School of Economics UNSW, Sydney 2052 Australia. Tariffs and Technology Transfer through an Intermediate Product

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1 chool of Economics UW, ydney 2052 Ausralia hp:// Tariffs and Technology Transfer hrough an Inermediae Produc Eiji Horiuchi and Joa Ishikawa chool of Economics Discussion Paper: 2007/15 The views expressed in his paper are hose of he auhors and do no necessarily reflec hose of he chool of Economic a UW. I IB

2 Tariffs and Technology Transfer hrough an Inermediae Produc Eiji Horiuchi Hiosubashi Universiy Joa Ishikawa Hiosubashi Universiy March 7, 2007 Absrac We examine he relaionship beween ariffs and echnology ransfer from he orh o he ouhinanoligopolisicmodel. Technologyisembodiedinakeycomponenwhichonlyhe orh firm can produce. Ineresingly, a decrease in he ariff on he final good as well as an increase may induce echnology ransfer. If he ouh subsidizes he final-good producion or impors of he inermediae good, echnology ransfer is also faciliaed. However, he welfare effecs are differen beween ariffs and subsidies. Our analysis suggess ha he ouh should ake pro-compeiive policies o induce echnology ransfer and enhance welfare. Keywords: echnology ransfer, inermediae producs, ariffs, licensing, orh-ouh rade JEL Classificaion: F12, F21, F23 This paper was wrien while Joa Ishikawa was visiing chool of Economics, Universiy of ew ouh Wales. Their hospialiy is graefully acknowledged. We are graeful o Gene Grossman and seminar paricipans a Ausralian aional Universiy, Hiosubashi Universiy, ingapore Managemen Universiy, Universiy of ew ouh Wales and Universiy of ydney for helpful commens. Joa Ishikawa acknowledges financial suppor from he Minisry of Educaion, Culure, pors, cience and Technology of Japan under he 21s Cenury Cener of Excellence Projec, he Japan Economic Research Foundaion, he omura Research Foundaion, and he Japan ecuriies cholarship Foundaion. Corresponding auhor: Faculy of Economics, Hiosubashi Universiy, Kuniachi, Tokyo , Japan; Fax: ; joa@econ.hi-u.ac.jp

3 1 Inroducion Technology ransfer from developed counries (he orh) o developing counries (he ouh) has received exensive aenion in he inernaional rade lieraure. The essence of echnology is ofen embodied in sophisicaed inermediae producs which he ouh is unable o produce. 1 In his case, even if know-how o produce final producs is known o he ouh, hey canno produce hose final producs by hemselves. To produce he final producs, hey have o impor such key inpus from he orh. For example, when Hyundai Moor Co. (a Korean auo maker) manufacured he firs Korean car in 1975, he engine was provided by Misubishi Moors Co. (a Japanese auo maker), which ransferred is echnology o Hyundai. 2 The orh-ouh echnology ransfer hrough rade in inermediae producs differs from licensing, which is a ypical channel of echnology ransfer, in he imporan way. The ouh governmens ofen demand echnology ransfer wihou any paymens for licensing. Even if licensing opporuniies are presen, he ouh governmens someimes impose various regulaions such as a cap on royaly raes. 3 Moreover, inellecual propery righs are ofen no well enforced in he ouh. Under such circumsances, licensing is likely o be discouraged. However, i is no necessarily he case for echnology ransfer embodied in inermediae producs, because he orh benefis from selling inermediae producs and he ouh may no be able o imiae hem. We consider he orh-ouh echnology ransfer hrough rade in inermediae producs. Building a simple oligopolisic model, we specifically examine he relaionship beween ariffs and echnology ransfer. The relaionship beween ariffs and foreign direc invesmen (FDI) has been explored exensively in he exising lieraure. 4 A well-known relaionship is ariff-jumping FDI, ha is, higher ariffs induce exporing firms o underake FDI. However, here have been few heoreical sudies (excep for hose menioned below) o invesigae he relaionship beween ariffs and echnology ransfer. AsinhecaseofFDI,anincreaseinheariff on he final good leads o ariff-jumping echnology ransfer in our model. The orh firm, which expors he final good o he ouh, loses as he ouh ariff rises. In order o offse he loss, i may have incenive o provide a poenial local enran (i.e., a ouh firm) wih is echnology by selling an essenial inermediae produc. Ineresingly, a ariff-reducion may also induce echnology ransfer. When he ariff is lowered, oher orh firms may ener he ouh marke, which is harmful o he incumben orh firm. To discourage such enry, he incumben orh firm may ransfer is echnology o a poenial local enran. Alhough he ouh firm eners he marke and becomes a compeior for he incumben orh firm, he loss is smaller because i can benefi from he sales of he 1 Coe e al. (1977) poin ou ha beween 1971 and 1977, R&D in he orh increased oal facor produciviy in he ouh hrough heir impors of inemediae producs and capial goods from he orh. 2 imilar examples include a Malaysian auo maker, Proon, esablished in 1983 and anoher Korean auo maker, amsung Moors, esablished in Misubishi Moors Co. and issan Moor Co., Ld., respecively, provided Proon and amsung wih echnological assisance. amsung iniially impored even nus and bols from Japan. 3 For example, see Davies (1977) for he Indian case and Peck and Tamura (1976) for he Japanese case. 4 ee Markusen (2002) and Barba avarei and Venables (2004), among ohers. 2

