A North-South model of outsourcing and growth

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1 A orh-souh model of ousourcing and growh Yuki Saio Sepember 217 Absrac I formulae a simple orh-souh R&D-based growh model where final goods firms in he orh endogenously deermine he range of inernaional ousourcing of inermediae goods o he Souh. I show ha a fall in he rade cos (rade liberalizaion) of inermediae goods in he orh: (i) reduces he relaive wage of he orh o he Souh; (ii) increases he ousourced variey of inermediae goods in he orh; and (iii) simulaes economic growh in all counries. Furhermore, conducing welfare analysis, I also show ha a fall in he rade cos of inermediae goods in he orh improves welfare in he Souh more han in he orh. JEL classificaion: F13, F43, O31 Keywords: Inernaional ousourcing; orh-souh; R&D-based growh; Trade liberalizaion; Welfare analysis The auhor is especially graeful o Koichi Fuagami, Yuichi Furukawa, Tasuro Iwaisako, Tadashi Moria, Akihisa Shibaa, Kouki Sugawara, Yoshihiro Tomaru, and seminar paricipans a Chukyo Universiy, Osaka Universiy and Oaru Universiy of Commerce for heir useful commens and suggesions. The auhor also graefully acknowledges financial suppor from he Japan Sociey for he Promoion of Science hrough a Gran-in-Aid for JSPS Fellows o. JP16J2242. The auhor akes responsibiliy for any errors. Graduae School of Economics, Osaka Universiy, 1-7 Machikaneyama, Toyonaka, Osaka 56-43, Japan. yuki.saio.r@gmail.com.

2 1 Inroducion In recen decades, because of a decline in he rade cos (e.g., coss of communicaion, search and ransporaion), he environmen for producion of final goods has changed. In paricular, final goods firms have ousourced he producion of some inermediae goods (or some producion asks) ha are needed o produce final goods, wihin he oal use of inermediae goods. If he price of an inermediae good in a foreign counry is cheaper han ha in he home counry, final goods firms purchase he inermediae good from he foreign counry o minimize heir producion cos: final goods firms deermine wheher hey buy an inermediae good from heir home counry or a foreign counry. For example, Feensra and Jensen (212) show ha impored inermediae inpus as a share of oal inermediae inpus in he U.S. manufacuring secor rose from abou 6% in 198 o abou 27% in Furhermore, ousourcing producion of inermediae goods also has an imporan impac on R&D aciviies. By imporing some varieies of inermediae goods from a foreign counry, firms can reallocae workers from he producion secor o R&D aciviies wihin he counries in which hey operae. Therefore, i is possible o shif from producion o R&D in he counry from which firms ousource. Many papers use an R&D-based growh model o invesigae fragmenaion issues such as ousourcing and offshoring. Glass and Saggi (21) and Glass (24) presen a orh Souh produc cycle model wih ousourcing. 2 In a orh Souh endogenous growh model wih offshoring, aghavi and Oaviano (29a, 29b) analyze he effec of conracs in relaion o offshoring. Moria (21) invesigaes no only seady-sae, bu also ransiion of an economy using a orh Souh endogenous growh model wih ousourcing. Rodríguez-Clare (21) analyzes he effec of offshoring on relaive wages in Eaon and Korum s (21, 22) models wih offshoring. Impullii (216) analyzes he effec of foreign echnological compeiion on he skill premium and residual wage inequaliy in a wo-region qualiy-ladder growh model wih offshoring. In hese papers, he range of ousourcing or offshoring wihin a firm s oal use of inpus is an exogenous consan: hey focus on he decision of wheher o ousource, or hey analyze he efecs of ousourcing or offshoring. However, in pracice, firms decide he range of 1 There are many empirical sudies ha analyze similar issues. See, for example, Feensra and Hanson (1996) and Hummels e al. (21). 2 Hsu (211), Chen (215), and Chu (215) also presen a orh Souh produc cycle model wih ousourcing. 1

