Intellectual Property Rights Protection and R&D in. North-South Trade with Foreign Direct Investment

Transcription

1 Itellectual Property Rights Protectio ad R&D i North-South Trade with Foreig Direct Ivestmet Naoto Jiji This versio: April 7, 2011 Abstract I examie the itellectual property rights (IPR) protectio i the South whe it affects techology spillovers. A Norther firm, which coducts cost-reducig R&D, chooses the mode of supply (export or foreig direct ivestmet (FDI)) to the Souther market. Spillovers occur uder FDI. I show that the possibility of the choice betwee exportig ad FDI ad the availability of a additioal policy istrumet (i.e., tariff) complicate the aalysis of the optimal IPR policy for the South. The optimal IPR protectio may be striget to attract FDI or lax to iduce exportig, depedig o parameter values. If the South ca use tariffs strategically, it maipulates the Norther firm s mode of supply to improve domestic welfare. If a tariff is ot a policy istrumet, o the other had, the optimal IPR protectio is always striget eough to attract FDI. Therefore, tariff reductios may give the South a icetive to stregthe its IPR protectio. Keywords: Itellectual property rights; foreig direct ivestmet; techology spillovers; process R&D; North-South trade. JEL classificatio: O34; F12; F13; F23; L13. Faculty of Ecoomics, Kyoto Uiversity, Yoshida-homachi, Sakyo-ku, Kyoto , Japa. Phoe & fax: jiji #at-mark# eco.kyoto-u.ac.jp. 1

2 1 Itroductio May developig coutries try to attract foreig direct ivestmet (FDI) from developed coutries. Oe of the mai motives for them to attract FDI is to obtai advaced techology from multiatioal eterprises (MNEs). For firms i developig coutries that have isufficiet capability to egage i research ad developmet (R&D) activities by themselves, it is importat to obtai advaced techology from MNEs that extesively coduct R&D. Although techology trasfers to subsidiaries of MNEs ad joit vetures betwee local firms ad MNEs are major sources of advaced techology for developig coutries, techology spillovers are also importat. 1 The chaels through which techology spillovers occur have bee well documeted (Masfield et al., 1981; Masfield, 1985; Neve ad Siotis, 1996). They iclude commo suppliers of iputs ad customers, turover of employees, ad iformal commuicatio etworks amog egieers ad scietists. Techology spillovers through FDI are empirically cofirmed by a umber of studies (Brastetter, 2006; Haskel et al., 2007; Javorcik, 2004; Keller ad Yeaple, 2009; Takii, 2005), while some studies do ot fid sigificat spillovers (Aitke ad Harriso, 1999; Haddad ad Harriso, 1993). 2 Amog these studies, Keller ad Yeaple (2009) fid that there are stroger techology spillovers to maufacturig firms i the Uite States (U.S.) from FDI tha from imports. Moreover, the aalyses by Javorcik (2004), Javorcik ad Spatareau (2008), ad Takii (2005) suggest that eve developig coutries beefit from spillovers through iward FDI. Some researchers argue that techology spillovers are greatly affected by a coutry s level of itellectual property rights (IPR) protectio. Coutries that implemet lax IPR protectio policies would beefit from spillovers to a large extet. However, this relatioship is ot so obvious oce the effects of IPR policy o MNEs locatio choices ad o their icetives to choose the extet of R&D activities are take ito accout. Idigeous firms i developig coutries would beefit from MNEs R&D to a larger 1 Techology spillover is distiguished from techology trasfer i the sese that the former is uiteded by the source of the kowledge. It is also distiguished from imitatio i the sese that the former does ot ecessarily require costly activities by those who obtai kowledge. 2 See Keller (2004, 2009) for surveys of this issue. 2

3 extet whe MNEs produce goods locally i developig coutries tha whe they produce goods i their ow or i third coutries ad export them to developig coutries. Although a lax IPR protectio policy would give rise to a high degree of spillovers, it may deter MNEs from ivestig i that coutry ad may also reduce icetives for them to egage i R&D. Cosequetly, the classical argumet o the optimal level of IPR protectio i the closed ecoomy, which ivolves a trade-off betwee gais from higher cosumer surplus ad techology spillovers ad losses from less R&D ivestmet by iovators, eeds to be modified from the viewpoit of developig coutries. 3 Sice profits of the iovatig firms (MNEs) are ot take ito accout, the optimal IPR protectio for developig coutries teds to be laxer tha that i the closed ecoomy. However, because of the optio for MNEs to export goods i respose to a lax IPR protectio, the IPR policy may eed to be striget eough to give MNEs a icetive to choose FDI. Therefore, the aalysis of the optimal IPR protectio for developig coutries is ot so straightforward. As is well kow, oe importat product of the Uruguay Roud of the Geeral Agreemet o Tariffs ad Trade (GATT) was the Agreemet o Trade-Related Aspects of Itellectual Property Rights (the TRIPS Agreemet) i This agreemet requires all members, icludig both developed ad developig coutries, to adopt a set of uiversal miimum stadards o IPR protectio. However, coutries like Chia, for example, have bee criticized for their isufficiet eforcemetof IPR protectio (USTR, 2010). 4 Thus, eve uder the TRIPS Agreemet, developig coutries may have a icetive to maipulate their IPR policy to facilitate techology spillovers from MNEs. The mai purpose of this paper is to examie developig coutries IPR policy whe it affects techology spillovers through FDI. While IPR policy covers both patets ad kow-how, the aalysis i this paper would be more relevat to the latter because this paper deals with cost-reducig R&D. 3 See Scotchmer (2004) for a survey of this issue. 4 The Uited States Trade Represetative (USTR) publishes aually its review of foreig coutries IPR practices. USTR (2010) idetifies 42 coutries or ecoomies with IPR-related problems. Eleve of them, icludig Algeria, Argetia, Chia, Idia, Idoesia, Pakista, Thailad, ad Veezuela, fall ito the priority watch list, which meas that IPR ifrigemet i those coutries merits close attetio. 3