4 inermediae produc o he ouh firm. Tha is, he incumben orh firm may sraegically generae enry-deerring echnology ransfer. Thus, a ariff-reducion as well as a ariff-increase may induce echnology ransfer. We should menion ha ariffs are no necessary for he enry-deerring echnology ransfer. Any policy which encourages enry could resul in echnology ransfer. This conrass wih a convenional policy inducing echnology ransfer hrough FDI. I has been observed ha he ouh governmen guaranees a orh firm marke power in reurn of echnology ransfer under an obligaion o form a join venure (JV) wih a ouh firm. 5 Ouranalysissuggesshaprocompeiive policy inducing more enry should work wihou forcing orh firms o ransfer echnology. Moreover, in our analysis, FDI is no indispensable for echnology ransfer. Lin and aggi (1999), Pack and aggi (2001) and Ishikawa and Horiuchi (2007) also consider sraegic uses of he orh-ouh echnology ransfer. 6 In paricular, Lin and aggi (1999) show in a dynamic orh-ouh model ha FDI makes he ouh firm s imiaion of an advanced echnology easier and inensifies compeiion in he ouh marke and hence FDI underaken by one of he orh firms may delay he oher orh firm s swich from expors o FDI. However, heir primary purpose is o show a paradoxical resul ha echnology spillover o local firms hrough FDI may faciliae FDI raher han discourage i. Kabiraj and Marji (2003) and Mukherjee and Pennings (2006) poin ou he possibiliy of ariff-induced echnology ransfer hrough licensing. Using a duopoly model, Kabiraj and Marji (2003) show ha he foreign firm has incenive o license is superior echnology o he domesic rival only if he iniial cos-difference beween he foreign and domesic firmsissmall. By reducing he cos-difference, a ariff may induce licensing. Mukherjee and Pennings (2006) consider he relaionship beween licensing by he foreign monopolis o poenial enrans and he iming of he imposiion of he (opimal) ariff. Alhough our analysis is relaed o heirs, our focus is quie differen from heirs. We consider ariff-reducions aswellasariff-hikes. In paricular, we show ha from he welfare poin of view, echnology ransfer induced by ariffreducions is beer han ha by ariff-hikes. We should menion ha in our model, we can simply reinerpre he sale of an inermediae produc as he licensing wih per-uni royaly wihou changing he main resuls. Thus, our analysis is also relaed o paen licensing in he indusrial organizaion lieraure. For insance, Rocke (1990) examines o whom echnology should be licensed in a closed economy. he paricularly poins ou ha a paenee-monopolis may have incenive o license is echnology o a weak enran o deer a srong enran from enering marke. Eswaran (1994) generalizes Rock- 5 For example, he Chinese governmen does no allow foreign auo makers o have heir own subsidiaries in China. They force foreign auo makers o form JVs wih local firms in order o accelerae echnology ransfer. In addiion, foreign auo makers have o obain Chinese governmen s permission o form JVs, which is fairly resricive. 6 Pack and aggi (2001) are concerned wih echnology ransfer from he downsream secor o he upsream secor hrough ousourcing. Ishikawa and Horiuchi (2007) show Pareo gains from echnology spillover hrough FDI in verically relaed markes. 3

5 e s (1990) analysis. 7 However, boh of hese sudies assume licensing wih wo-par ariffs (i.e. a fixed fee plus per-uni royaly); 8 besides hey do no consider welfare implicaions. More imporanly, heir main concerns are abou he indusrial or marke srucures under he possibiliy of licensing, while ours are raher abou he orh-ouh echnology ransfer hrough rade in an inermediae good and is policy implicaions. The res of he paper is organized as follows. ecion 2 presens he basic model. ecion 3 invesigaes he effecs of an increase in he ariff on he final good on echnology ransfer, while secion 4 examines hose of a decrease in he ariff. ecion 5 analyzes economic welfare. ecion 6exploresheeffecs of subsidies on echnology ransfer and compare hem wih he effecs of ariffs onhefinal good. ecion 7 discusses some alernaive assumpions. ecion 8 concludes he paper. 2 The Basic Model There are wo counries, he orh and he ouh. We consider he ineracions among an incumben, a orh firm (firm 1 ), and wo poenial enrans, a orh firm (firm 2 )anda ouh firm (firm ), in he ouh marke. Firms produce homogenous final goods. Firms 1 and 2 expor heir final goods o he ouh. 9 Firm 2 has o incur fixed coss (FCs), f 2,oserve he ouh marke. To sar producion, firm needs o have he echnology ransferred from firm 1,hais,firm has o purchase a key inermediae good from firm 1.Firm 2 does no supply is inermediae good o firm. 10 If more han wo firms serve he ouh marke, hey compee in quaniies wih Courno conjecures. The inverse demand is given by he following linear funcion: 11 p(x) =b ax, where p and X are, respecively, he price and he demand of he final good. a and b are parameers. One uni of he inermediae good is required for each uni of he final good. In he orh, he marginal cos (MC) o produce he inermediae produc is normalized o be zero. Firm 1 sells firm is inermediae good a price r. The MC o produce he final produc from he inermediae good is c in he orh and c in he ouh. Even if he echnology is ransferred, firm 1 is more efficien in he final-good producion han firm. pecifically, c <c as well as b>c + which are necessary for our benchmark case (i.e., he monopoly by firm 1 )oexisin 7 Eswaran (1994) shows ha in he presence of a poenial enran, an incumben may invie ousiders as licensees. 8 The licensing lieraure has exensively compared beween per-uni royaly and fixed fee. ee, for example, Wang (1998) and Kamien and Tauman (2002). 9 We assume away FDI by he orh firms. Firms refrain from FDI in he presence of high seup coss of FDI and high risk of expropriaion, for example. 10 For example, his could be he case if firm 2 has o incur large FCs o expor he inermediae good. ee also ecion Even if he demand funcion is non-linear, he essence of our resuls would no change. 4

