Solving a hold-up problem may harm all firms: Downstream R&D and transport-price contracts

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1 Solvng a hold-up problem may harm all frms: Downstream R&D and transport-prce contracts Kazuhro Takauch Tomomch Mzuno March 2017 Dscusson Paper No.1707 GRADUATE SCHOOL OF ECONOMICS KOBE UNIVERSITY ROKKO, KOBE, JAPAN

2 Solvng a hold-up problem may harm all frms: downstream R&D and transport-prce contracts Kazuhro Takauch Faculty of Busness and Commerce, Kansa Unversty Tomomch Mzuno Graduate School of Economcs, Kobe Unversty Ths verson: March 13, 2017 Abstract In vertcal relatons, by rasng nput prce after downstream research and development (R&D) nvestment, upstream frms can extract the R&D beneft and have an ncentve to set hgher nput prce. As downstream frms undernvest for fear of ths hold-up by upstream frms, outputs and nput-demand shrnk, and all frms become worse off. Prevous lterature emphaszes that a fxed-prce contract n whch upstream frms frst commt themselves to nput prces and downstream frms subsequently nvest can resolve the hold-up problem and make all frms better off. By contrast, we show that n a vertcal relaton between frm-specfc carrers and exporters, the fxed-prce contract of transport prce can make all frms worse off because an effcency mprovement n exporters ntensfes nter-regonal competton. We also dscuss the robustness of the result. Key words: Transport-prce contracts; Downstream R&D; Frm-specfc carrer; Holdup problem JEL classfcaton: L13; F12; O31; R40 Faculty of Busness and Commerce, Kansa Unversty, Yamate-cho, Suta, Osaka , Japan. E-mal: kazh.takauch@gmal.com; Tel.: ; Fax: Graduate School of Economcs, Kobe Unversty, 2-1 Rokkoda-cho, Nada-ku, Kobe-Cty, Hyogo , Japan. E-mal: mzuno@econ.kobe-u.ac.jp; Tel.: ; Fax:

3 1 Introducton In vertcal relatons, research and development (R&D) nvestments by downstream frms gve upstream agents an ncentve for opportunstc behavor. Suppose that, for example, a downstream frm nvests to reduce ts producton cost. After observng the nvestment actvty, by settng hgher nput-prce, the upstream tradng partner can extract the R&D beneft from the downstream frm. Some fear that the downstream nvestment s held-up by the upstream frm. Addtonally, the upstream frm s hold-up reduces downstream nvestment, 1 and hence, t tends to decrease both upstream and downstream frms proft. Other studes fnd that an effectve way to overcome ths problem s to fx the nput-prce through a long-term prce agreement,.e., a fxed-prce contract (Banerjee and Ln, 2003; Zkos and Kesavayuth, 2010) because the downstream frm decdes ts nvestment level as nput-prce gven, so t does not mnd a proft reducton from a hgher nput prce. Ths hold-up problem also can appear n a vertcal relaton between exportng and transportng frms. Internatonal transportaton s an essental servce to shp products overseas, and an exportng frm pays freght rates to cargo carrers to export. Hence, by settng a hgher prce after the exportng frm s nvestment, t s possble for the carrer to extract the R&D beneft. 2 Actually, transport cost s a major trade barrer, as much 1 The mportance of upstream frms opportunstc behavor, whch causes downstream frms to undernvest (.e., the hold-up problem) s wdely recognzed among researchers. For example, Glbert and Cvsa (2003) gve an example of a key-component suppler such as Intel and the nvestment by a PC maker such as Dell n the computer ndustry, and emphasze that ths sort of hold-up problem s very lkely to occur n supply chans such that downstream frms depend on ther tradng partners for both knowledge and capacty. Banerjee and Ln (2003) also gve a smlar example from the computer ndustry. 2 Hummels et al. (2009) emprcally show that transport prces, such as the ocean freght rate, s a mark-up prce and carrers have monopoly power. Ths emprcal evdence mples that carrers possbly 1