4 To address this issue, I costruct a simple North-South trade model i which a Norther firm ad a Souther firm compete i the Souther market. The Norther firm ca choose either to export goods to the Souther market or to udertake FDI i the South. Iitially, these two firms have access to the same techology. The Norther firm ca coduct cost-reducig R&D, or process iovatio. The Norther firm may be very efficiet i its R&D, which meas that margial cost of productio is greatly reduced by a small ivestmet i R&D, or may be less efficiet i its R&D, which meas that oly a small cost reductio is attaied eve by a relatively large ivestmet i R&D. I the model, the efficiecy of the Norther firm s R&D is captured by a parameter. As log as the Norther firm produces goods i its ow coutry, kowledge does ot leak out to the Souther firm. However, if the Norther firm ivests i the South, spillovers of kowledge occur, beefitig the Souther firm from the Norther firm s R&D. The degree of spillover depeds o the Souther IPR protectio policy. If the Souther IPR protectio policy is striget, spillovers are low. If it is lax, o the other had, spillovers are high. Sice the Souther govermet also imposes tariffs o imports, the Norther firm faces a trade-off betwee protectig its kowledge by keepig its plat i the North ad avoidig tariffs by udertakig FDI. 5 The market structure i the South is edogeously determied. Eve whe the Norther firm exports goods to the Souther market, the market structure may be duopoly, if efficiecy of R&D is low or if tariff protectio is high eough. The Souther govermet may maipulate its IPR policy to attract FDI or to iduce the foreig firm to export. The mai results are as follows. First, whe the efficiecy of R&D is low, the Souther govermet may choose a striget IPR policy to iduce the Norther firm to udertake FDI or a eve more striget IPR policy to stimulate the Norther firm s icetive to egage i a higher level of R&D. I these cases, the Souther firm beefits from spillovers. Secod, whe the efficiecy of R&D is medium, the South sets a lax IPR policy to iduce the Norther firm to export. I exportig, the Norther firm becomes a moopolist because of a large techology gap betwee the two firms. Third, with high R&D 5 I this sese, the model i this paper has some features i commo with models i the literature o tariff-jumpig FDI uder oligopoly (e.g., Smith, 1987; Motta, 1992). 4

5 efficiecy, the South sets a striget IPR policy to allow moopoly by the Norther firm uder FDI. I this way, I fid a o-mootoic relatioship betwee the optimal Souther IPR policy ad efficiecy of R&D. Moreover, I also show that if the Souther govermet chooses both IPR ad tariff policy before firms act, it may strategically set a high tariff to attract FDI or a low tariff to lead to exportig, depedig o parameter values. If tariffs are ot a policy istrumet but there are exogeous trasport costs for cross-border shipmet of goods, o the other had, the Souther govermet tries to attract FDI by settig a striget IPR policy. Except for those additioal effects, the properties of the basic results are kept uder these alterative assumptios. The results i this paper suggest that lax IPR protectio i developig coutries may be related with discretioary powers to impose tariffs. As trade liberalizatio proceeds further uder the multilateral egotiatio at the World Trade Orgaizatio (WTO), developig coutries may have a icetive to stregthe their IPR protectio. I the literature, a large umber of studies have ivestigated the effects of IPR policy through spillovers of product iovatio, which is aimed at developig ew products or improvig the quality of existig products, i the North-South trade (Deardorf, 1992; Helpma, 1993; Taylor, 1994; Lai, 1998; Glass ad Saggi, 2002; Lai ad Qiu, 2003; Qiu ad Lai, 2004). There are a relatively small umber of studies o IPR policy related to spillovers of process iovatio (Chi ad Grossma, 1990; Taylor, 1993; Steurs, 1997; Žigić, 1998, 2000; Naghavi, 2007; Kim ad Lapa, 2008; Liao ad Wog, 2009).6 This is rather surprisig because studies o spillovers of iovatio have maily focused o process iovatio (Katz, 1986; d Aspremot ad Jacquemi, 1988; Kamie et al. 1992; Suzumura, 1992). Chi ad Grossma (1990) ad Žigić (1998, 2000) explore the effects of the Souther IPR policy o the Norther firm s R&D ad welfare i each coutry. Kim ad Lapa (2008) exted the model to the case of oe iovatig orther firm ad heterogeeous souther firms ad aalyze how heterogeeity amog souther coutries affects orther firm s R&D ad IPR protectio policy i souther coutries. 6 Diwa ad Rodrik (1991) cosider a geeral model that fits both product ad process iovatio. They assume a cotiuum of potetial techologies, with a differet distributio of prefereces for these i the North ad the South. 5

6 Steurs (1997) ivestigates how the level of R&D spillover that is cotrolled by a supra-atioal social plaer who maximizes the world welfare will differ, depedig o whether markets are segmeted or itegrated. Liao ad Wog (2009) aalyze the iteractio betwee Souther IPR policy ad Norther R&D subsidy policy. These papers focus o iteratioal spillovers of kowledge ad do ot cosider the possibility of FDI. Taylor (1993) examies the effects of Souther IPR protectio whe the Norther firm edogeously chooses maskig product techology ad the Souther firm egages i reverse egieerig. I his aalysis, while the Souther firm s productio cost falls due to its reverse egieerig, the Norther firm does ot directly coduct process iovatio. Naghavi (2007) is the most similar to my paper. Like my paper, he examies the Souther coutry s icetives to use its IPR policy to maipulate the Norther firm s decisios o R&D ad plat locatio. Ulike my paper, however, he assumes the Norther firm ca moopolize the Souther market by exportig. This simple differece makes the results i the two papers quite differet. I his study, the Souther govermet always tries to attract FDI by choosig a striget IPR policy, ad the optimal IPR policy is characterized by corer solutios. I my paper, these results do ot ecessarily hold. The rest of the paper proceeds as follows. Sectio 2 sets up the model. Sectio 3 aalyzes the Norther firm s choice of exportig or FDI. Sectio 4 examies the optimal IPR protectio. Sectio 5 discusses how a chage i the assumptio alters the optimal IPR policy. Sectio 6 cocludes. 2 The Model There are two coutries, the North ad the South. I each coutry, there is oly oe firm. I call them firm N ad firm S respectively. These firms produce a homogeeous good. The markets i the two coutries are segmeted. I focus o the Souther market. The iverse demad i the Souther market is give by p(y + y s )=a (y + y s ), where a>0 is a parameter for measurig the market size ad y ad y s are outputs of firms N ad S, respectively. The firms compete i Courot fashio. Iitially, these two firms have access to the same old techology, which is expressed by a costat 6

