2. Solving tese optimization problems, we obtain te total payo in tis scenario of bi-sourcing as were T 1 A B = B (I) 1 1 Y 1 1 wf B (10) B = 1 T 1 (1 O ) 1 (1 ) w 1 [1 (T + (1 )(1 O ))]; (1 ) (1 ) 1 1 = O I +(1 O ) I + A O (1 I ) 1 ; A A = 1 + O I 2 O (1 O )(1 I ) 1 1 (1 ) > 1: Using te same backward induction approac, we can analyze te case were te eadquarters H rst negotiates wit te external supplier M 2 and ten te internal supplier M 1. But we can sow tat, under tis sequence of negotiation, bi-sourcing will collapse into single outsourcing. Speci cally, Lemma 1 If te eadquarters H negotiates wit te external supplier M 2 before te internal supplier M 1, te bi-sourcing scenario is reduced to te single outsourcing case. Te intuition of Lemma 1 rests upon te following two e ects. (i) From te property rigts teory of te rm, we know tat te internal supplier as a lower incentive to invest tan does te external supplier, because it does not own te assets for component manufacturing (called ownersip effect). Matematically, for any given investment level, te marginal return from investment of te internal supplier is always lower tan tat of te external supplier (i.e. MR 1 < MR 2 ). (ii) For eac supplier, te marginal return from investment is decreasing (i.e. MR i (x + y) < MR i (x), for any x; y > 0) (called sequence e ect). Wen negotiated later, te internal supplier makes investment after te external supplier does. In tis case, bot te sequence e ect and te ownersip e ect work against te internal supplier, wit its marginal return from investment always lower tan te wage rate, i.e., MR 1 (m 2 + m 1 ) < MR 1 (m 2 ) < MR 2 (m 2 ) = w. Here te rst inequality comes from te sequence e ect, te second inequality re ects te ownersip e ect, and te last equation is te rst-order condition of te external supplier s program in making investment coice. Hence te internal supplier would not make any investment and te case collapses to single outsourcing. Notice te same problem does not occur wen te external supplier is negotiated later, because in tat case te external supplier s disadvantage in te sequence e ect could be overcome by its advantage in te ownersip e ect. 10

11 It is clear from te above discussion tat, in our setting, dual outsourcing will be reduced to single outsourcing, because te two external suppliers ave te same ownersip e ect but te sequence e ect works against te second external supplier. Similarly, dual insourcing will be reduced to single insourcing. Tese results imply tat, wile dual insourcing or outsourcing may ave impacts on production cost or consumer demand as studied in te industrial organization literature, neiter arrangement as any di erent e ect on te incentives for investment from tose of single insourcing or outsourcing in te framework of incomplete contracts. Te focus of tis paper, owever, is about te impacts of sourcing strategies on te incentives for investment. Bi-sourcing as been sown to impact te incentives for investment di erently from single insourcing or single outsourcing. 3.3 Coice of Organizational Form Wit ex ante lump-sum transfers, te eadquarters will pick te organization wit te igest total payo. It is clear from equations (6) and (10) tat te total payo ( i ) in any scenario is a linear function of (I) 1 1 Y 1 1, and it just di ers in te slope and te intercept term across te scenarios. Te intercept terms are te negative of te xed organization costs, and teir comparison is straigtforward. So we will focus on te comparison of te slope term, i, wic will be referred to as production e ciency in te rest of tis paper. Production e ciency is in turn determined by te equilibrium investment levels (m for components and for eadquarters service). We will rst sow tat, under fairly general conditions, bi-sourcing as iger production e ciency tan do bot insourcing and outsourcing. Lemma 2 So long as I is not su cient large, te equilibrium investment levels under bi-sourcing are iger tan tose under bot insourcing and outsourcing. >From te work of Grossman and Hart (1986) and Antràs and Helpman (2004), we know te eadquarters as a iger incentive to invest under insourcing tan under outsourcing. It is because te eadquarters as iger e ective bargaining power under insourcing tan under outsourcing. As sown in Figure 1, te optimal reaction curve of te eadquarters under insourcing (denoted by I ) lies above tat of outsourcing (denoted by O ). Under bi-sourcing, te eadquarters bargains wit bot te internal and external suppliers, and as a result its combined e ective bargaining power sould presumably be between tat of insourcing and tat of outsourcing. However, te eadquarters can make use of te cross-treat in bargaining 11