4 as or larger than other representatve polcy barrers 3 and affects frms nnovaton actvtes. For example, because a hgher transport cost lmts access to foregn markets and nhbts export producton, t affects ncentves to nnovate, such as cost-reducng R&D. 4 We consder a hold-up problem n nternatonal transportaton and show that a fxed-prce contract that resolves the problem n ths transport market has entrely dfferent effects than those found n the exstng lterature. Our model s based on a Brander and Krugman (1983)-type two-country duopoly competton. There are two frm-specfc carrers upstream and two exporters downstream. Each country has both a carrer and an exportng frm. Each carrer takes a per-unt transport charge from ts domestc exportng frm and shps products to the foregn market. Each exportng frm pays a transport charge to ts country s carrer n order to export, whle t freely supples to the domestc market. Suppose that n ths market structure, exporters can commt to zero exports. Then, each exportng frm s a monopoly frm n ts local market and can thus gan maxmum proft. We expect that a commtment to fewer exports benefts exporters. If there s the hold-up problem, exporter wll have a hgh margnal cost because ther nvestment becomes small. Hence, the hold-up problem s equal to a commtment to fewer exports. At the same tme, the margnal cost of domestc producton also extract rent from exporters thorough prce settng. 3 Accordng to Anderson and Van Wncoop (2004), the ad-valorem tax equvalent of transport costs s 10.7%, whle that of tarff and non-tarff barrers s 7 % n developed natons. 4 Innovaton ncentves are nfluenced by such factors as market access and the ntensty of competton. Snce transport cost affects all of these factors, t ultmately affects producer s nnovaton ncentves. See, for example, Aghon et al. (2004, 2005). 2

5 becomes large, whch lowers exporters proft. Exporters face ths trade-off and beneft from the hold-up problem f the commtment effect of fewer exports resultng from the hold-up problem s domnant. In our analyss, when the fxed-prce contract s not employed and exporters can commt to fewer exports, they can maxmze ther proft because they can create a stuaton close to domestc monopoly by adjustng the transport prce through ther nvestment decson. By contrast, when the fxed-prce contract s employed, the exporter s proft s mnmzed because carrers set a lower prce to promote exporters nvestments and exports become the most actve. Furthermore, when the cost-reducng R&D s hghly effcent, carrers proft less compared to other contract schemes because carrers set consderably lower prces to promote nvestments. Thus, the market structure s one n whch the fxed-prce contract harms all frms. We further dscuss the robustness of our results n two cases: one wth a postve spllover n R&D, and the other wth horzontally dfferentated domestc and foregn products. We fnd that our result holds n these extended cases. Ths study s closely related to Takauch s (2015a, b) consderaton of R&D rvalry 5 wth nternatonal transportaton. 6 Takauch (2015a) examnes the effects of the tech- 5 Ghosh and Lm (2013), Haaland and Knd (2008), and Long et al. (2011) also consder the relatonshp between trade costs and nnovaton. They examne the effects of reduced exogenous trade-cost on R&D nvestment. 6 Other studes also consder an mperfectly compettve transport sector n nternatonal trade (e.g., Abe et al., 2014; Behrens et al., 2009; Francos and Wooton, 2001; Ishkawa and Taru, 2015; Matsushma and Takauch, 2014). Francos and Wooton (2001) and Behrens et al. (2009) examne the roles of transport prces and transportng frms market power n general equlbrum settngs. Usng a two-country olgopoly model, Abe et al. (2014) examne the effects of emssons tax n the transport sector, whle Ishkawa and Taru (2015) examne the effects of several trade polces on the transport market. Matsushma and Takauch (2014) consder how seaport prvatzaton nfluences ther usage fees (trade cost) and welfare n an nternatonal olgopoly. 3

6 ncal effcency of R&D on exporters proft and shows that hgher R&D effcency can reduce ther proft. Takauch (2015b) consders the effects of transport effcency, R&D spllovers, and transport market competton on nvestment and welfare. The author shows that competton n the transport market may harm consumers. Although these works share a basc market structure exporters freely supply to ther domestc market whle they must pay freght rates for cargo carrer to export wth ths study, we ncorporate transport prce contracts and examne the effects on proft and welfare. Ths study s also related to works on nput-prce contracts wth downstream nvestment (Banerjee and Ln, 2003; Glbert and Cvsa, 2003; Kesavayuth and Zkos, 2009; Zkos and Kesavayuth, 2010). Banerjee and Ln (2003) show that fxed-prce contracts make all frms better off n a market wth an upstream monopoly and a downstream olgopoly. Zkos and Kesavayuth (2010) confrm that Banerjee and Ln s result always holds, even f R&D spllovers exst. Glbert and Cvsa (2003) consder the role of fnal demand uncertanty n a supply-chan wth one suppler and one buyer. They show that the suppler prefers a commtment to wholesale prces f the demand fluctuatons are not too large, and the buyer always profts more when the suppler makes a prce commtment. Kesavayuth and Zkos (2009) examne the role of R&D spllovers and the mportance of wages for labor unons on an endogenous choce of contract form for wages n a unon frm par. However, these analyses are all lmted to the domestc market and do not consder nternatonal trade and transportaton. We beleve that our analyss complments the exstng lterature. The rest of the paper proceeds as follows. Secton 2 presents the model. Secton 4