3 ousourcing wihin oal use of inermediae goods. Gao (27) shows ha a reducion in rade coss increases he number of inermediae goods produced in he Souh and he growh rae of he world in a orh Souh endogenous growh model. In a orh Souh model of direced echnical change, Acemoglu e al. (215) and Chu, Cozzi, and Furukawa (215) invesigae he effecs of offshoring on skill-biased echnical change. Hashimoo (215) analyzes he impac of ariff in a wo-counry model wih offshoring and labor marke imperfecion. In hese models, he share of ousourcing or offshoring wihin oal inpus is endogenously deermined. 3 However, hese works do no conduc welfare analysis. 4 Conrasing o exising lieraures, in he presen paper, he range of ousourcing wihin a firm s oal use of inermediae goods is endogenously deermined and welfare analysis can be conduced analyically. In he presen paper, I consruc a simple orh-souh R&D-based growh model where final goods firms in he orh endogenously deermine he exen of inernaional ousourcing of inermediae goods o he Souh, where he Souh engages only in inermediae goods producion. In order o endogenize he exen of ousourcing in each firm, I incorporae Dornbusch e al. s (1977) coninuum-good Ricardian model ino Grossman and Helpman s (1991) qualiy ladder model. 5 Using his model, I examine he impacs of a fall in he rade cos (or of rade liberalizaion) of inermediae goods in he orh. Then, I show ha a fall in he rade cos of inermediae goods in he orh: (i) reduces he relaive wage of he orh o he Souh; (ii) increases he ousourced variey of inermediae goods in he orh; and (iii) simulaes economic growh in all counries. The above second resul of his paper is consisen wih he following relaionship. In pracice, he rade cos, mainly he coss of ransporaion and communicaion, has declined, and, during he same period, he volume of ousourcing has increased in developed counries. The hird resul of his paper comes from he reallocaion of orhern labor from producion o R&D as a consequence of ousourcing. Moreover, conducing welfare analysis, I show ha a 3 Davis and aghavi (211) examine he relaionship beween rade liberalizaion, offshoring, and labor allocaion in an endogenous growh model in which here is heerogeneiy of workers skills. They focus on he workers who work in he offshored secor among he oal number of Souhern workers, bu do no conduc welfare analysis. 4 Gao (27) focuses on he seady sae and briefly discusses he welfare effec. Acemoglu e al. (215) only conduc quaniaive welfare analysis. 5 Taylor (1993, 1994) develops a wo-counry qualiy-ladder model incorporaing rade in final goods based on Dornbusch e al. (1977). 2

4 fall in he rade cos of inermediae goods in he orh improves welfare in all counries, and he posiive impac of a fall in he rade cos of inermediae goods in he orh on welfare in he Souh is larger han ha in he orh. The presen paper also relaes o he lieraure on rade liberalizaion in an endogenous growh model. In paricular, aio (212) examines he effec of unilaeral rade liberalizaion in a wo-counry model, based on Acemoglu and Venura (22) and Dornbusch e al. (1977), and shows ha a fall in rade cos in any one counry simulaes economic growh and improves welfare in all counries. 6 However, in aio s (212) model, inermediae goods are produced from using capial and a endogenous growh mechanism is based on he AK model. By conras, in he presen model, inermediaes goods are produced from using labor and a endogenous growh mechanism is based on R&D aciviy. The remainder of he paper is organized as follows. Secion 2 describes he model. Secion 3 derives he marke equilibrium pah of his model. Secion 4 analyzes he effecs of rade liberalizaion of he inermediae goods secor. Concluding remarks are given in he final secion. 2 The model In his paper, I consruc a orh-souh model, wih inernaional ousourcing by orhern final goods firms. The economy comprises wo counries, orh and Souh. Hereafer, he superscrip (S ) represens he orh (Souh). Final goods ha orhern and Souhern households consume are produced only in he orh, and are freely raded. Each final good, indexed by i [, 1], is produced from a uni coninuum of inermediae goods (or asks), indexed by z [, 1]. Boh he orh and Souh can underake he producion of inermediae goods (or producion asks). The disribuion of produciviy of inermediae goods across he orh and Souh is based on Dornbusch e al. s (1977) coninuum-good Ricardian model. In he orhern final goods secor, produciviy improves as a resul of R&D aciviies, following Grossman and Helpman s (1991) qualiy ladder model. Only in he orh are hese R&D aciviies conduced, using orhern labor only. 6 aio (217) examines he effec of rade liberalizaion in a muli-counry model based on Acemoglu and Venura (22) and Eaon and Korum (22). 3