6 he following analysis. For example, c <c reflecs he managerial inefficiency of firm. The ouh governmen imposes a specific ariff,, onhefinal good and no ariff on he inermediae good. The profis of firms 1, 2,and are, respecively, given by π 1 = π 1f + π 1m =[p (c + )]x 1 + rx, π 2 = π 2f =[p (c + )]x 2 f 2, π = [p (c + r)]x, where x i (i = 1, 1,) is he oupu of firm i; and π if and π 1m are, respecively, he profis from he final-good marke and he inermediae-good marke. The model involves four sages of decision. In sage 0, he ouh governmen deermines he ariff rae. In sage 1, firm 1 decides wheher o expor he inermediae good o firm and wheher o serve he final-good marke. If i decides o expor he inermediae good, firm 1 deermines he inermediae-good price and makes a ake-i-or-leave-i offer o firm, whichin urn decides wheher o accep i. In sage 2, firm 2 decides wheher o ener he marke. In sage 3, he firms compee in he final-good marke. The game is solved by backward inducion. There are seven possible equilibria in sage 3: a monopoly by firm 1,or, or 2 ; a duopoly beween firms 1 and, orbeween 1 and 2, or beween and 2 ; and an oligopoly among hree firms 1, 2 and. However, firm 2 canno be a monopolis in equilibrium. Moreover, he duopoly beween firms and 2 does no arise in equilibrium, because firm 1 never has incenive o swich he marke srucure from he duopoly beween firms 1 and o he duopoly beween firms and 2. 3 The Effecs of Tariff-hikes This secion analyzes he effecs of ariff-hikes on echnology ransfer. In our analysis, he benchmark is he monopoly by firm 1 (henceforh he monopoly) under a non-negaive ariff. 12 Tha is, firm 1 iniially monopolizes he marke. Then he equilibrium is given by 13 x 1 () = b c > 0, (1) 2a p () = b + c +, (2) 2 π 1 () = (b c ) 2. (3) 4a An increase in makes he poenial profis of firm 2 lower and hence does no induce firm 2 s enry. Thus, he possible equilibria are he monopoly, he duopoly beween firms 1 and (henceforh he duopoly), and he monopoly by firm (henceforh he monopoly). 12 The ariff raes under which he monopoly by firm 1 is acually he iniial equilibrium will be se ou laer. 13 ubscrips sand for he final-good marke srucure: () ishemonopolybyfirm 1 (); ()ishe duopoly beween firms 1 and ( 1 and 2 ); and is he oligopoly among hree firms. 5

7 In he las sage, he duopoly equilibrium is given by 14 x 1,x (r, ) = b +(c + ) 2(r + c ), (4) 3a (r, ) = b +(r + c ) 2(c + ) 3a p (r, ) = b +(r + c )+(c + ), (5) 3 π 1 b +(r + c (r, ) = ) 2(c + ) 2 9a b +(c + ) 2(r + c ) 2 π (r, ) = and he monopoly equilibrium is 9a + r b +(c + ) 2(r + c ), (6) 3a, (7) x (r) = b (r + c ), (8) 2a p (r) = b + r + c, (9) 2 π 1 (r) = r b (r + c ), (10) 2a b (r + c π ) 2 (r) =. (11) 4a In sage 1, given, firm 1 can choose he mos preferable marke srucure hrough echnology ransfer. Obviously, he echnology is no ransferred under he monopoly. Under he duopoly, firm 1 deermines r so as o maximize he profis π 1 subjec o π > 0 and π 1f > 0 (i.e., x > 0 and x 1 > 0). We check under wha condiion x > 0 and x 1 > 0 hold. In view of (4), he consrains are equivalen o 15 2(c + ) (b + c ) er <r<r b + c + 2c. 2 On he oher hand, r ha maximizes π 1 wihou any consrain is given by r 5b (c + +4c ). (12) 10 We can easily verify ha er <r < r holds if and only if c c <<e 5b +2c 7c. (13) 7 When er <r < r, we can obain he duopoly equilibrium by subsiuing r ino (4)-(7): x 1 () = 5b 7(c + )+2c,x 10a () = 4(c + c ), (14) 10a p () = 5b +3(c + )+2c, (15) 10 π 1 () = 5[b (c + )] 2 +4(c + c ) 2, (16) 20a π () = 4(c + c ) 2. (17) 25a 14 The general form of equilibrium in he las sage is given in he appendix (equaions (A1)-(A7)). 15 er < r holds wih b c >0. 6