7 3 examnes transport-prce contracts. We dscuss the robustness of the man result n Secton 4. Secton 5 concludes. We provde the proofs n the appendx. 2 Model We consder a two-way trade model wth frm-specfc carrers, as n Takauch (2015a, b). Two symmetrc countres, H and F, have a homogeneous product market. Each country has a sngle exportng frm (called frm, = H, F ) and a frm-specfc cargo carrer (called carrer ). The nverse market demand n country s p = a q q j (, j = H, F ; j ), where p s the product prce, q s frm s domestc supply, q j s frm j s exports, and a > 0. Whle frm freely supples to the domestc market, t must use carrer and pay a per-unt transport-prce, t, to shp ts product to an overseas market. Before producton, frm nvests n R&D to reduce margnal producton cost c (> 0); after the nvestment, the margnal cost s c x, where x s the nvestment level. We assume that the R&D cost functon s γx 2 ; γ (> 0) denotes the techncal effcency n R&D. 7 Frm s proft s gven by Π (a q q j (c x ))q + (a q jj q j (c x ) t )q j γx 2, where, j = H, F ; j. Carrer makes a take-t-or-leave-t offer to frm and decdes ts transport prce. Each carrer s proft s π t q j. 8 We consder three transport-prce contract schemes. The frst s a fxed-prce contract where each carrer frst sets ts transport prce and frms subsequently nvest. The 7 Ths s a popular settng. See, for example, d Aprémont and Jacquemn (1988), Ghosh and Lm (2013), Haaland and Knd (2008), and Takauch (2015a). 8 Our man result does not change, though the other trade cost τ exsts (.e., π (t τ)q j). 5

8 second s a floatng-prce contract where frms frst nvest and each carrer subsequently sets ts transport prce. The thrd s a smultaneous move scenaro where carrers and frms smultaneously decde transport prces and nvestment levels. In all schemes, each frm decdes ts output (.e., domestc supply and exports) n the fnal stage of the game and competes à la Cournot n both markets n countres H and F. The game s solved by backward nducton. 3 Results In the fnal stage, each frm decdes ts outputs to maxmze ts proft. The frst-order condtons (FOCs) for proft maxmzaton are Π / q = a c 2q q j +x = 0 and Π / q j = a c 2q j q jj +x t = 0. These yeld q (t j, x) = (a c+t j +2x x j )/3 and q j (t, x) = (a c 2t + 2x x j )/3. Let x = (x, x j ). Fxed-prce contract. In the second stage, frm chooses an nvestment level, x, takng t as gven. From the frm s FOC, the second-stage nvestment level s x (t) = 4(3γ 4)(a c) 4(3γ 2)t + 6γt j, j. (1) (3γ 4)(9γ 4) Let t = (t, t j ). From the thrd-stage exports q j (t, x) and (1), carrer s maxmzaton problem s t [9γ(3γ 4)(a c) 2(3γ 1)(9γ 8)t + 8(3γ 1)t j ] max. t 3(3γ 4)(9γ 4) Ths yelds the followng equlbrum transport prce: t fx = 9γ(3γ 4)(a c) 4(3γ 1)(9γ 10). (2) 6

9 The outcome n the fxed-prce contract s labeled fx. From (2), we have the equlbrum nvestment and outputs: x fx = (189γ2 276γ + 80)(a c) 2(3γ 1)(9γ 10)(9γ 4). (3) q fx = 3γ(135γ2 210γ + 64)(a c) 4(3γ 1)(9γ 10)(9γ 4) ; qfx j = The carrer s proft and the frm s profts are 3γ(9γ 8)(a c) 2(9γ 10)(9γ 4), (4) π fx = 27γ2 (3γ 4)(9γ 8)(a c) 2 8(3γ 1)(9γ 10) 2 (9γ 4), Π fx = γ(190269γ γ γ γ γ 25600)(a c) 2 16(3γ 1) 2 (9γ 10) 2 (9γ 4) 2. (5) To ensure a postve quantty, we assume the followng throughout the analyss. 9 Assumpton 1. γ > 4/3. Floatng-prce contract. In ths contract scheme, carrer decdes ts transport prce, t, n the second stage of the game. The carrer s maxmzaton problem yelds the followng second-stage transport prce: t (x) = 1 4 (a c x j + 2x ), j. (6) From (6) and the frm s proft, the equlbrum nvestment level s Π (x) x = 1 72 (43(a c) 22x j (144γ 65)x ) = 0, j x l = 43(a c) 144γ 43. (7) The outcome n the floatng-prce contract s labeled l. From (7), we get the followng 9 As long as Assumpton 1 holds, the second-order condtons for the carrers and frms proft maxmzaton are satsfed. 7