7 margial cost, c. I assume that c<aholds. However, firm N is capable of coductig process iovatio, or cost-reducig R&D. Followig Chi ad Grossma (1990), I assume that by ivestig x i the process iovatio, firm N s margial cost is reduced by f(x) =(γx) 1/2,whereγ>0isaparameterfor measurig the efficiecy of the process iovatio. The choice of x is restricted to the rage of x<c 2 /γ. Firm N decides whether to produce goods i the North ad export them to the South, or to ivest i the South ad produce goods locally. Whe it exports, it faces a specific tariff t 0. Whe it udertakes FDI, techology spillovers occur. The degree of spillovers depeds o the Souther IPR policy. I assume that the degree of techology spillovers is iversely proportioal to the strigecy of the Souther IPR policy. For simplicity, I assume that both the degree of spillovers ad the strigecy of the Souther IPR policy are captured by a sigle parameter. 7 The, the level of Souther IPR protectio, or the degree of techology spillovers, is measured by s [0, 1]. s = 0 correspods to full protectio (i.e., o spillovers) ad s = 1 correspods to o protectio (i.e., perfect spillovers). The profits of firms N ad S are respectively give by {p(y + y s ) t (c f(x))} y x, if firm N exports, π (y,y s,x) = {p(y + y s ) (c f(x))} y x, if firm N udertakes FDI, {p(y + y s ) c} y s, if firm N exports, π s (y,y s,x) = {p(y + y s ) (c sf(x))} y s, if firm N udertakes FDI. The Souther govermet chooses a tariff t 0 ad the IPR protectio level s [0, 1] to maximize welfare i the South, which is give by π s (t)+cs(t)+ty, W (t, s) = π s (s)+cs(s), if firm N exports, if firm N udertakes FDI, where CS is cosumer surplus i the South, which is give by CS =(y + y s ) 2 /2. Sice the mai focus of this paper is the IPR policy, I assume that the Souther govermet chooses its IPR policy before 7 I priciple, two differet parameters should be used for the degree of techology spillovers ad the strigecy of IPR policy. However, usig a sigle parameter for them makes the model tractable. Actually, such a treatmet is quite popular i the literature. See, for example, Chi ad Grossma (1990), Žigić (1998, 2000), ad Naghavi (2007). 7

8 firm N decides whether to udertake FDI, whereas it chooses a tariff after firm N decides to export to the South. 8 This assumptio prevets the Souther govermet from imposig a excessive tariff strategically to iduce firm N to udertake FDI, coupled with a lax IPR policy. The timig of the policy decisio is also based o the fact that the IPR policy ivolves a loger period of legislative procedure. The tariff policy is, i cotrast, relatively flexible, because policy istrumets uder the GATT/WTO rule, icludig atidumpig measures ad coutervailig duties, ca be implemeted withi a relatively short period. The timig of the game is as follows: I stage 1, the Souther govermet chooses s to maximize domestic welfare; I stage 2, firm N decides whether to export or ivest; I stage 3, the Souther govermet chooses t if firm N exports; I stage 4, firm N chooses the level of process R&D; I stage 5, firms compete i Courot fashio. 9 The solutio cocept is the subgame perfect Nash equilibrium. 3 Market Structure ad the Edogeous Mode of Supply I this sectio, I first aalyze the market structure i cases where firm N exports ad where it udertakes FDI. The, I ivestigate firm N s decisio o the mode of supply. 3.1 Stages 3 to 5 i the subgame i which firm N exports Whe firm N chooses to export goods to the Souther market, there are three possible market structures: (i) duopoly; (ii) moopoly by firm N (which I call foreig moopoly ); ad (iii) domestic moopoly. I look at these three cases i order. 8 Naghavi (2007) cosiders the same game structure. I Sectio 5.1, I briefly discuss the case i which the Souther govermet chooses both IPR policy ad tariffs before firm N decides whether to udertake FDI. Moreover, i Sectio 5.2, I cosider the case i which tariffs are ot a policy istrumet but there are trasport costs. 9 I Sectio 5.1, the Souther govermet chooses both s ad t i stage 1. I that case, the model is reduced to a three-stage game. Similarly, i Sectio 5.2 tariffs are ot a policy istrumet. Thus, the model is agai reduced to a three-stage game. 8

9 3.1.1 The case of duopoly Whe duopoly is a viable market structure, each firm chooses its quatity to maximize its ow profits at the fial stage, give the duopolistic market structure, tariff level, ad its rival s output level. The first-order coditios (FOCs) are give by π / y =0ad π s / y s = 0. Each firm s outputs ad profits are respectively give by y Ed = y Ed a c 2t +2(γx)1/2, π Ed 3 s = a c + t (γx)1/2 3 =, ad π Ed s = where the superscript Ed idicates variables uder exportig with duopoly. ( ) a c 2t +2(γx) 1/2 2 x, (1) 9 ( ) a c + t (γx) 1/2 2, (2) 9 I stage 4, firm N chooses x to maximize π Ed. The optimal level of R&D is give by Substitute (3) ito (1) to obtai x Ed = 4γ(a c 2t)2 (9 4γ) 2. (3) y Ed 3(a c 2t) = 9 4γ ad π Ed = (a c 2t)2. (4) 9 4γ I order for the duopolistic market structure to emerge, t (a c)/2 must hold The case of foreig moopoly Firm N ca attai a moopoly positio by choosig a high level of R&D that makes it uprofitable for firm S to produce goods, if it is optimal for firm N to do so. From y Ed s =0,use(2)toobtai x Em = (a c + t)2, (5) γ where the superscript Em deotes variables uder exportig with foreig moopoly. Firm N s output ad profits are respectively give by y Em = a c t +(γx)1/2 2 = a c ad π Em =(a c) 2 (a c + t)2. (6) γ As see i (6), y Em is idepedet of t ad γ. This property partly comes from the liearity of the demad but is robust for geeral f(x). I order for this case to occur, t (γ 1/2 1)(a c) must hold. For γ 9/4, (γ 1/2 1)(a c) (a c)/2 holds. 9