5 2.1 Households In boh counries, here is a uni coninuum of idenical households who canno move beween counries. The households living in counry k {, S } have he following lifeime uiliy: where: U k = e ρ ln u k d, (1) ( 1 ) u k = exp ln x k (i)di, (2) where ρ > is he common subjecive discoun rae for he wo counries, ln u k represens insananeous uiliy, and x k (i) denoes he consumpion level of final good i by households living in counry k a ime. The represenaive household in counry k {, S } maximizes his or her lifeime uiliy (1) under he following budge consrain: Ḃ k = r k B k + w k L k E k, (3) where r k is he rae of reurn on asses in counry k a ime, B k denoes he value of asses held by households in counry k, and E k = 1 p x,(i)x k (i)di represens he expendiure in counry k a ime. p x, (i) is he inernaional price of final good i a ime. 7 Each household in counry k inelasically supplies L k unis of labor o earn he wage w k. I solve his household s uiliy maximizaion problem in wo sages. From he saic uiliy maximizaion problem, he saic demand for x k (i) is: x k (i) = Ek p x, (i). (4) ex, ineremporal uiliy maximizaion requires he familiar Euler equaion as follows: Ė k E k = r k ρ. (5) 2.2 Final goods Only in he orh, here is a uni coninuum of final goods indusries indexed by i [, 1]. Each final good i is emporarily produced by a curren monopolisic leader who succeeded wih he 7 The demand price of each final good i, p x, (i) is common o orh and Souh because each final good i is freely raded and is produced only in orh. 4

6 laes innovaion unil he arrival of he nex innovaion, and is produced from a uni coninuum of inermediae goods (or asks) indexed by z [, 1]. I assume ha here are no rade barriers facing final goods (i.e., final goods are freely raded). The producion funcion for he final good leader i is: ( 1 ) x (i) = λ Q (i) exp ln y (i, z)dz. (6) x (i) is he oupu of final good i a ime. The parameer λ > 1 is he exogenous common invenion sep of each produciviy improvemen. Q (i) is he number of innovaions ha have occurred in indusry i as of ime. y (i, z) is he inermediae good (ask) z, which is used (needed) for he producion of final good i a ime. orhern final goods firms can buy (assign) inermediae goods (asks) from (o) boh he orh and Souh: orhern final goods firms can ousource heir producion process. To minimize heir producion cos, orhern final goods firms choose he source of each inermediae good (ask). Given he produciviy improvemen, λ Q (i), he marginal cos of producion for x (i) is: where P y, MCx,(i) = P y, λ, (7) Q (i) ( ) 1 exp ln p y,(z)dz is he price index for inermediae goods and py,(z) is he demand price of y (i, z). Following Grossman and Helpman (1991), I assume ha he curren leader and he former leader, who succeeded wih he second-laes innovaion, engage in Berrand compeiion. Furhermore, in he presen model, I consider complee paen proecion as in Grossman and Helpman (1991). 8 Under hese circumsances, he curren leader charges he following profimaximizing price, which is a consan markup over is marginal cos: p x, (i) = λmc x,(i) = λ P y, λ Q (i). (8) Given (6)-(8), he amoun of monopolisic profi is: ( ) ( ) λ 1 λ 1 π x,(i) = p x, (i) x (i) = [E + E S ] (9) λ λ 8 A number of sudies analyze he effec of paen proecion in R&D-based growh models. See, for example, he early paper by Li (21), Goh and Olivier (22), Iwaisako and Fuagami (23), Kwan and Lai (23), and O Donoghue and Zweimuller (24). 5