10 outcomes: t l = q l = 36γ(a c) 144γ 43, (8) 60γ(a c) 144γ 43 ; 24γ(a c) ql j = 144γ 43, (9) π l = 864γ2 (a c) 2 (144γ 43) 2 ; Πl = γ(4176γ 1849)(a c)2 (144γ 43) 2. (10) Smultaneous move scenaro. In ths case, both transport prces and nvestments are decded n the frst-stage of the game smultaneously. Eqs. (1) and (6) yeld the followng: t s = x s = q s = 9γ(a c) 2(18γ 7), (11) 7(a c) 18γ 7, (12) 15γ(a c) 2(18γ 7) ; 3γ(a c) qs j = 18γ 7, (13) π s = 27γ2 (a c) 2 2(18γ 7) 2 ; Πs = The outcome n the smultaneous move scenaro s labeled s. From (3), (7), and (12), we obtan Lemma 1. γ(261γ 196)(a c)2 4(18γ 7) 2. (14) Lemma 1. () x fx > x s > xl. () xk / γ < 0 for all k {fx, l, s}. The logc behnd part () s as follows. In the floatng-prce contract, frms frst nvest and carrers subsequently charge transport prces. Then, f frms nvest a hgher amount, carrers set a hgher transport prce and can extract a beneft from the R&D. Hence, to keep lower transport prce, frms have an ncentve to make smaller nvestments. Accordng to ths strategc motve, the floatng-prce contract wll have the smallest nvestment among all of the schemes. By contrast, carrers frst charge transport prces 8

11 and frms subsequently nvest n the case of a fxed-prce contract. Lower transport prces enhance transport demand and, can thus rase nvestments. As found n the second-stage nvestment, x (t), a lower t ncreases x, so carrer sets a lower transport prce. The strategc motve of carrer makes the transport prce the lowest among all of the schemes. Correspondng to ths low transport prce, the nvestment level becomes the largest. On the one hand, n the smultaneous move scenaro, frms cannot drectly reduce transport prces by settng a smaller nvestment; hence, the nvestment s larger than that n the floatng-prce contract case (x s > xl ). Carrers also cannot drectly rase nvestment by settng a lower transport prce; thus, the nvestment s smaller than that n the fxed-prce contract case (x s < xfx ). Part () s ntutve. A smaller γ mproves effcency n R&D and strengthens nnovaton ncentves. The nvestment rses as γ decreases (see Fg. 1). 0.5 x k a c Γ Fgure 1: R&D nvestment Note: Black lne s k = fx; Gray lne s k = l; Dashed lne s k = s. Eqs. (2), (8), and (11) yeld Lemma 2. 9

12 Lemma 2. () t s > tl > tfx. () If γ > 2 ( )/ , t fx / γ < 0, and f γ < 2 ( )/ 3, t fx / γ > 0. t l / γ < 0 and ts / γ < 0. Part () of Lemma 2 has the followng ntutve explanaton. In the fxed-prce contract, carrers commt to lower transport prces n order to ncrease nvestment, and therefore, the prce n that scheme becomes the lowest. In the floatng-prce contract and smultaneous move scenaro, the frms nvestment level s a gven for carrers. In these schemes, f a realzed nvestment becomes larger, frms producton expands, ncentvzng carrers to set a hgher prce. As shown n Lemma 1, nvestment n the smultaneous move scenaro s larger than that n the floatng-prce contract, so the transport prce n the smultaneous move scenaro s hgher than that n the floatngprce contract. We next consder part () of Lemma 2. As n part () of Lemma 1, a smaller γ enhances nvestment ncentves. In the fxed-prce contract, carrers can rase nvestments by commttng to lower transport prces. If carrers reduce transport prces when γ s small enough, and hence frms nvestment ncentves are large enough, t s possble to further ncrease nvestments. Hence, when γ falls below a certan level, the transport prce also decreases. By contrast, n a floatng-prce contract and smultaneous move scenaro, carrers have no transport prce commtment. An ncrease n nvestment due to a lower γ promotes producton actvtes, so the transport prce ncreases as γ decreases. Fg. 2 llustrates Lemma 2. Eqs. (4), (9), and (13) yeld Lemma 3. Lemma 3. () For exports: q fx j > q s j > ql j ; for domestc supply: f γ > (