8 When becomes high enough, firm 1 exis from he final-good marke and expors only he inermediae good whose price is deermined so as o maximize π 1. I is sraighforward o show such r is given by r = b c (18) 2 and hence he equilibrium is given by x = b c 4a, (19) p = 3b + c, 4 (20) = (b c ) 2, 8a (21) π = (b c ) 2. 16a (22) π 1 = π1 We are now ready o pin down he marke srucures. Firs, we can easily verify π 1 a.thus,firm 1 sars exporing he inermediae good once = holds. We nex derive he ariff rae,, under which firm 1 sops serving he final-good marke. From π 1 = π1, we obain =(c c )+ (b c )(10 10). 18 I should be noed ha is less han e and hence x 1 > 0 a.evenifx 1 > 0, iisprofiable for firm 1 o sop serving he final-good marke. Moreover, is greaer han and hence he final-good marke srucure never direcly shifs from he firm 1 s monopoly o he firm s monopoly. The above analysis esablishes he following proposiion. Proposiion 1 uppose firm 1 iniially monopolizes he ouh final-good marke. Then boh firms 1 and serve he ouh final-good marke if <<,whilefirm monopolizes he marke if. Thus, an increase in he ariff on he final good induces echnology ransfer from firm 1 o firm. The inuiion for echnology ransfer is sraighforward. As he ariff increases, he profis of firm 1 decrease. In order o offse he loss, i ransfers is echnology o a poenial local enran by selling he essenial inermediae produc, which generaes profis for firm 1. Tha is, an increase in he ariff on he final good causes he ariff-jumping echnology ransfer. 4 The Effecs of Tariff-reducions In his secion, we examine a decrease in he ariff. As in he las secion, he benchmark is he monopoly wih a non-negaive ariff. Thisis,heariff rae under he benchmark, 0,saisfies 0 0. To make he following analysis meaningful, we assume c b 3 p af 2 c, i.e., (b c ) 2 f 2 (b c ) 2. (23) 9a 9a 7

9 As we see below, under his assumpion, he marke srucure acually changes from he monopoly as falls. 16 Inhefollowing,weinvesigaehowhemarkesrucureshifs. In he absence of firm 2, a decrease in never resuls in echnology ransfer. When becomes low enough for firm 2 o cover is FC, however, firm 2 sars exporing o he ouh. For firm 1, he duopoly beween firms 1 and (henceforh he duopoly) is preferable o he duopoly beween firms 1 and 2 (henceforh he duopoly), because no only firm 1 gains from selling he inermediae good o firm bu also firm is less efficien han firm 2.Thus, firm 1 les firm ener jus before firm 2 eners. This implies ha he price of he inermediae good se by firm 1 is lower han he monopoly price so as o cause firm s enry. Firm 1 sraegically ransfers is echnology o firm o deer firm 2 from enering he marke. We le denoe he ariff rae a which he profis of firm 2 under a duopoly beween firms 1 and 2 are zero, ha is, firm 2 eners he marke in he absence of firm if he ariff rae is lower han.underhe duopoly, he following holds π 2 () = 1 µ b c 2 f 2. (24) a 3 Thus, firm 1 sars exporing he inermediae good o firm a he ariff rae which saisfies π 2 () =0, i.e., = b c 3 p af 2. (25) In view of (23), 0. ince firm 1 iniially monopolizes he marke, we implicily assume ha he iniial ariff is beween and. I should be noed ha < ( c c )holds, because of (23). Once lowers o he level of, firm 1 ransfers is echnology o firm o deer firm 2 s enry and hence he duopoly prevails. The price of he inermediae good charged by firm 1 is derived as follows. When hree firms compee in he marke, he profis of firm 2 are given by π 2 b 2(c (r, ) = + )+(r + c ) 2 f 2. 16a Firm 1 ses r such ha firm eners he marke and π 2 =0,hais,17 r =2 +4 p af 2 +2c c b. (26) 16 A decrease in he ariff mayleadoanegaiveariff (i.e., an impor subsidy), which we allow in our analysis. 17 We use subscrips o disinguish he duopoly obained by reducing he ariff from ha brough by raising he ariff. 8

10 ubsiuing r ino (4)-(7), we can obain he duopoly equilibrium x 1 () = 4 f 2 3 a,x () = 3b 3(c + ) 8 af2, (27) 3a p () = 3(c + )+4 af 2, (28) 3 π 1 () = [2 +4 af 2 +2c c b][3b 3(c + ) 8 af 2 ] + 16f 2 3a 9, (29) π () = [3b 3(c + ) 8 af 2 ] 2. (30) 9a As falls, firm 1 has o decrease r o deer firm 2 s enry. When r becomes low enough, firm 1 may lose incenive for such enry deerrence. If his is he case, here are wo possibiliies. One is o le firm 2 simply ener he marke and he oher is o le firm 2 ener he marke bu le firm exi from he marke. Firm 1 compares he profis under he oligopoly among hree firms (henceforh he oligopoly) wih hose under he duopoly. If he laer are greaer han he former, firm 1 sops providing firm wih he inermediae good and firm is forced o exi from he marke, ha is, he foreclosure happens. If he laer is less han he former, on he oher hand, he oligopoly prevails. The equilibrium under he duopoly is given by x 1 () = x 2 () =b c, 3a (31) p () = b +2(c + ), 3 (32) π 1 () = (b c ) 2, 9a (33) π 2 () = (b c ) 2 f 2. 9a (34) The criical level of under which firm 1 is indifferen beween he duopoly and he duopoly is given by 29b 38c +9c 84 q 9 af 2 b c af af 2. (35) 38 The appendix shows he following lemma and hence only he duopoly arises under <. Lemma 1 An oligopoly equilibrium arises only if > ( b +9c 8c )/8. However, > holds wih (23), and hence any oligopoly equilibrium is no observed. Inuiively, firm 1 can sill earn some profis by selling he inermediae good o firm under he oligopoly, bu his is in exchange a he cos of he smaller profis in he final-good marke. ince he laer negaive effec dominaes he former posiive effec, firm 1 verically forecloses. 9