7 for i [, 1], and he second equaliy of (9) follows from he marke-clearing condiion for final good i (i.e., x (i) = x (i) + x S (i)) and (4). Finally, he demand for inermediae good z in indusry i is: y (z) = y (i, z) = E + E S py,(z)λ (1) for i [, 1]. 2.3 Inermediae goods The seing of his secor is based on Dornbusch e al. (1977). Each inermediae good z, indexed by z [, 1], is produced using only labor under perfec compeiion in he orh or Souh. The producion echnology for variey z in counry k {, S } is as follows: ly,(z) k = a k (z)ỹ k (z), (11) where l k y,(z) is he labor inpu used in he producion of inermediae good z in counry k, a k (z) represens he consan uni labor requiremens of inermediae good z in counry k, and ỹ k (z) is he supply of inermediae good z in counry k a ime. Following Dornbusch e al. (1977), I le ω represen he relaive wage of he orh o he Souh (i.e., ω w /w S ), and I label he varieies so ha he produciviy of inermediae goods firms in he orh relaive o he Souh diminishes wih z: A(z) as (z) a (z) ; A (z) <, z [, 1]. (12) I also inroduce iceberg rade cos for impors τ y > 1. 9 In he presen model, iceberg rade cos τ y a reducion in τ y represens no only non-ariff barriers, bu also inernaional ousourcing cos: implies no only rade liberalizaion, bu also a reducion in inernaional ousourcing cos in he orh. Hereafer, a reducion in τ y means rade liberalizaion including a decrease in inernaional ousourcing cos or non-ariff barriers. orhern final goods firms purchase (assign) inermediae goods (asks) from (o) he counry wih he lowes prices (coss). Thus, he orh (Souh) underakes producion of inermediae good z if and only if he marginal cos of inermediae good z in he orh (Souh) is less han or equal o ha in he Souh (orh): 9 See, for example, Dornbusch e al. (1977) and Eaon and Korum (22). 6

8 ω τ y A(z) produces z S produces 1 z Fig. 1. The disribuion of inermediae goods producion locaions. w a (z) τ y w S a S (z) or ω τ y A(z) (w a (z) τ y w S a S (z) or ω τ y A(z)). Therefore, given he relaive wage, he hreshold variey z is implicily deermined by: ω = w w S = τ y A(z ). (13) Figure 1 shows he disribuion of inermediae goods producion locaions. The orh underakes producions of he varieies in [, z ] wih is supply price given by p y,(z) = w a (z). Similarly, he Souh underakes producion of he varieies in [z, 1] wih is supply price given by p S y,(z) = w S a S (z). 2.4 R&D The expeced value of an invenion relevan o final good i is denoed by V (i). Following he lieraure, I focus on a symmeric equilibrium ha feaures an equal arrival rae of innovaion across indusries. Because π x, = π x,(i) for i [, 1] from (9), V equilibrium. In his case, he no-arbirage condiion for V is: = V (i) in he symmeric r V = π x, + V ι V, (14) where ι denoes he counry-level Poisson arrival rae of innovaion in he orh. The lef-hand side of (14) is he reurn on asses in he orh. The righ-hand side of (14) is he sum of he following: (a) monopolisic profi π x,, or he paen holder s dividend; (b) capial gain V ; and (c) he expeced capial loss ι V due o creaive desrucion. 7

9 ex, I consider he process of innovaion. Only in he orh, here is a uni coninuum of R&D firms indexed by j [, 1]. An R&D firm j conducs R&D using only orhern labor l R, ( j). The expeced profi for R&D firm j is: π R, ( j) = V ι ( j) w l R, ( j), (15) where ι ( j) = φ l R, ( j) is he firm-level Poisson arrival rae of innovaion for R&D firm j, and φ represens R&D produciviy. Following he sandard approach in he lieraure, I impose he following free-enry condiion for R&D: V = w φ. (16) Finally, in equilibrium, he counry-level Poisson arrival rae of innovaion in he orh saisfies ι = 1 ι ( j)d j = φ 1 l R, ( j)d j. 2.5 Markes Firs, he demand prices of inermediae goods in he orh are expressed as: p y,(z) = a (z)w py,(z) z [, z ] =. (17) τy p S y,(z) = τy a S (z)w S z [z, 1] Using he expressions (17), he price index of inermediae goods is as follows: ( z 1 ) Py, = (w ) z (τ y w S ) 1 z exp ln a (z)dz + ln a S (z)dz. (18) z Second, he marke-clearing condiions for inermediae goods are given by: ỹ (z) = y (z) z [, z ], (19) ỹ S (z) = τ y y (z) z [z, 1]. (2) Finally, he marke-clearing condiions for labor in boh he orh and Souh are given by: L = L S = z 1 z l y,(z)dz + 1 l R, ( j)d j, (21) l S y,(z)dz. (22) 8