12 wit bot te internal and external suppliers i.e., use its payo from one supplier as its outside option in bargaining wit te oter supplier to enance its incentive to invest. It is sown in te Appendix (available upon request) tat so long as I is not su ciently large, te cross-treat e ect dominates so tat te eadquarters as a iger incentive to invest under bi-sourcing scenario tan se does in insourcing. Tus, te optimal reaction curve of te eadquarters under bi-sourcing (denoted by B ) is above tat of insourcing (denoted by I ), as illustrated in Figure 1. Meanwile, as sown in Lemma 1, under bi-sourcing, it is optimal for te eadquarters to bargain wit te internal supplier rst and ten wit te external supplier. Te component investment can be viewed as te internal supplier rst making investment m 1, and ten te external supplier making investment m 2. As te external supplier is te later one of te two suppliers making te component investment, te optimal reaction curve for component investment under bi-sourcing (denoted by m B ) sould be te same as tat of outsourcing (denoted by m O ), as sown in Figure 1. Furtermore, based on te work of Grossman and Hart (1986) and Antràs and Helpman (2004), te optimal reaction curve for component investment under outsourcing is located to te rigt of tat under insourcing (denoted by m I ), because te external supplier owns te assets and tus as more incentives to invest. Taken togeter, te equilibrium point under bi-sourcing (represented by point B in Figure 1) is determined by te intersection of te optimal reaction curve of te eadquarters and tat of te supplier, and it is located to te norteast of te equilibrium points under single sourcings (denoted by O and I for outsourcing and insourcing, respectively). As investment levels under any sourcing strategy are below te rst-best ones, greater investment levels imply iger production e ciency. It follows tat te investments under bisourcing are iger tan tose under bot insourcing and outsourcing, and so are te production e ciency. Te comparison of insourcing and outsourcing as been analyzed by Antràs and Helpman (2004). In a eadquarters-intensive industry, te eadquarters investment is more important to te production process tan is te component supplier s. Hence it can be sown tat te production e ciency is iger under insourcing tan under outsourcing. In a component-intensive industry, te component supplier plays a more important role in te cooperative relationsip tan te eadquarters does, and ence production e ciency is iger under outsourcing tan under insourcing. Tus, in combination wit Lemma 2, we ave te following lemma. Lemma 3. In a eadquarters-intensive industry, production e ciency is te igest under bi-sourcing, followed by insourcing and ten outsourcing. 12

13 In a component-intensive industry, production e ciency is te igest under bi-sourcing, followed by outsourcing and ten insourcing. Te tree sourcing strategies also di er in xed costs as detailed in equation (5). Togeter we ave: Proposition 1 (1) In a eadquarters-intensive industry, te rms wit ig productivity adopt te bi-sourcing strategy, te rms wit low productivity adopt te outsourcing strategy and tose intermediate rms coose te insourcing strategy. (2) In a component-intensive industry, te rms wit ig productivity adopt te bi-sourcing strategy wile tose wit low productivity adopt te outsourcing strategy Bi-sourcing in te Global Economy Now we turn to te open-economy case were tere are te ig-waged Nort and te low-waged Sout. Let w N denote te wage rate in te Nort and w S denote tat in te Sout were t wn > 1: For simplicity, it is assumed w S tat te eadquarters service () can only be produced in te Nort, wereas te manufactured component (m) can be produced eiter in te Nort or in te Sout. As single sourcing strategies ave been analyzed by Antràs and Helpman (2004), we will only examine bi-sourcing strategies in te global economy. Tere are four types of bi-sourcing: (i) bi-sourcing in te Nort (denoted by NN), (ii) bi-sourcing in te Sout (denoted by SS), (iii) bisourcing wit insourcing in te Nort and outsourcing in te Sout (denoted by N S), and (iv) bi-sourcing wit insourcing in te Sout and outsourcing in te Nort (denoted by SN). As in te closed-economy setting, te coice among te four bi-sourcing arrangements depends on te interplay between te organizational xed cost and te production e ciency. However, we know tat te organizational xed costs ave predictable impacts on te organizational coice (te igerproductivity rms versus lower-productivity rms arguments). Tus, in tis section we would like to focus on te production e ciency (denoted by ) as te key criterion for determining te optimal bi-sourcing strategy. Indeed, te insigts from te property-rigts teory of te rm are about te impacts of organizational coice on te incentive to invest and production e ciency. It is straigtforward to sow tat production e ciency under bi-sourcing in 10 In tis case, insourcing is always dominated by outsourcing because of its lower production e ciency and iger xed costs. 13