10 3.1.3 The case of domestic moopoly uder prohibitive tariff If the Souther govermet imposes a prohibitive tariff, which is t>(a c)/2, firm S becomes the moopolist i the Souther market. Sice this is the stadard moopoly case, firm S s output ad profits are respectively give by y Ep s =(a c)/2 adπ Ep s =(a c) 2 /4, where the superscript Ep deotes variables uder exportig with a prohibitive tariff. Cosumer surplus is give by CS Ep =(a c) 2 /8 ad Souther welfare is give by W Ep = CS Ep + π Ep s = 3(a c)2. (7) The optimal tariff I stage 3, the Souther govermet chooses t to maximize domestic welfare i the South. Firm S s output uder duopoly is obtaied by substitutig (3) ito (2): y Ed s = (3 2γ)(a c)+3t. (8) 9 4γ Thus, y Ed s 0holdsforallt 0wheγ 3/2. Souther welfare uder duopoly is W Ed (t) = ((3 2γ)(a c)+3t)2 (2(3 γ)(a c) 3t)2 (9 4γ) 2 + 2(9 4γ) 2 + 3t(a c 2t). (9) 9 4γ The tariff that maximizes (9) for γ 3/2 isgiveby t = 3(3 2γ)(a c). (10) 27 16γ It holds that t (a c)/2 forγ 9/4. Substitute t ito (9) to obtai W Ed (t )= 3(7 4γ)(a c)2. (11) 2(27 16γ) For γ (3/2, 9/4), dw Ed /dt < 0fort 0. From (8), y Ed s > 0holdsfort> t, where t (2γ 3)(a c). (12) 3 Note that t <(γ 1/2 1)(a c) holds. 10

11 Souther welfare i the case of foreig moopoly is give by W Em (t) = (a c)2 2 + t(a c). (13) Sice dw Em /dt = a c>0, the optimal tariff is the highest level that is cosistet with this regime. From (4) ad (6) it yields π Ed πem = {3(a c + t) 2γ(a c)} 2 /(9 4γ)γ 0forγ 9/4, i.e., firm N prefers duopoly to foreig moopoly. Sice duopoly emerges for t> t, the highest tariff cosistet with foreig moopoly is t = t. From (9) ad (13), it is show that W Ed (t) (resp. <) W Em (t) holdsfort (resp. >) t. The situatio is depicted i figure 1. I the figure, the W Ed curve ad the W Em curve are draw. Sice foreig moopoly prevails for t< t ad duopoly does for t> t, the Souther welfare that is actually attaied is give by the thick parts of the curves. The followig lemma is the obtaied. Lemma 1 Whe firm N exports, (i) for γ (0, 3/2], the Souther govermet imposes a tariff t, which is defied by (10), ad the market structure is duopoly; (ii) for γ (3/2, 9/4), the Souther govermet imposes a tariff t, which is defied by (12), ad the market structure is foreig moopoly. Proof. See the Appedix. This propositio implies that oce firm N decides to export to the Souther market, it is ever optimal for the South to impose a prohibitive tariff. 3.2 Stages 4 ad 5 i the subgame i which firm N udertakes FDI I ow tur to the case i which firm N udertakes FDI. Whe firm N udertakes FDI, duopoly or foreig moopoly emerges The case of duopoly As i the case of exportig, uder duopoly FOCs yield each firm s outputs ad profits: y Fd = y Fd s = ( a c +(2 ) s)(γx)1/2 a c +(2 s)(γx), π Fd 1/2 2 3 = x, (14) 9 ( a c (1 ) 2s)(γx)1/2 a c (1 2s)(γx), ad πs Fd 1/2 2 =, (15)

12 where the superscript Fd idicates variables uder FDI with duopoly. I stage 4, the optimal level of R&D is give by Substitute (16) ito (14) to yield y Fd x Fd = γ(2 s)2 (a c) 2 (9 γ(2 s) 2 ) 2. (16) = 3(a c) 9 γ(2 s) 2 ad π Fd = (a c) 2 9 γ(2 s) 2. (17) The case of foreig moopoly As i the case of exportig, firm N ca attai a moopoly positio by choosig a high level of R&D. From y Fd s = 0, use (15) to obtai x Fm = (a c)2 γ(1 2s) 2, (18) where the superscript Fm deotes variables uder FDI with foreig moopoly. Firm N s output ad profits are respectively give by y Fm (1 s)(a c) = 1 2s ad π Fm = (γ(1 s)2 1)(a c) 2 γ(1 2s) 2. (19) 3.3 Stage 2: Firm N s choice of the mode of supply I stage 2, firm N chooses whether to export to the South or udertake FDI, give the Souther IPR policy. Before aalyzig firm N s choice of the mode of supply, I examie which market structure emerges if firm N udertakes FDI The market structure uder FDI Whe firm N udertakes FDI, from (17) ad (19), it yields π Fd πfm = {γ(2 s)(1 s) 3} 2 (a c) 2 /γ(1 2s) 2 (9 γ(2 s) 2 ) 0forγ<9/(2 s) 2. Thus, as i the case of exportig, firm N prefers duopoly to foreig moopoly. Firm S s output uder duopoly is obtaied by substitutig (16) ito (15) ys Fd (3 γ(2 s)(1 s))(a c) = 9 γ(2 s) 2. (20) 12

13 Thus, ys Fd 0forγ 3/(2 s)(1 s). Sice 3/(2 s)(1 s) 3/2, ys Fd 0alwaysholdsforγ 3/2, which implies that a duopoly always emerges for γ 3/2. For γ>3/2, a duopoly is ot feasible for 3/(2 s)(1 s) γ. Thus, firm N behaves as a moopolist for 3/(2 s)(1 s) γ, ors s 1,where s 1 3 (1 + 12/γ)1/2. (21) 2 The above results are summarized i the followig lemma. Lemma 2 Whe firm N decides to udertake FDI, (i) for γ (0, 3/2], the market structure is duopoly; (ii) for γ (3/2, 4), the market structure is foreig moopoly for s s 1 ad duopoly for s>s 1,where s 1 is defied by (21) Export vs. FDI Give the viable market structure i each regime, firm N decides whether to export or udertake FDI. Its choice depeds o the efficiecy of R&D. For γ 3/2, a duopoly emerges, whether firm N exports or udertakes FDI. Substitutig (10) ito (4) yields π Ed (9 4γ)(a (t c)2 )= (27 16γ) 2. (22) From (17) ad (22), firm N is idifferet betwee exportig ad FDI if s = s, where { ( 64γ 2 ) 1 } γ 162 s 2 1. (23) γ(9 4γ) Note that 64γ γ 162 > 0 if ad oly if γ (( )/128, ( )/128), where ( )/ ad ( )/ Sice d s/dγ < 0forγ>( )/128 ad s =1ifγ = γ 13/8 217/ , the π Fd γ [ γ, 3/2], π Fd (s) >πed (t )alwaysholdsforγ γ. For (s) > (resp. <) πed (t )ifs<(resp. >) s. Notethat s =0wheγ =3/2. For γ>3/2, foreig moopoly emerges uder exportig, while duopoly or foreig moopoly does uder FDI, depedig o s. Substitutig (12) ito (6) yields π Em ( t) = (9 4γ)(a c)2. (24) 9 13