11 The following should be noed. Firs, r =0may hold wih >. We le denoe he ariff rae which resuls in r =0: b + c 2c 4 af 2. (36) 2 AsshowninheproofofLemma1,> holds. Thus, we obain 18 Lemma 2 Firm 1 sells is inermediae good o firm even below he MC in order o deer firm 2 from enering he marke. econd, noing 0, we can easily verify <. Therefore, when falls, he marke srucure does no direcly shif from he firm 1 s monopoly o he duopoly. I is always beneficial for firm 1 o deer firm 2 s enry unless is oo low. The above analysis esablishes he following proposiion. Proposiion 2 uppose ha firm 1 iniially monopolies he ouh final-good marke. Firms 1 and serve he ouh final-good marke if <,whilefirms 1 and 2 serve he marke if <. Thus, a decrease in he ariff on he final good induces echnology ransfer from firm 1 o firm. However, if he decrease is large enough, echnology ransfer may no occur. In view of Proposiions 1 and 2, he relaionship beween ariff raes and he marke srucures is summarized in Figure 1. Figure 1 around here 5 Welfare Analysis In his secion, we analyze welfare in he ouh, measured by he sum of consumer surplus, profis and ariff revenue. W U(X) p(x)x + π + (x 1 + x 2 ), (37) where du/dx = p. In paricular, we examine he relaionship beween welfare and ariff raes and obain he opimal ariff. We firs compare welfare under he monopoly wih ha under he duopoly. When, he marke is monopolized by firm and welfare is given by W = 3(b c ) 2, (38) 32a which is obviously independen of. Welfare under he duopoly is given by he following quadraic funcion wih respec o : W () = 32(c + c ) 2 + 5b 3(c + ) 2c b 7(c + )+2c, (39) 200a 18 r<0 does no necessarily imply ha he acual price of he inermediae good is negaive, because he MC o produce he inermediae produc is simply normalized o be zero. 10

12 which is convex. Wihou any consrain on, W akes is maximum value W = 49(c ) (c ) 2 50bc 24bc 48c c +37b 2 198a (40) a = (35b 29c 6c )/99, whichislesshan because =[( )(b c ) + ( )(c c )]/198 > 0. ince W ( ) W = (b c )[( )(b c )+( )(c c )] 1440a holds, W >W ( ) >W.Thais, Lemma 3 The maximum welfare under he duopoly is greaer han W. > 0 (41) We nex compare welfare under he duopoly wih welfare under he monopoly. When, he marke is monopolized by firm 1 and welfare is given by W () = (b c +3)(b c ), (42) 8a which is quadraic and convex. Wihou any consrain on, W akes is maximum value W = b c 2 6a (43) a = (b c )/3. raighforward bu edious calculaion reveals (i) W ( )=W ( ),(ii) < if and only if b +2c 3c > 0, (iii) < if and only if 40b +100c 140c < 11 10(b c ), and (iv) < if and only if 2b 2c 9 af 2 > 0, i.e., f 2 < 4(b c ) 2 /81a. Therefore, if b +2c 3c > 0, hemaximumwelfare, W c, is obained under he duopoly. If b+2c 3c < 0, on he oher hand, he maximum welfare is obained under he monopoly. In his case, we have W c = W if and W c = W ( ) if <. 19 Lemma 4 The maximum welfare under he duopoly is greaer han ha under he monopoly if and only if b +2c 3c > 0. The inuiion of his lemma is as follows. We can rewrie he condiion b +2c 3c > 0 as b c > 3(c c ). The LH is relaed o he marke size, while he RH is relaed o he difference in efficiency. This condiion is likely o hold when he marke is relaively large and/or firm is no very inefficien relaive o firm 1. Consumer surplus is smaller under he duopoly han under he monopoly. 20 However, when he marke is relaively large and/or firm is no very inefficien relaive o firm 1,hefirm s profis are relaively large and an increase in he ariff is likely o raise he ariff revenue under he duopoly. 19 <, i.e., 2b 2c 9 af 2 > 0 implies <,i.e.,b +2c 3c < The price of he final good monoonically rises as he ariff rises. p () =p () holds a. 11