14 te Nort (NN) is strictly lower tan tat under bi-sourcing in te Sout (SS) due to te iger wage in te Nort. Tus, we will only compare SN, NS, and SS in te following analysis. 4.1 Cost E ect and Balancing E ect Following te same line of analysis as in Section 3.2, we derive te production e ciency () under SN, NS, and SS as follows >< >: SS = T x SS 1 [t(1 O )] NS = T (x NS ) 1 [t(1 O )] 1 (1 ) w N 1 1 (1 ) w N SN = T (x SN ) 1 (1 O ) 1 (1 ) w N 1 1 [1 (T x SS +(1 )(1 O ))] 1 T (x NS ) + (1 )(1 O ) x NS 1 T (x SN ) + (1 )(1 O ) txsn t+1 tx SN (11) were 12 8 T (x i ) = O I +(1 O ) I (x i ) (1 ) + O (1 I ) (1 x i ) (1 ) ; i 2 fss; NS; SNg >< >: x SS = x NS = x SN = i 1 (1 O )(1 I ) 1 (1 ) 1+ O I 2 O (1 O )(1 I ) t(1 O ) O (1 I ) t(1 O )(1 I ) (1 O ) t O (1 I ) i 1 1 (1 ) i 1 1 (1 ) Similar to wat is sown in te proof of Lemma 2 in te Appendix (available upon request), T (x i ) is te slope of te eadquarters optimal reaction curve under bi-sourcing, and tus it represents te eadquarters incentive to invest. x i is te sare of manufactured component made by te internal supplier. 13 As in our analysis of bi-sourcing in te closed economy (Section 3.3), te production e ciency ( i ) is determined by te equilibrium investment levels, wic are an outcome of te intersection between te eadquarters optimal reaction curve ( i ) and te external supplier s optimal reaction curve (m i ). 14 Te di erence among te tree bi-sourcing strategies (SS, SN, and NS) lies in te location coice for te internal and external suppliers. Wen te 11 It is assumed tat te e ective bargaining power between te eadquarters and te suppliers remains constant across te locations (See Grossman, Helpman and Szeidle (2004) for making te same assumption.) 12 It is noteworty tat in order to ave te SN case, te wage di erence between te Sout and te Nort cannot be too large, i.e., t < 1 1, oterwise te SN case reduces I to single insourcing in te Sout. 13 Note tat T (x i ) is same in functional form as T A 1 in te close-economy case of Section Recall tat it is te external supplier wo makes investment after te internal supplier does, and wo e ectively determines te total component supply (m 1 + m 2 ). 14 t+x NS 1 i

15 external supplier moves from te ig-wage Nort (i.e. SN) to te low-wage Sout (i.e. SS or N S), its optimal reaction curve sifts to te rigt (i.e., from curve m SN to curve m NS or m SS as in Figure 2 and Figure 3), tereby lifting te production e ciency. Hencefort tis e ect is called te cost e ect. Meanwile, te location coice for te internal and external suppliers affects te equilibrium component manufacturing by te two suppliers, and consequently te sare of manufactured component made by te internal supplier (x i ). It is straigtforward to sow tat x SN > x SS > x NS. Intuitively, te internal supplier produces te most relative to tat of te external supplier wen it is located in te low-wage Sout but te external supplier is located in te ig-wage Nort. Hence te rm can make use of te location coice to alter te relative production sare of te internal and external suppliers (i.e., x i ) and tus adjust te eadquarters bargaining power vis-a-vis tat of te component suppliers to increase te eadquarters incentives to invest (i.e., T (x i )), wic subsequently leads to a sift of te eadquarters optimal reaction curve. Tis e ect is called te balancing e ect. However, te relative position of te eadquarters optimal reaction curves under te tree types of bi-sourcing strategies is not straigtforward, wic will be analyzed in te next subsection. 4.2 Caracterization of Optimal Bi-sourcing Strategy To caracterize te optimal bi-sourcing strategy in te global economy, we need to compare te magnitude of te balancing e ect (i.e., T (x)) across te tree types of bi-sourcing strategies. It can be sown tat T (x) is concave in x. Let x be te x tat maximizes T (x). It can be furter sown tat tere exists a value of I, denoted by I, under wic x SS = x (te proof is provided in te Appendix wic is available upon request). For illustration, we give a numerical example. Numerical example: Set = 0:2, = 0:5, and O = 0:5. 15 It is easy to derive x = 1 I 0:9 + 1 and x SS = 1 I 0:9. By equating x to x SS, I I p5 0:9 1 we can derive I = :6. Wen I = I, bi-sourcing strategy SS as te igest balancing e ect, and in combination wit its advantageous cost e ect, SS emerges as te 15 We follow Krugman and Venables (1995) in setting te values of and. And we assume equal bargaining between te eadquarters and te external suppiler (i.e., = 0:5), wic is commonly used in te literature on te teory of te rm. 15