10 3 Marke equilibrium pah In his secion, I show he unique marke equilibrium pah. I choose labor in he Souh as he numeraire (i.e., w S = 1 ). Therefore, he relaive wage of he orh o he Souh becomes ω = w /w S = w. To simplify he analysis, I follow Dinopoulos and Segersrom (21) by assuming ha monopolisic firms creaed by he innovaions of domesic R&D firms are owned by he domesic households (i.e., here is home bias in asse holding ). 1 Lemma 1 Suppose ha here exiss a unique balanced-growh pah (BGP) along which he aggregae rae of innovaion in he orh is posiive and inernaional ousourcing of orhern final goods firms occurs (i.e., ι > and z (, 1)). The economy jumps immediaely o he unique BGP along which he equilibrium values of he relaive wage of he orh o he Souh, ω, and he hreshold variey, z, are consan. The equilibrium values, ω and z, are uniquely deermined by he following balance of rade (BT) and comparaive advanage (CA) schedules: ( L S λ 1 BT : ω = L + (ρ/φ ) 1 z 1 ) BT(z ), (23) λ CA : ω = τ y A(z ). (24) Proof. See Appendix A. Lemma 1 shows ha he economy is always on he BGP, which is he marke equilibrium pah and has no ransiion dynamics. In order o ensure he equilibrium, I assume ha τy A() > BT(). 11 Figure 2 plos he BT schedule (23) and he CA schedule (24). The BT schedule slopes upward from a posiive inercep o infiniy and he CA schedule slopes downward in (z, ω) space. 1 Some sudies also impose he same assumpion. See, for example, Chu and Peng (211) and Chu, Cozzi, Lai, and Liao (215). 11 For example, suppose ha he uni labor requiremen funcions are given by a (z) = z, a S (z) = 1 z. Then, I have A(z) = a S (z)/a (z) = (1/z) 1, A() =, and A(1) =. In his case, τ y A() > BT() always holds. 9

11 BT τ y ω CA produces z S produces 1 z Fig. 2. The seady sae values of ω and z. On he BGP, he expendiure in each counry and he aggregae level of innovaion rae in he orh ake he following consan values: ( E = ω L + ρ ), (25) φ E S = L S, (26) ( ) [( λ 1 ι = φ L n + ρ ) ] + LS ρ. (27) λ φ ω Appendix B provides a deailed derivaion of hese values. 4 Effecs of rade liberalizaion In his secion, I examine he effecs of rade liberalizaion of inermediae goods markes (a decrease of τy ) on he relaive wage, he range of inernaional ousourcing, growh raes and welfare. 4.1 Relaive wage and inernaional ousourcing The equilibrium levels of he relaive wage of he orh o he Souh ω and he hreshold variey z are uniquely deermined by (23) and (24). As shown by (23) and (24), a decrease in τy does 1