14 The, π Em( t) isequaltoπ Fd(s), which is give by (17), whe s = s 2,where { ( ) 1 } 2 γ 2 s (25) γ(9 4γ) Thus, if s (s 2, 1], π Em π Fm ( t) >π Fd (s) >πfm (s) holds. Ifs (s 1,s 2 ), π Fd (s) >πem ( t) adπ Fd (s) > (s) hold. Ifs [0,s 1 ), π Fm (s) >π Em ( t) adπ Fm (s) >π Fd (s) hold. Note that s 2 > 1for γ (ˇγ, 2], where ˇγ (26) s 2 becomes a complex umber for γ>2. Thus, for γ>ˇγ, firm N ever exports. The above results are summarized i the followig lemma: Lemma 3 (i) For γ (0, γ], where γ 1.362, firm N chooses FDI for all s [0, 1]; (ii) For γ ( γ, 3/2], firm N chooses FDI if s s ad exportig if s> s, where s is defied by (23); (iii) For γ (3/2, ˇγ], whereˇγ is defied by (26), firm N chooses FDI with foreig moopoly if s s 1,FDI with duopoly if s (s 1,s 2 ],adexportigifs>s 2,wheres 1 ad s 2 are defied by (21) ad (25), respectively; (iv) For γ (ˇγ, 4), firm N chooses FDI with foreig moopoly if s s 1 ad FDI with duopoly if s (s 1, 1]. Firm N s choices of the mode of supply are draw i figure 2. I figure 2, γ is take i the horizotal axis ad s is take i the vertical axis. FM stads for foreig moopoly. I the area left of the s curve, firm N chooses duopoly uder FDI, while i the area betwee the s ad s 2 curves, firm N chooses exportig. I that area, the market structure is duopoly for γ 3/2 ad foreig moopoly for γ>3/2. Moreover, i the area right of the s 2 curve, firm N chooses FDI. The market structure is duopoly above the s 1 curve ad foreig moopoly below the s 1 curve. Iterestigly, firm N chooses FDI for both low ad high γ, eve whe the Souther IPR protectio is lax. Whe γ is low, sice the size of the cost reductio is small, the damage for firm N from spillovers is likewise small. Thus, firm N prefers FDI to exportig because the beefit from avoidig tariffs domiates the loss from spillovers. Whe γ>3/2, the market structure uder exportig is foreig moopoly. I that case, as γ rises, firm N s profits uder exportig fall because it faces a higher tariff ad hece has 14

15 to ivest i R&D more to become a moopolist. As is see from (12) ad (24), t icreases ad π Em( t) decreases as γ icreases. I cotrast, π Fd icreases as γ icreases, which ca be easily show from (17). Because of these effects, for γ>3/2, firm N teds to prefer FDI more as γ becomes higher. Note that the assumptio that the Souther govermet imposes the optimal tariff is crucial for this result. As is see from (6), π Em (t)/ γ > 0, which implies that if t is exogeously give, firm N s profits uder exportig with foreig moopoly icrease as γ icreases. 4 The Optimal IPR Protectio I this sectio, I aalyze the optimal IPR protectio by the Souther govermet i stage 1. As show above, firm N s choice of the mode of supply depeds o the efficiecy of R&D. Thus, I explore the optimal IPR policy for differet levels of R&D efficiecy. 4.1 Low R&D efficiecy Ifirstexamiethecaseofγ 3/2. I this case, the market structure is a duopoly, whether firm N udertakes FDI or exportig. Uder FDI, Souther welfare is give by W Fd (s) = (3 γ(2 s)(1 s))2 (a c) 2 (9 γ(2 s) 2 ) 2 + (6 γ(2 s)(1 s))2 (a c) 2 2(9 γ(2 s) 2 ) 2. (27) Uder exportig, Souther welfare is give by (11). Differetiatig (11) with respect to γ yields dw Ed (t )/dγ =6(a c) 2 /(27 16γ) 2 > 0. Sice W Ed (t ) γ=0 =7(a c) 2 /18 ad W Ed (t ) γ=3/2 = (a c) 2 /2, it holds W Ed (t ) [7(a c) 2 /18, (a c) 2 /2] for γ 3/2. The optimal IPR policy ad the resultig market structure i equilibrium are as follows. Propositio 1 Defie s by s arg max W Fd (s). (i)wheγ γ 1.362, the optimal IPR policy is s = s ad firm N chooses FDI; (ii) Whe γ ( γ, 3/2], the optimal IPR policy is (a) s = s, (b) s = s, where s is defied by (23), or (c) ay s ( s, 1]. FirmNchoosesFDIi(a)ad(b)ad exportig i (c). 15

16 Proof. See the Appedix. Typical examples for γ ( γ, 3/2] are draw i figures 3 to 5. I these figures, s is measured o the horizotal axis, ad Souther welfare is measured o the vertical axis. To draw these figures, umerical simulatios are ru by ormalizig (a c) to oe. The actual values of Souther welfare ca be obtaied by multiplyig umbers i these figures by (a c) 2. I each figure, the W Fd curve ad the W Ed (t ) curve are depicted. Sice W Ed (t ) is idepedet of s, thew Ed (t ) curve is a horizotal lie. Figure 3 shows the case of γ = I this case, s 0.96 ad s Sice firm N chooses FDI for s< s ad exportig for s> s, the feasible part of each curve is as beig thickeed. Sice s < s, theoptimal IPR policy is s = s, i.e., a iterior solutio. Figure 4 shows the case of γ =1.4. I this case, s 0.59 ad s Sice s <s, the optimal IPR policy is s = s, which is the lowest level of protectio at which firm N udertakes FDI. Fially, figure 5 shows the case of γ =1.45. I this case, s 0.24 ad s As show i the figure, s is lower tha the s ( 0.43) at which W Fd (s) =W Ed (t )holds. Thus, the welfare level i the feasible part of the W Fd curve is lower tha the value of W Ed (t ), which implies that the optimal IPR policy is ay s ( s, 1] to iduce firm N to export. 4.2 Medium ad high R&D efficiecy I the case of γ>3/2, uder FDI the market structure is either duopoly or foreig moopoly. I call the case of γ (3/2, ˇγ] the medium R&D efficiecy ad the case of γ (ˇγ, 4) the high R&D efficiecy, where ˇγ is defied by (26). Souther welfare uder duopoly is give by (27). Souther welfare uder foreig moopoly is give by W Fm (s) = (1 s)2 (a c) 2 2(1 2s) 2. (28) Uder exportig, from Lemma 1 the optimal tariff is t ad Souther welfare is give by W Em ( t) =W Ed ( t) = (4γ 3)(a c)2. (29) 6 The followig lemma is the obtaied. Lemma 4 (i) W Fd (s 1 )=W Fm (s 1 ) for γ (3/2, 4); (ii) s 1 <s 2 for γ (3/2, 2); (iii) dw Fm (s)/ds > 16