16 optimal bi-sourcing strategy. Wen I is not equal to I, tere exist two possible scenarios: one is I < I (called strong internal supplier") and te oter is I > I (called weak internal supplier"). Te case of "strong internal supplier" is illustrated by Figure 2. Intuitively, wen te internal supplier as too strong bargaining power compared wit te external supplier, te eadquarters would ave too strong crosstreat in negotiating wit te external supplier but too weak cross-treat in negotiating wit te internal supplier. Suc imbalance is te most serious wen te eadquarters orders te internal supply from te low-cost Sout and external supply from te ig-cost Nort (i.e., bi-sourcing strategy SN), implying tat te eadquarters optimal reaction curve under SN lies below tose under SS and NS (see Figure 2 for an illustration). However, by relocating te internal supplier from te cost-advantageous Sout to te cost-disadvantageous Nort (i.e., from bi-sourcing strategy SS to bi-sourcing strategy N S), te eadquarters can acieve a better balancing e ect, wic will increase its incentives for investment (i.e., te optimal reaction curve NS lies above SS in Case A of Figure 2) so long as te wage di erence between te Nort and te Sout (i.e., t) is not too large. In tis case, te equilibrium investment levels under bi-sourcing strategy N S (represented by point NS in Case A of Figure 2) lies to te norteast of equilibrium points SS and SN, implying tat bi-sourcing strategy NS as te igest production e ciency. Wen te wage di erence between te Nort and te Sout is too big, owever, te sift from SS to N S would dampen te internal supplier s incentive to invest so muc tat te eadquarters optimal reaction curve NS lies below 0 SS as illustrated in Case B of Figure 2. In tis case, bi-sourcing strategy SS turns out to ave te igest production e ciency. To summarize, we ave te following proposition Proposition 2 In te case of strong internal supplier (i.e., I < I): (i) locating insourcing in te Nort and outsourcing in te Sout ( NS) is te optimal bi-sourcing strategy so long as te wage di erence between te two countries is not su ciently large; (ii) oterwise, locating bot insourcing and outsourcing in te Sout is te optimal bi-sourcing strategy. In te case of "weak internal supplier", te internal supplier as too weak bargaining power as compared wit te external supplier. Suc imbalance is te most severe wen te weak internal supplier is located in te cost-disadvantageous Nort but te strong external supplier is in te costadvantageous Sout, implying tat te eadquarters optimal reaction curve under NS lies below tose under SS and SN (see Figure 3 for an illustration). Wen te wage di erence between te Nort and te Sout is not 16