13 Welfare under he duopoly is W () = 3 b c af2 + 4 af 2 b c 2 af 2, (44) 2a 3a which is quadraic and concave. Wihou any consrain on, W akes he minimum value a = (3b 3c 8 af 2 )/3. ince >, W is decreasing for [, ] and hence W akes is maximum value a = : W ( )= a Welfare under he duopoly is (729(b c ) 2 + 8(371b 722c + 351c ) af 2 +{81(b c ) af 2 }q b c af af 2 (45) W () = 2(b c )(b c +2), (46) 9a which is quadraic and convex. Wihou any consrain on, W akes is maximum value b c W 2 = 4a a = (b c )/4 > 0. Tedious calculaion leads o he following lemmas. (47) Lemma 5 uppose b +2c 3c > 0. Then W ( ) is greaer han he maximum welfare under he duopoly and eiher W ( ) or W ( ) is he global maximum. Lemma 6 uppose b +2c 3c 0. Then W ( ) is greaer han he maximum welfare under he monopoly. If he opimal ariff under he duopoly is he inerior soluion (i.e., < ), W ( ) is he he global maximum. If he opimal ariff under he duopoly is he corner soluion (i.e., ), on he oher hand, eiher W ( ) or W ( ) is he global maximum. Therefore, we obain he following proposiion. Proposiion 3 The ouh can aain he highes welfare by lowering he ariff. Under he opimal ariff, eiher he duopoly or he duopoly arises. Figures 2-4 show hree possible cases. The horizonal axis measures ariff rae. The verical axis measures ouh welfare, profis of firm 1,profis of firm, priceofhefinal good, and ariff revenue, TR. In Figures 2 and 3, ouh welfare is maximized under he duopoly. Whereas b +2c 3c 0 holds in Figure 2, and b +2c 3c > 0 in Figures 3. In Figure 4, ouh welfare is maximized under he duopoly. Figures 2-4 around here 12

14 6 The Effecs of ubsidies In his secion, we invesigae he effecs of subsidies on echnology ransfer. We firs show ha a producion subsidy o firm may also induce echnology ransfer. To compare subsidies wih ariffs, we keep he monopoly as our benchmark equilibrium. Tha is, 0 0 c c (where he ariff rae 0 is consan in his secion) holds. By providing a specific producion subsidy, s, ofirm, iseffecive MC becomes c e c s. imply replacing c in he previous analyses wih c e, we can verify ha he duopoly arises if and he monopoly arises if s>s c c 0 s>s 18(c c 0 )+(b c )(10 10) Inuiively, he subsidy allows firm 1 o charge he higher price for he inermediae good r = 5b [c + +4(c s)],r = b (c s) 10 2 and hence firm 1 has more incenive o sell he inermediae good. Through he price hike, a par of he subsidy shifs from firm o firm We nex consider an impor subsidy o he inermediae good. In he case of he impor subsidy, he price of he inermediae good becomes lower by s relaive o he case of he producion subsidy. A par of he impor subsidy shifs from firm 1 o firm due o he lower impor price. In fac, we can easily confirm ha he oher equilibrium values are idenical beween he wo subsidies. This is because he ouh does no produce he inermediae good. In our model, herefore, we obain Proposiion 4 Aspecific producion subsidy o he final good and a specific imporsubsidyo he inermediae good se a he same levels are equivalen. A subsidy may induce echnology ransfer from firm 1 o firm. ex we explore he welfare effec. Obviously, a subsidy has no effec on he economy under he monopoly. Under he duopoly, welfare is given by W (s) = 1 200a [44s b +28c 8c s + c c (c ) 2 36(c ) 2 +12c 0 +10b 3c c 25b 2 ]. The subsidy rae ha maximizes W (s) wihou any consrain is given by s 5b 7c +2c ee Ishikawa and pencer (1999) for he ren-shifing in verically relaed markes. 13

15 oing 0 c c,wecanshow (b c s s ) + 60(c c 0 )+( ) 0 = > ince W (0) = W (s )=W (s ) holds, an increase in s improves welfare under he duopoly only if s <s. Under he monopoly, we obain W (s) = (3b 3c 5s)(b c + s). 32a Thus, as s rises, welfare deerioraes under he monopoly. Moreover, W (s ) >W (s ) holds. Thus, he globally opimal subsidy is 0 if s s and s oherwise. We have s s = 5[ b +2c 3c +( 0 c + c )]. (48) 22 If b +2c 3c 0, (48) has he non-negaive sign because 0 c c. Therefore, welfare is maximized under he monopoly (i.e., s =0). If b +2c 3c > 0, on he oher hand, s <s may hold. In his case, he maximum welfare is obained under he duopoly a s Ṫhus, he following proposiion is esablished. Proposiion 5 The opimal producion or impor subsidy is zero if b +2c 3c 0 and eiher zero or s if b +2c 3c > 0. The opimal subsidy resuls in echnology ransfer when i is s. We now compare he maximum welfare under he subsidy wih ha under he ariff on he final good. When b +2c 3c 0, i is obvious ha he maximum welfare is higher under he ariff han under he subsidy. Thus, we examine he case wih b +2c 3c > 0. Wehave W ( ) W (s ) = 1 b c 3 0 5b 2c 3c a > 1 b +2c 3c [5(b +2c 3c )] > 0, 99a where he inequaliy comes from 0 c c. Therefore, we obain Proposiion 6 The maximum welfare obained under he producion or impor subsidy is less han ha under he ariff on he final good. 7 Discussion To make our poin as clearly as possible, we have considered a highly sylized model. Thus, one may wonder o wha exen our resuls are robus. In his secion, we discuss some alernaive assumpions o gain some more insigh. 14