12 no affec he BT schedule and shifs he CA schedule downward. 12 Therefore, a reducion in τy decreases he relaive wage, ω, and he hreshold variey, z. Recall ha he range of ousourced variey of inermediae goods in he orh is [z, 1]. A decrease in z brings abou an increase in he range of ousourced variey of inermediae goods in he orh. Proposiion 1 A fall in he rade cos of inermediae goods in he orh decreases he relaive wage of he orh o he Souh and increases he range of ousourced variey of inermediae goods in he orh. Proof. Proven in he ex. The inuiion of Proposiion 1 is as follows. A reducion in he rade cos of inermediae goods (a decrease in τy ) lowers he prices of inermediae goods in he Souh relaive o he orh. This gives orhern final goods firms an incenive o ousource he producion of inermediae goods o he Souh. Then, he supply of inermediae goods and he demand for labor in he orh decrease, and he supply of inermediae goods and he demand for labor in he Souh increase. Thus, he relaive wage of he orh o he Souh falls. Therefore, a reducion in he rade cos of inermediae goods decreases he orh s relaive wage and increases he range of ousourced variey of inermediae goods in he orh. 4.2 Growh raes I derive he growh raes of insananeous uiliy in boh counries and invesigae he effec of a fall in he rade cos of inermediae goods on growh raes. Subsiuing (4), (8), and (18) ino (2) yields orhern insananeous uiliy on he BGP as follows: [ ( ln u = ln ω L + ρ )] ln λ + ln Λ φ z ln ω ( z (1 z ) ln τy ln a (z)dz + 1 z ) ln a S (z)dz, (28) 12 See Figure 2. 11

13 ( ) 1 where Λ exp Q (i)di ln λ = exp ( ι h dh ln λ), where he second equaliy follows from he law of large numbers. Similarly, I obain Souhern insananeous uiliy on he BGP: ln u S = ln L S ln λ + ln Λ z ln ω ( z (1 z ) ln τy ln a (z)dz + 1 z ) ln a S (z)dz. (29) Differeniaing (28) and (29) wih respec o yields: g = g S = ι ln λ, (3) where g k is he growh rae in counry k {, S }, and ι is given by (27). In he presen model, he growh raes in all counries are idenical because he engine of economic growh is one in he world economy, ha is, he orh s innovaion. Proposiion 2 A fall in he rade cos of inermediae goods in he orh simulaes economic growh in all counries. Proof. From proposiion 1, a decrease in τ y reduces ω. As shown by (27), ι is decreasing in ω. Therefore, a decrease in τ y raises ι, and hus a decrease in τ y increases g and g S from (3). The reasoning for Proposiion 2 is as follows. Inuiively, i is useful o recall he labor marke-clearing condiion in he orh (21). This condiion implies ha, in he orh, he consan labor supply mus be equal o he sum of he labor inpus ino R&D aciviies and ino he producion of inermediae goods. A lower labor inpu ino producion makes i possible o allocae more labor for R&D. In he presen model, a fall in he rade cos of inermediae goods in he orh affecs he labor inpu ino producion of inermediae goods hrough he following hree channels. As shown by Proposiion 1, a fall in he rade cos of inermediae goods in he orh reduces he relaive wage of he orh o he Souh and increases he range of ousourced inermediae goods in he orh. Firs, a reducion in he relaive wage brings abou a reducion in expendiure in he orh ha sifles he demand for inermediae goods. 13 Thus, he labor inpu ino producion of inermediae goods decreases. Second, a reducion in he relaive 13 See Eq. (1). 12

14 wage lowers he prices of inermediae goods produced in he orh and raises he demand for inermediae goods. Thus, he labor inpu ino producion of inermediae goods increases. Third, an increase in he range of ousourced inermediae goods in he orh implies ha he number of varieies produced in he orh decreases. Thus, he labor inpu ino producion of inermediae goods decreases. The firs and hird negaive effecs always dominae he second posiive effec. Hence, a fall in he rade cos of inermediae goods in he orh reduces he labor inpu ino producion of inermediae goods and raises he labor inpus ino R&D aciviies. Therefore, a fall in he rade cos of inermediae goods in he orh simulaes R&D in he orh and he growh raes in all counries. 4.3 Welfare On he BGP, he insananeous uiliy in counry k {, S } grows a consan rae g k (i.e., u k = u k egk ). In his case, he lifeime uiliy in counry k is as follows: U k = 1 ] k gk [ln u +, (31) ρ ρ where g k is given by (3). The iniial levels of insananeous uiliy in he orh and Souh can be obained by: ( ln u [ω = ln L + ρ )] ln λ z ln ω φ ( z (1 z ) ln τy ln a (z)dz + 1 ( z ln u S = ln LS ln λ z ln ω (1 z ) ln τy ln a (z)dz + z ) ln a S (z)dz, (32) 1 z ) ln a S (z)dz, (33) where Λ is normalized o uniy. Social welfare in counry k is deermined by he growh rae g k and he iniial level of insananeous uiliy ln u k. Proposiion 3 A fall in he rade cos of inermediae goods in he orh improves welfare in all counries. The volume of posiive impac of a fall in he rade cos of inermediae goods in he orh on welfare in he Souh is larger han ha in he orh. Proof. See Appendix C. 13