17 su ciently large, owever, te eadquarters can acieve a better balancing e ect by moving te external supplier from te Sout to te Nort (i.e., from bi-sourcing strategy SS to bi-sourcing strategy SN), wit te eadquarters optimal reaction curve of SN lying above tat of SS (see Case A of Figure 3). In tis case, te equilibrium investment levels of SS are iger tan tose of N S, but te comparison between equilibrium investment levels of SS and tose of SN is not obvious. It can be formally proved tat te production e ciency under SS is iger tan tat under SN, implying te optimally of bi-sourcing strategy SS. Wen te wage rate in te Nort is too muc iger tan tat in te Sout, moving te external supplier from te Sout to te Nort would overly correct te imbalance of power between te internal and external suppliers, causing te eadquarters optimal reaction curve of SN to lie below tat of SS (see Case B of Figure 3 for an illustration). In tis case, it is obvious tat te equilibrium point of bi-sourcing strategy SS lies in te norteast of tose of SN and NS, implying te optimally of bi-sourcing strategy SS again. To summarize, we ave: Proposition 3 In te case of weak internal supplier (i.e., I > I), locating bot suppliers in te Sout is always te optimal bi-sourcing strategy. Before concluding our analysis, we give a numerical example illustrating te results of Propositions 2 and 3. As sown in Table 1, for te case of strong internal supplier ( I = 0:501 < I), te bi-sourcing strategy of NS is te optimal one wen t is small (i.e., t = 1:05), but te bi-sourcing strategy of SS becomes te optimal strategy wen t is large (i.e., t = 1:1). For te case of weak internal supplier ( I = 0:700 > I), owever, te bi-sourcing strategy of SS is always te optimal strategy. 5 Conclusion In tis paper, we extend te framework of Antràs and Helpman (2004) to study te growing business strategy of bi-sourcing, tat is, rms adopt insourcing and outsourcing simultaneously in acquiring te same set of intermediate inputs. We sow tat by conducting bi-sourcing rms can take advantage of te cross-treat in trilateral negotiations to mitigate te inerent problems of bot insourcing and outsourcing. Given tat bi-sourcing contains te xed costs of bot insourcing and outsourcing, our model predicts tat only te most productive rms will be able to adopt bi-sourcing strategy. Wen conducting bi-sourcing in te global economy, multinational enterprises need to coose te location of internal and external suppliers, i.e., in 17

18 te ig-waged Nort or low-waged Sout. We identify two factors. One is te cost e ect resulting from te wage di erences between te Nort and Sout, and te oter is te balancing e ect in keeping a balance in bargaining power between te internal and external suppliers. Our analysis sows tat in many cases locating bot suppliers in te low-cost Sout generates te igest production e ciency. Wen one supplier is too strong relative to te oter supplier in bargaining power, owever, multinational enterprises may coose to locate te strong supplier in te cost-disadvantageous Nort and te weak supplier in te cost-advantageous Sout to acieve a better balancing e ect. In concluding, it sould be pointed out tat tere are oter possible reasons for te use of bi-sourcing strategy. For example, in-ouse production units may face capacity constraints, under wic it could be optimal to meet te uctuations in demand troug external supply. It is also possible tat external suppliers may face less problems of unionization tan internal production units as in te case of te U.S. automotive industry. Yet anoter possible reason for bi-sourcing is te use of external suppliers as a source of learning te best practices by internal production units. Tese possibilities of bi-sourcing are wort investigating in te future. References Anton, J., Yao, D., Second Sourcing and te Experience Curve: Price Competition in Defence Procurement. RAND Journal of Economics 18, Antràs, P., Firms, Contracts, and Trade Structure. Quarterly Journal of Economics 118, Antràs, P., Property Rigts and te International Organization of Production. American Economic Review (Papers and Proceedings) 95, Antràs, P., Garicano, L., Rossi-Hansberg, E., O soring in a Knowledge Economy. Quarterly Journal of Economics 121, Antràs, P., Helpman, E., Global Sourcing. Journal of Political Economy 112, Carey, S., Frangos, A., Facing Cost Pressures, U.S. Airlines Outsource Crucial Safety Functions. Asian Wall Street Journal, January 24, page 1. Cae, S., Yang, J., Te Unique Perfect Equilibrium of an N-person Bargaining Game. Economics Letters 28, Cae, S., Yang, J., An N-person Pure Bargaining Game. Journal of Economic Teory 62,

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21 m I O m B m = B B I I O O m = m 1 + m 2 Figure 1 21

22 m SN SS m NS m = NS NS SS SS SN SN m = m 1 + m 2 Case A: wen t is not sufficiently large m SN SS m NS m = NS SS SS NS SN NS m = m 1 + m 2 Case B: wen t is sufficiently large Figure 2: wen β I < β I 22

23 m SN SS m NS m = SN SN SS SS NS NS m = m 1 + m 2 Case A: wen t is not sufficiently large m SN SS m NS m = SS SS SN SN NS NS m = m 1 + m 2 Case B: wen t is sufficiently large Figure 3: wen β I > β I 23

24 Table 1: Numerical Results β = β = I t = 1.05 t = t = t = φ φ φ φ NS SS SN I N Note: setα = 0. 2, η = 0. 5, β = 0. 5, and = 1 O w. t / N S = w w. φ is te production efficiency. 24