17 0 for s<1/2; (iv)w Fd (s 1 ) W Fd (s) for all s [s 1, 1] ad for γ (3/2, 4); ad(v)w Fm (s 1 ) < W Em ( t) for γ (3/2, 2]. Proof. See the Appedix. A importat implicatio of Lemma 4 is that, with medium R&D efficiecy, the South caot improve its domestic welfare by maipulatig its IPR protectio policy so that firm N udertakes FDI ad firm S stays i the market to extract the beefits of spillovers. Usig Lemmas 2-4, the followig propositio is obtaied for medium R&D efficiecy. Propositio 2 Whe γ (3/2, ˇγ], where ˇγ is defied by (26), the optimal IPR protectio is ay s (s 2, 1], wheres 2 is defied by (25), ad firm N chooses exportig. Proof. See the Appedix. A typical example of medium R&D efficiecy is draw i figure 6, i which γ =1.6. Basic features of figure 6 are the same as those of the previous three figures, except that i figure 6 three curves are depicted: the W Fd, W Fm,adW Em ( t) curves. Sice firm N chooses FDI with foreig moopoly for s<s 1, FDI with duopoly for s (s 1,s 2 ), ad exportig for s>s 2, the feasible part of each curve is as beig thickeed i the figure. The highest level of Souther welfare uder FDI is give by the itersectio betwee the W Fd ad W Fm curves at s = s 1. However, that level of welfare is lower tha W Em ( t), which implies that the optimal IPR protectio is characterized by ay s (s 2, 1] to iduce firm N to choose exportig. For high R&D efficiecy, the followig propositio is obtaied. Propositio 3 Whe γ (ˇγ, 4), whereˇγ is defied by (26), the optimal IPR protectio is s = s 1, where s 1 is defied by (21), ad firm N chooses FDI with foreig moopoly. Proof. See the Appedix. Whe γ (ˇγ, 4), all parts of the W Em ( t) curve are ifeasible ad hece the optimal IPR policy is s = s 1, which maximizes Souther welfare uder FDI by iducig firm N to become the moopolist. 17

18 Note that, ulike the case of low R&D efficiecy, Propositios 2 ad 3 show that spillovers ever occur whe the efficiecy of R&D is medium or high. Note also that whe γ 4, as was show i Lemma 4, s 1 is ot well defied. I this case, y Fm goes to ifiity as s approaches 1/2. Thus, the optimal IPR policy is also ot well defied. 5 The Optimal IPR Policy i Two Alterative Cases I this sectio, I examie two cases with alterative model structures to examie how a chage i the assumptio of tariff policy will affect the results i the previous sectios. 5.1 Strategic tariff policy I first cosider the case i which the Souther govermet chooses s ad t i stage 1. I this case, the model is reduced to a three-stage game: I stage 1, the Souther govermet chooses s ad t; I stage 2, firm N decides whether to export or FDI ad chooses the R&D level; I stage 3, firms compete i Courot fashio. As I have argued above, whe a tariff is set before firm N s locatio choice, the Souther govermet may strategically impose a excessive tariff to iduce firm N to udertake FDI. It may also strategically impose a lower tariff to iduce firm N to export if Souther welfare is higher uder exportig but firm N prefers FDI uder the optimal tariff. Except for these strategic roles, the optimal tariff is the same as that i sectio 3.1.4, because tariffs do ot affect the outcomes i the subgames uder FDI. Now, defie γ by W Ed (t ; γ) =W Fd (s ; γ). It is show that γ The, for γ (0, γ], W Ed (t ; γ) <W Fd (s ; γ) holds. The optimal policy is a combiatio of s = s ad ay t such that π Ed (t) <πfd (s ). Firm N chooses FDI ad Souther welfare is W Fd (s ; γ). For γ (γ, 3/2], it holds that W Ed (t ; γ) >W Fd (s; γ), s. Figure 7 shows a example of this case where γ =1.49. The optimal policy is a combiatio of ay s ( s, 1] ad t = t, which yields the same outcome as Propositio 1 (ii) (c). Firm N chooses exportig ad Souther welfare is W Ed (t ; γ). Compared with Propositio 1, 18

19 choosig t at stage 1 eables the South to attract FDI wheever Souther welfare is higher uder FDI. For some parameter values, a laxer IPR policy is chose, compared with the case where a tariff is set after firm N s decisio to export. For γ (3/2, ˇγ], the highest possible Souther welfare uder exportig is W Em ( t) ad that uder FDI is W Fm (s 1 ). FromLemma4(v),W Fm (s 1 ) <W Em ( t) holdsforγ (3/2, 2]. Cosequetly, the optimal policy is a combiatio of ay s (s 2, 1] ad t = t, which yields the same outcome as Propositio 2. Defie t by π Em ( t) =π Fd s=1. Note that t t holds. Also, defie `γ by W Fm (s 1 )=W Em ( t;`γ). It is show that ˇγ < `γ < 2.1 holds. The, for γ (ˇγ, `γ], Souther welfare is higher uder exportig, while firm N chooses FDI eve with s =1ift = t. The Souther govermet tries to iduce firm N to export by lowerig the tariff from t ad settig the lowest IPR protectio. The optimal policy is a combiatio of s = 1 ad t = t. Firm N chooses exportig with foreig moopoly ad Souther welfare is W Em ( t;`γ). Moreover, for γ (`γ, 4), sice W Fm (s 1 ) >W Em ( t;`γ), the Souther govermet has o further icetive to iduce firm N to export. The optimal policy is a combiatio of s = s 1 ad ay t such that π Em (t) <π Fm (s 1 ). The outcome is the same as Propositio 3. Thus, the result is differet from Propositio 3 oly i the rage of γ (ˇγ, `γ], i which the South strategically chooses a lower tariff to iduce firm N to export. 5.2 Exogeous trasport costs I ext tur to the case i which the Souther govermet caot use tariffs but there are exogeous trasport costs for cross-border shipmet of goods. I this case, the model becomes a three-stage game. Let τ be per-uit trasport costs that firm N has to pay whe it exports goods to the South. Assume τ (a c)/2 so that firm N actually has a icetive to export goods to the South. Sice the South does ot ear tariff reveues, Souther welfare i the case of firm N exportig is chaged from (9) ad (13) ad is give by W Ed (τ) = ((3 2γ)(a c)+3τ)2 (2(3 γ)(a c) 3τ)2 (9 4γ) 2 + 2(9 4γ) 2 (30) 19