15 To beer undersand Proposiion 3, I now differeniae he orhern lifeime uiliy on he BGP (31) wih respec o τ y. ρ U τ y = 1 ( E ω ) E ω τy } {{ } Expendiure effec ( ) ( z ω ) + 1 z ω τy τy } {{ } Price effec (+) + 1 ) ( g, (34) ρ τy } {{ } Growh effec (+) where E / ω >, ( ω/ τ y ) <, and ( g / τ y ) >. 14 From (34), I obain he following inuiion. A fall in he rade cos of inermediae goods in he orh brings abou reducions in ω and z ha lead o he following four effecs. Firs, a decrease in ω leads o a negaive expendiure effec by decreasing expendiure in he orh. Second, a fall in τ y affecs he prices of final goods hrough wo channels. A fall in τ y reduces he prices of inermediae goods ha are produced in he Souh and ω. Furhermore, a decrease in ω reduces he prices of inermediae goods ha are produced in he orh. Thus, a decrease in τ y leads o a posiive price effec by decreasing he producion coss and prices of final goods. 15 Third, from Proposiion 2, a fall in τ y leads o a posiive growh effec by enhancing economic growh in he orh. The second and hird posiive effecs always dominae he firs negaive effec, and hus a fall in he rade cos of inermediae goods in he orh always improves orhern welfare. The reason a fall in he rade cos of inermediae goods in he orh improves Souhern welfare is similar o he orhern case. In he Souhern case, here is no negaive expendiure effec from decreasing expendiure in he Souh. 16 Only he posiive price and growh effecs operae. Therefore, a fall in he rade cos of inermediae goods in he orh always improves Souhern welfare. Finally, he inuiion of he resul ha he posiive impac of a fall in he rade cos of inermediae goods in he orh on welfare in he Souh is larger han ha in he orh is as follows. In he presen model, he growh raes in all counries are idenical. Then, he posiive growh effecs in all counries are idenical. Moreover, in he presen model, he orhern and Souhern households purchase he final goods from he same orhern final goods firms under free rade. Then, he posiive price effecs in all counries are also idenical. Therefore, he posiive impac of a fall in he rade cos of inermediae goods in he orh on welfare in he orh is lower 14 See Eq. (25), Proposiions 1 and See Eqs. (7), (17), and (18). 16 See Eq. (26). 14

16 han ha in he Souh because he negaive expendiure effec is only in he orh. 5 Concluding remarks In he presen paper, I consruced a simple orh-souh R&D-based growh model where final goods firms in he orh endogenously deermine he range of inernaional ousourcing of inermediae goods o he Souh. In conras o he exising lieraure, he presen paper focused on each firm s range of ousourcing. Wihin his framework, I showed ha rade liberalizaion of inermediae goods in he orh is he rigger o shif from producion o R&D aciviies in he orh hrough an increase in he ousourcing of orhern producion of inermediae goods o he Souh. Furher, I have shown ha o accelerae economic growh and improve global welfare, he message for policy-makers is ha he orh should liberalize rade in inermediae goods. Appendix A. Proof of Lemma 1 In his appendix, I derive he marke equilibrium pah. I choose labor in he Souh as he numeraire and normalize w S o one (i.e., w S = 1 ). Thus, I obain ω = w /w S = w. In he presen model, I assume ha here is home bias in asse holding. Therefore, all monopolisic firms in he orh, creaed by he innovaions of orhern R&D firms, are owned by orhern households, and hus i follows ha B = V, B S =, and Ḃ S = (i.e., here are no asses in he Souh). From he budge consrain on Souhern households (3), I obain he following consumpion expendiure in he Souh: E S = L S. (A.1) ex, I consider expendiure in he orh. From ω = w ω /φ. Combining B yields: and (16), i follows ha V = = V, V = ω /φ, and he orhern households budge consrain (3) V r = r V = V V + ω L E φ L + E V. (A.2) 15