13 t k a c Γ Fgure 2: Transport prces Note: Black lne s k = fx; Gray lne s k = l; Dashed lne s k = s. 239 )/ , q s > qfx > q l and f γ < ( )/ 225, q s > ql > qfx. () Comparatve statcs of exports: qj k / γ < 0 for all k {fx, l, s}. Comparatve statcs of domestc supply: f γ < ˆγ , q fx q l / γ < 0 and qs / γ < 0. / γ > 0 and f γ > ˆγ, qfx / γ < 0. We frst consder the rankng n output. Although a lower transport prce promotes exports and mpedes domestc supply, t s > tl and qs j > ql j hold. These results depend on an nvestment rankng of x s > x l. In the floatng-prce contract, frms commt to a smaller nvestment. Ths commtment lowers the degree of the producton cost reducton, so t does not suffcently promote the whole producton, and hence leads to qj s > ql j and qs > ql. Comparng the smultaneous move scenaro wth the fxed-prce contract, q fx j > qj s and qs > qfx. Ths corresponds to the fact that the transport prce s the hghest n the smultaneous move scenaro and s the lowest n the fxed-prce contract among all schemes, t s > tl > tfx (part () of Lemma 1). Carrers commt to 11

14 a lower transport prce n the fxed-prce contract. The carrer s commtment lowers the trade barrer and promotes exports. Because competton n the domestc market becomes more ntense, domestc supply decreases. On the one hand, the smultaneous move scenaro wll have a hgher transport prce, whch mpedes exports and promotes domestc supply. From these arguments, the export rankng s q fx j domestc supply rankng s q s > ql and qs > qfx. > qj s > ql j, and the The domestc supply rankng between the fxed-prce and floatng-prce contracts and part () of Lemma 3 are explaned as follows. A smaller γ enhances frm s nnovaton ncentves and rases nvestment (part () of Lemma 1). Because a decrease n γ leads to a reducton n producton cost, a decrease n γ ncreases both domestc supply and exports. However, f γ s small, the domestc supply n the fxed-prce contract decreases as γ decreases. Ths result depends on a change n the transport prce for γ. As n part () of Lemma 2, when γ s small, the transport prce n the fxed-prce contract falls as γ decreases. A lower transport prce promotes exports, ncreases competton n the domestc market, and decreases domestc supply. Hence, q fx / γ > 0 f γ s small. Furthermore, whle a lower γ reduces the domestc supply n the fxed-prce contract, t ncreases the domestc supply n the floatng-prce contract. Therefore, f γ s small enough, the domestc supply n the fxed-prce contract can be smaller than that n the floatng-prce contract. Fg. 3 llustrates Lemma 3. Comparng (5), (10), and (14), we establsh Proposton 1. Proposton 1. () Π l > Πs > Πfx γ > γ, π s > πfx > π l.. () If γ < γ , π s > πl > πfx, and f 12

15 q k j a c q k a c Γ Γ Fgure 3: Graph of outputs (Exports on the left; domestc supply on the rght) Note: Black lne s k = fx; Gray lne s k = l; Dashed lne s k = s. Ths result mples that a better outcome for both carrers and frms can appear when carrers do not commt to a transport prce level. The rankng n frm s proft (part () of Proposton 1) nversely corresponds to the rankng n exports (see part () of Lemma 3). Ths s because, n our two-way duopoly model, the prohbtve transport prce level gves the hghest proft for frms. That s, the proft n a domestc monopoly (there s no export) s hgher than the stuaton wth aggressve exports. 10 When frms can commt to an nvestment level, t s possble for them to create a stuaton close to a domestc monopoly because they can adjust the transport prce through ther nvestment decson. Hence, the floatng-prce contract s the best scheme for frms. In contrast, the carrer s prce commtment adjusts the frm s nvestments and exports. The carrer s lower prce commtment ncreases the aggressveness of the frm s export actvtes, and t puts frms n a stuaton furthermost from a domestc monopoly. The fxed-prce contract s the worst for frms. In the smultaneous move scenaro, carrers 10 Usng the thrd-stage outcomes and condtons x j = x and t j = t, ths fact s mmedately found. 13