20 uder duopoly ad W Em (τ) = (a c)2 2 (31) uder foreig moopoly. Differetiate (30) with respect to τ to yield W Ed (τ) τ 3{2γ(a c) 9τ} = (9 4γ) 2. Thus, for τ < (2/9)γ(a c), it holds that W Ed (τ)/ τ < 0. I cotrast, (31) shows that Souther welfare is idepedet of τ uder foreig moopoly. Note that Souther welfare uder FDI remais the same as that i Sectio 4. The, from the aalysis i Sectio 3, we kow that for γ (0, 3/2] the market structure is duopoly, whether firm N chooses exportig or FDI. For s arg max W Fd (s), where W Fd (s) is give by (27), we ca defie implicitly τ such that π Ed (τ )=π Fd (s ), (32) where π Fd (s) adπed (τ) are respectively give by (17) ad (4). Solve (32) for τ to yield τ = (a c) 2 { ( 1 9 4γ 9 γ(2 s ) 2 ) 1 } 2. It the ca be show that W Fd (s ) W Ed (τ) for ay τ τ. O the other had, for τ<τ we ca defie implicitly ŝ such that π Fd (ŝ) =π Ed (τ). Note that ŝ<s holds. That is, ŝ is more striget tha s. It the ca be show that W Fd (ŝ) W Ed (τ) for ay τ<τ. Thus, Propositio 1 is partially correct eve uder exogeous trasport costs. Ulike Propositio 1, however, the optimal IPR protectio without tariff policy is ever a lax oe that iduces firm N to choose exportig. For γ (3/2, 4), from Lemma 3 we kow that firm N chooses exportig with moopoly or FDI (either dupoly or moopoly) for γ (3/2, ˇγ], where ˇγ is defied by (26) ad that firm N chooses FDI (either dupoly or moopoly) for γ (ˇγ, 4). Moreover, from Lemma 4 we kow that for γ (3/2, 4) Souther welfare uder FDI is maximized by settig s = s 1 to iduce foreig moopoly, where s 1 is defied by 20

21 (21). The, sice s 1 < 1/2 holds ad from (28) ad (31) it is easy to show that W Fm (s) W Em (τ) holds for s [0, 1/2), the optimal IPR protectio for γ (3/2, 4) is s = s 1 ad firm N chooses FDI with foreig moopoly. Thus, Propositio 3 is valid uder exogeous trasport costs, while Propositio 2 eeds to be modified. I summary, without tariff policy, the optimal IPR policy for the South is always striget eough to attract FDI. As i Sectio 4, however, actual techology spillovers from firm N to firm S occurs oly i the case of low R&D efficiecy. 6 Cocludig Remarks I this paper, I have ivestigated the optimal choice of IPR protectio policy by a Souther coutry whe a Norther ad a Souther firm compete i the Souther market. The Norther firm egages i cost-reducig R&D, which may allow kowledge spillovers to the Souther firm, depedig o the Souther IPR protectio. Whe the Norther firm udertakes FDI to produce goods locally i the South, techology spillovers occur. Whe the Norther firm produces goods i the North ad exports them to the South, techology spillovers would ot occur. Uder exportig, however, the Norther firm faces a tariff optimally set by the Souther govermet. Ulike the results of Žigić (2000) ad Naghavi (2007), I have show that for certai parameter values the optimal IPR protectio policy by the South is characterized by a iterior solutio, which is more striget tha the level at which the Norther firm is just idifferet betwee exportig ad udertakig FDI. Moreover, ulike Naghavi (2007), I have also show that the South does ot always try to attract FDI. For certai parameter values, the South prefers the Norther firm to egage i exportig rather tha udertakig FDI, though techology spillovers do ot take place. I also aalyzed the optimal IPR policy i two alterative model structures. First, if the Souther govermet strategically uses a tariff, it may impose a excessive tariff to iduce FDI or a lower tariff to iduce exportig, depedig o parameter values. Secod, if tariffs are ot a policy istrumet for 21

22 the Souther govermet, it chooses a striget IPR policy to attract FDI. The results i this paper imply that lax IPR protectio i developig coutries may be related with the availability of tariffs as a policy tool. Negotiated tariff reductios at the WTO may give developig coutries to stregthe their IPR protectio. For future research, there are a umber of potetially iterestig extesios of the aalysis. First, I have cosidered oly costless spillovers of techology. I the real world, may firms egage i costly imitatio activities. A umber of studies, icludig Helpma (1993), Lai (1998), ad Glass ad Saggi (2002), have examied imitatio ad IPR protectio. Thus, it is practically importat ad perhaps theoretically iterestig to exted the aalysis by itroducig a costly imitatio by the Souther firm. Secod, although the appropriability of iovatio is set exogeously by the stregth of Souther IPR policy i this paper, it may be quite iterestig to edogeize the appropriability regime by cosiderig the possibility of maskig product techology by the Norther firm, as Taylor (1993) did. Third, as Chi ad Grossma (1990) have examied, the possibility of licesig superior techology ca be itroduced. Licesig is also a importat source of obtaiig superior techology for developig coutries. Empirical studies (e.g., Smith, 2001) suggest that IPR protectio affects iteratioal licesig. Ackowledgemets I would like to thak Shoji Harua, Kaz Miyagiwa, Tetsuya Shikai, ad participats of semiars at Kwasei Gakui Uiversity, ad Otaru Uiversity of Commerce, cofereces at Okayama Uiversity, Hitotsubashi Uiversity, ad RIEB (Kobe Uiversity), Japaese Ecoomic Associatio Meetig, Asia- Pacific Trade Semiars (APTS) Meetig, ad Europea Trade Study Group (ETSG) Meetig for helpful commets ad suggestios o earlier versios of the paper. Fiacial support from the Japa Society for the Promotio of Sciece uder the Grad-i-Aid for Scietific Research (B) is gratefully ackowledged. The usual disclaimer applies. 22