17 Subsiuing (A.2) ino he Euler equaion for he orh (5) yields: Ė E = V V φ L + E V ρ. I define χ E /V. Using his expression, (A.3) can be rewrien as follows: χ χ = E E V V (A.3) = χ φ L ρ. (A.4) This differenial equaion has a unique bu unsable non-zero seady-sae, which is given by: χ = φ L + ρ. (A.5) The pah along which χ diverges o infiniy violaes feasibiliy, and he pah along which χ converges o zero violaes he following ransversaliy condiion lim e ρ V /E = lim e ρ /χ =. Therefore, χ mus always jump o χ = φ L + ρ and is consan. Subsiuing χ = E /V and V = ω /φ ino (A.5), I obain he following relaionship beween E and ω : ( E = ω L + ρ ). (A.6) φ Finally, I characerize he equilibrium values of E, ω, and z. From (1), (11), (17), and (2), I derive labor demand for producion of inermediae good z [z, 1] in he Souh as follows: l S y, = l S y,(z) = (E /λ)+(e S /λ) for z [z, 1]. Subsiuing his labor demand expression ino (22) yields: ( ) E E S = L S = (1 z ) + E S. (A.7) λ Eq. (A.7) represens he BT. By using (A.1) and (A.6), Eq. (A.7) can be rewrien as: ( L S λ 1 ω = L + (ρ/φ ) 1 z 1 ). (A.8) λ Eqs. (12) and (A.8) deermine he unique and consan equilibrium values of he relaive wage, ω, and he hreshold variey, z. Eq. (A.6) and ω = ω imply ha expendiure in he orh is also consan on a BGP. Appendix B. Derivaion of he equilibrium values On he BGP, he relaive wage and he hreshold variey are consan. From (A.1), (A.6), and ω = ω, I obain he equilibrium levels of expendiure in boh counries, (25) and (26). Eq. (25) 16

18 implies ha Ė =, and hus r = ρ holds from he Euler equaion in he orh. Moreover, on he BGP, V yields: = since V = V = ω/φ. Combining V =, V = ω/φ, r = ρ, and (14) ι = φ π x, ω ρ = φ ( λ 1 λ ) [( L n + ρ φ ) ] + LS ρ, ω (B.1) where he second equaliy of (B.1) can be obained by using (9), (25) and (26). Eq. (B.1) represens he equilibrium aggregae innovaion rae in he orh, which is consan on he BGP. Appendix C. Proof of Proposiion 3 Recall ha ( g k / τ y ) >, k {, S } and ( ω/ τ y ) <. Differeniaing he orhern lifeime uiliy on he BGP (31) wih respec o τ y ln a (z )) yield: ρ U τ y = 1 g + 1 z ρ τy τy } {{ } + and using (24) ( or ln(ω/τ y ) = ln a S (z ) 1 τ y ω ω τ y } {{ }. (C.1) If 1 (τ y /ω)( ω/ τ y ) holds, he sign of (C.1) is always posiive. Subsiuing (24) ino (23), I obain: ω ( L S λ 1 L + (ρ/φ ) 1 A 1 (ω/τy ) 1 ) λ =, (C.2) where A 1 (ω/τ y ) is he inverse funcion of A(z ). Applying he implici funcion heorem o (C.2) yields: ω τ y = L S λ ω [L +(ρ/φ )]A (z ) (1 z ) 2 (τy ) 2 1 L S λ 1 [L +(ρ/φ )]A (z ) (1 z ) 2 (τy ), (C.3) where A (z ) <. Muliplying boh sides of (C.3) by (τ y /ω) yields: τ y ω ω τ y = ω L S λ ω [L +(ρ/φ )]A ( ) (1 z ) 2 (τy ) L S λ ω [L +(ρ/φ )]A ( ) (1 z ) 2 (τy ) < 1. (C.4) 17

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