16 We firs consider he assumpion abou he price-seing of he inermediae good. We have assumed ha firm 1 ses he price of he inermediae good regardless of a single buyer, i.e., firm. Thisisbasicallybecausefirm has o purchase he inermediae good o sar producion, bu his assumpion is no essenial o he basic insigh of our analysis. An alernaive assumpion could be bargaining beween firms 1 and. Whenfirm has some bargaining power, he equilibrium price of he inermediae good becomes lower. However, he wo moives for echnology ransfer would no disappear. In fac, Lemma 2 suggess ha in he case of enry-deerring echnology ransfer, firm 1 has incenive o provide firm wihheinermediaegoodeven wihou any charge. On he oher hand, firm 1 may have complee bargaining power so ha i decides boh price and supply of he inermediae good. In his case, firm 1 can exrac all surplus and hence boh moives are reinforced. For simpliciy, we have assumed ha only firm 1 can ransfer echnology o firm. I is worhwhile modeling a sage ha deermines which orh firm ransfers he echnology. In he following siuaion, however, our model and resuls do no require any major changes. Two orh firms, firms 1 and 2 have wo differen echnologies and compee in echnology ransfer o firm. Each echnology requires a specific inermediae good. Tha is, he inermediae goods produced by firms 1 and 2 are differeniaed. Firm adops eiher of he wo echnologies. Once one echnology is adoped, he oher is idle. Moreover, consumers regard he final good produced by firms 1 and 2 as homogeneous. 22 For example, ypical eco-friendly cars are currenly hybrid vehicles and diesel vehicles. Their engines are compleely differen. Once a firm decides o manufacure hybrid cars, for insance, diesel engines are useless. 23 If firm 1 can produce is inermediae good more cheaply han firm 2,henicanlefirm adop is echnology and become he sole supplier of he inermediae good. We have also assumed a single poenial enran in he ouh. If here are muliple poenial enrans in he ouh, an oligopoly among he incumben firm and muliple ouh firms could arise insead of he duopoly. If his is he case, he possibiliy of echnology ransfer expands. I is of ineres o examine he echnology ransfer wih general number of he firms. However, i is likely ha enry-deerring echnology ransfer as well as ariff-jumping echnology ransfer sill arise even in more general seings. 8 Concluding Remarks We have examined he relaionship beween ariffs onafinal good and echnology ransfer in verically relaed markes. pecifically, echnology is embodied in a key componen which only he orh firm can produce. Ineresingly, no only ariff-hikes bu also ariff-reducions may lead o echnology ransfer. Tariff-jumping echnology ransfer may occur in he case of ariff-hikes, 22 Even if he final goods are also differeniaed, our resuls are sill valid as long as hey are close subsiues. 23 imilar examples include plasma display panel vs. liquid crysal display panel in TV producion and Blu-ray Disc vs. High-Definiion Digial Versaile Disc (HD DVD) in DVD-player producion. 15

17 while enry-deerring echnology ransfer may occur in he case of ariff-reducions. Alhough ariff-jumping echnology ransfer is somewha similar o ariff-jumping FDI, enry-deerring echnology ransfer is specific o echnology ransfer. In paricular, our policy implicaion ha he ouh should ake pro-compeiive policies o faciliae echnology ransfer seems o be novel. Besides ariff-reducions, pro-compeiive policies include any measures o decrease he seup cos o sar expors, for example. We have also shown ha a producion subsidy o he final good or an impor subsidy o he inermediae good may lead o echnology ransfer. This is because he orh firmcanearnmore profi by selling he inermediae good o he ouh firm. However, a decrease in he ariff on he final good generaes higher welfare han he subsidies. We can easily incorporae licensing ino our analysis. In paricular, we can simply reinerpre he price of he inermediae good as he sum of he price of he inermediae good and he per-uni royaly. 24 Thus, he analysis on ariffs onhefinal good needs no modificaion even if he inermediae good is replaced by echnology licensing. There are several reasons why we have specifically considered echnology ransfer hrough rade in a key componen. Firs, he orh firm can easily sop ransferring echnology by foreclosure. In he case of licensing, on heoherhand,imaybedifficul for he licensor o compleely sop echnology ransfer afer he licensee has learned he know-how. econd, we can ge rid of argumens over he opimal licensing conracs. There are a number of variaions in licensing conracs. In paricular, he licensing lieraure has exensively compared beween per-uni royaly and fixed fee. Third, we can examine he relaionship beween echnology ransfer and policies relaed o he inermediae good. Las and more imporanly, considering he inermediae-produc marke raher han he licensing marke, we can paricularly argue ha orh firms may have incenive o ransfer heir echnologies o ouh firms even if he licensing marke does no exis or is resriced, which has been observed in many developing counries. 24 We analyze his aspec in deail elsewhere (Horiuchi and Ishikawa, 2007). 16