23 A Appedix: Proofs of Lemmas ad Propositios A.1 Proof of Lemma 1 (i) For γ (0, 3/2], sice moopoly by firm N is ot feasible, the possible market structure is oly duopoly ad domestic moopoly. From (7) ad (11), it yields that W Ed (t ) W Ep = 3(7 4γ)(a c)2 2(27 16γ) 3(a c)2 8 = 3(a c)2 8(27 16γ) > 0. (ii) For γ (3/2, 9/4), W Ed (t) > (resp. <) W Em (t) holdsfort<(resp. >) t. Sice duopoly is feasible oly for t> t, the highest possible welfare level is attaied whe t = t, which is give by (29). From (7)ad(29),ityieldsthat W Em ( t) W Ep = (4γ 3)(a c)2 6 3(a c)2 8 = (16γ 21)(a c)2, 24 which is positive for γ>21/ A.2 Proof of Propositio 1 (i) Whe γ γ, from Lemma 3 firm N chooses FDI for all s [0, 1]. By defiitio s = s is optimal. (ii) Whe γ ( γ, 3/2], if s < s ad W Ed (t ) <W Fd ( s), s is optimal ad firm N chooses FDI. If s <s ad W Ed (t ) <W Fd ( s), the optimal s is just to iduce firm N to udertake FDI, which is give by s, ad firm N chooses FDI. If s <s ad W Ed (t ) >W Fd ( s) orifs < s ad W Ed (t ) >W Fd (s ), Souther welfare is higher uder exportig. Thus, ay s that leads to exportig is optimal. A.3 Proof of Lemma 4 (i) By defiitio, π Fd (s 1 )=π Fm x Fm (s 1 ). It also implies that ys Fd(s 1)=0. Thus, W Fd (s 1 )=π Fd s (s 1 ) holds, which implies that y Fd (s 1 )=y Fm (s 1 )adthatx Fd (s 1 )= (s 1)+ (yfd (s 1)+y Fd s (s 1)) 2 2 = (yfm (s 1)) 2 2 = W Fm (s 1 ). 23

24 From (19), y Fm is o-egative ad fiite oly for s<1/2. Similarly, from (17) ad (20), both y Fd ad y Fd s are o-egative ad fiite oly for s>s 1 ad s>2 3/γ 1/2. This implies that for γ 4, s>1/2 is ecessary for o-egative ad fiite y Fd (ii) From (21) ad (25), it yields that { s 2 s 1 = ad ys Fd. Hece, for γ 4, s 1 is ot well defied. ( 2 γ γ(9 4γ) ) 1 } 2 3 (1 + 12/γ)1/2 2 = γ1/2 (9 4γ) 1/2 +(9 4γ) 1/2 (12 + γ) 1/2 12(2 γ) 1/2 2γ 1/2 (9 4γ) 1/2, which is show to be zero whe γ =3/2 adpositiveforγ (3/2, 2). (iii) Differetiate W Fm (s) with respect to s to yield dw Fm (s)/ds =(1 s)(a c) 2 /(1 2s) 3, which is positive for s<1/2. (iv) It is easily show that s 1 γ=3/2 =0,ds 1 /dγ =3/γ 2 (1 + 12/γ) 1/2 > 0, ad s 1 γ=4 =1/2. Differetiate (27) with respect to s to obtai dw Fd (s) ds = 3γ{36(1 s) γ(2 s)(19 25s +10s2 )+γ 2 (1 s)(2 s) 3 }(a c) 2 (9 γ(2 s) 2 ) 3. It is show that dw Fd (s)/ds evaluated at γ =3/2 has a local miimum at s ad a local maximum at s s max Sice W Fd (0) γ=3/2 =(a c) 2 /2ad W Fd (s max ) γ=3/ (a c) 2,theforγ =3/2, W Fd (s 1 ) W Fd (s) holdsforalls [s 1, 1]. For 1.5 <γ 1.696, a proof is give i a similar way. For <γ<4, dw Fd /ds < 0 for all s [s 1, 1]. Thus, W Fd (s 1 ) W Fd (s) holds for all s [s 1, 1]. (v) Use (29) ad substitute (21) ito (28) to obtai W Em ( t) W Fm (s 1 ) = = (4γ 3)(a c)2 6 (4γ 3)(a c)2 6 (1 s 1)(a c) 2 2(1 2s 1 ) 2 (γ γ1/2 (γ + 12) 1/2 ) 2 (a c) 2 8(2γ γ 1/2 (γ + 12) 1/2 ) 2, which is show to be zero whe γ =3/2 adpositiveforγ (3/2, 2]. 24

25 A.4 Proof of Propositio 2 From Lemma 2 (ii), whe firm N udertakes FDI, the market structure is foreig moopoly for s s 1 ad a duopoly for s>s 1. The, from Lemma 4 (i)-(iv), the highest level of Souther welfare uder FDI is give by W Fd (s 1 )=W Fm (s 1 ). However, from Lemma 4 (v), W Fd (s 1 )=W Fm (s 1 ) <W Em ( t) holds, which implies that Souther welfare is highest whe firm N exports. Sice W Em ( t) is idepedet of s ad sice s>s 2 iduces firm N to export, the optimal IPR policy is ay s (s 2, 1] if s 2 1. A.5 Proof of Propositio 3 From Lemma 3 (iv), for γ>ˇγ, firm N ever chooses exportig. Moreover, from Lemma 2 (ii), whe FDI is udertake, the market structure is foreig moopoly for s s 1 ad a duopoly for s>s 1. The, from Lemma 4 (i), (iii), ad (iv), the optimal IPR policy is give by s = s 1 i the rage of γ (ˇγ, 4). 25

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