18 Appendix The general form of he equilibrium in he las sage x i = x = ( (b c )+n (r+c c ) if n 6=0 a(n +n +1) 0 if n =0 ( (b r c )+n (c + r c ) a(n +n +1) if n 6=0 0 if n =0, (A1), (A2) p = b + n (r + c )+n (c + ) n + n, (A3) +1 X = (n + n )b n (r + c ) n (c + ), (A4) π if = π 1m = π = 1 a a(n + n +1) h (b c )+n (r+c c ) n +n +1 0 if n =0 ( r (b r c )+n (c + r c ) a(n +n +1) 0 if n =0 1 a h (b r c )+n (c + r c ) n +n +1 0 if n =0 i 2 fi if n 6=0, (A5), (A6) i 2 if n 6=0, (A7) where n and n are, respecively, he number of he orh and he ouh firms in he final-good marke and f 1 =0. ProofofLemma1 Under he oligopoly among hree firms, firm 1 offers firm he inermediae-good price ha maximizes π 1, subjec o π 0. The consrain can be rewrien as x 0 and hence r r b 3c +2(c + ). 3 On he oher hand, r ha maximizes π 1 wihou any consrain is given by r = 3b 5c +2c Thus, r r holds if and only if > ( b +9c 8c )/8. This implies ha he oligopoly among hree firms prevails only if >. By noing = 5b 5c 16 af 2 < 0 8 under (23), he oligopoly equilibrium does no arise if < holds (where is defined by (36)). In he following, herefore, we show <. 17

19 = 1 10b +10c +8 p s µ af b c p 2 af af 2 = 1 10[(b c (4/5) p s µ af 2 (c c )] + 9 b c p 2 af af 2 Wih (23), b c (4/5) af 2 > 0 holds. Thus, we obain ( 10b +10c +8 af 2 > 0 if c +(b c (4/5) af 2 ) <c 10b +10c +8 af 2 0 if c c +(b c (4/5) af 2 ) Then, < holds when c +(b c (4/5) af 2 ) <c. We now prove < also holds when c c +(b c (4/5) af 2 ).Forhis,weshow s µ 9 µ 9 b c b c p af af 2 > 10b 10c 8 p af 2 p af af 2 > 19(b c 4 p af 2 )(b c +12 p af 2 ) > 0 ³ 10b 10c 8 p af 2 2 In view of (23), b c 4 af 2 < 0. Alsonoingc c b c (4/5) af 2,wehave b c +12 p af 2 =(b c 3 p af 2 )+15 p af 2 (c c ) > (b c 3 p af 2 )+15 p af 2 (b c 5p 4 af2 ) = 64 p af2 > 0 5 Thus, < also holds when c c +(b c (4/5) af 2 ). 18

20 References [1] Barba avarei, Giorgio and Venables, Anhony J. (2004), Mulinaional Firms in he World Economy, Princeon Universiy Press. [2] Coe, D.T., Helpman, E., and Hohhmaiser, A.W. (1997), orh-ouh R&D pillover, Economic Journal 107, [3] Davies, H. (1977), Technology Transfer hrough Commercial Transacions, Journal of Indusrial Economics 26, [4] Eswaran, M., (1994), Licensees as Enry Barriers, Canadian Journal of Economics 27, [5] Horiuchi E. and Ishikawa, J. (2007) Licensing wih inermediae and capial goods, mimeo. [6] Ishikawa, J. and Horiuchi, E. (2007) raegic Technology Transfer hrough FDI in Verically Relaed Markes, mimeo. [7] Ishikawa, J. and pencer, B. J., (1999), Ren-shifing Expor ubsidies wih an Inermediae Produc, Journal of Inernaional Economics 48, [8] Kabiraj and Marji (2003) Proecing Consumers hrough Proecion: The Role of Tariffinduced Technology Transfer, European Economic Review 47, [9] Kamien, M., Tauman, Y. (2002), Paen Licensing: The Inside ory, Mancheser chool 70, [10] Lin, P. and aggi, K., (1999), Incenives for Foreign Direc Invesmen under Imiaion, Canadian Journal of Economics 32, [11] Markusen, James R. (2002) Mulinaional Firms and he Theory of Inernaional Trade, Cambridge, MA, MIT Press. [12] Mukherjee, A. and Pennings, E. (2006) Tariffs, Licensing and Marke rucure, European Economic Review 50, [13] Pack H. and aggi K. (2001) "Verical Technology Transfer via Inernaional Ousourcing", Journal of Developmen Economics, 65, [14] Peck, M.J. and Tamura,. (1976), Technology, In Parick, H. and Rosovsk, H. eds. Asia s ewgian:howhejapaneseeconomyworks, Brookings Insiuion: Washingon. [15] Rocke, K. E., (1990), Choosing he Compeiion and Paen Licensing, RAD Journal of Economics 21, [16] Wang, X.H. (1998), "Fee versus royaly licensing in a Courno duopoly model", Economics Leers 60,

21 duopoly duopoly monopoly duopoly monopoly Figure 1: Tariffs and marke srucures

22 4000 W 300 p * π TR π a b c c f Figure 2: Welfare-maximizing marke srucure: he duopoly ( b + 2 c 3 c 0 )

23 W * p π TR π a b c c f Figure 3: Welfare-maximizing marke srucure: he duopoly ( b + 2 c 3c > 0)

24 10000 W 500 p * π TR 5000 π a b c c f Figure 4: Welfare-maximizing marke srucure: he duopoly