16 and frms have no commtment, so the proft n that scheme s ntermedate for frms. The carrer s proft rankng (part () of Proposton 1) depends on the transport prce and export volume. In the smultaneous move scenaro, the transport prce s hghest among all contract schemes and the exports are of ntermedate sze, so the proft becomes the largest among all schemes. On the one hand, profts n fxed-prce and floatng-prce contracts can be reversed accordng to the degree of γ. Ths s because, as n part () of Lemma 3, a smaller γ ncreases exports n both schemes and rases the transport prce n the floatng-prce contract, whle t can reduce the transport prce n the fxed-prce contract (see also Fg. 2). Then, a smaller γ ncreases proft n the floatng-prce contract. In contrast, a smaller γ decreases proft n the fxed-prce contract when γ s small. If γ s small enough, (.e., γ < γ ), proft n the fxed-prce contract s the worst among all contract schemes k a c Γ Π k a c Γ Fgure 4: Graph of profts (frm s proft on the left; carrer s proft on the rght) Note: Black lne s k = fx; Gray lne s k = l; Dashed lne s k = s. Welfare analyss. Here, we consder welfare n all contract schemes. Country s consumer surplus n each contract scheme s gven by CS k = (q k + qk j )2 /2, where 14

17 k {fx, l, s}. Ths yelds the followng: CS fx = 9γ2 (189γ 2 276γ + 80) 2 (a c) 2 32(9γ 4) 2 (9γ 10) 2 (3γ 1) 2 ; CSl = 3528γ2 (a c) 2 (144γ 43) 2, CS s = 441γ2 (a c) 2 8(18γ 7) 2. (15) Each country s socal surplus conssts of consumer surplus CS k, frm s proft Πk, and carrer s proft π k. The socal surplus n each contract scheme s W fx = γ(86751γ γ γ γ )(a c) 2 32(9γ 10) 2 (3γ 1) 2, (9γ 4) W l γ(8568γ 1849)(a c)2 = (144γ 43) 2 ; W s 7γ(153γ 56)(a c)2 = 8(18γ 7) 2. Eqs. (15) and (16) yeld the followng result. (16) Proposton 2. () CS fx > CS s > CS l and W k / γ < 0. and W fx > W s > W l. () CSk / γ < 0 The welfare rankng corresponds to the nvestment rankng (see part () of Lemma 1). When frms ncrease ther nvestment level, the margnal producton cost falls and producton effcences mprove, whch undoubtedly ncreases total sales and consumer surplus. Because the mprovement n consumer beneft s domnant, the socal surplus also ncreases. From the welfare pont of vew, the best scheme s the fxed-prce contract n whch nvestment s maxmzed, and the worst scheme s the floatng-prce contract n whch nvestment s mnmzed. Furthermore, a reducton n γ enhances effcences n R&D and rases nvestment, so t also ncreases welfares. 15

18 4 Dscusson We have two robustness checks on the man result (Proposton 1). We frst relax the assumpton of no R&D spllover and examne a case wth a postve spllover. Subsequently, we argue a case contanng domestc and foregn product dfferentaton. 4.1 R&D spllovers Here, we ntroduce an exogenous spllover rate of R&D, δ, n the prevous settng. Snce the developed-knowledge of the rval frm s transmtted, frm s margnal producton cost s rewrtten as c x δx j ( j). We assume that the spllover rate s not very large: 0 δ < ( )/44 ( ). We exclude the case wth a hgh spllover rate for the followng reason. In the prevous secton, R&D nvestments are strategc substtutes. However, under a rather hgh spllover rate, the nvestment decsons become strategc complements. Hence, under a hgh spllover rate, we do not have a mechansm n the prevous secton and we obtan a sgnfcantly dfferent proft rankng. Hence, we omt the case wth a hgh spllover rate. Frm s proft s Π (δ) = (a q q j (c x δx j ))q + (a q jj q j (c x δx j ) t )q j γx 2 and carrer s proft s π (δ) = t q j. We consder the same contract schemes and the same tmng of the game. The equlbrum outcomes under 16

19 the fxed-prce contract are x fx (δ) = (a c)(δ 2)[ 189γ2 + 6γ(10δ 2 43δ + 46) + 20(δ 2) 2 (δ 2 1)] (9γ + 2δ 2 2δ 4)[108γ 2 39γ(δ 2) 2 10(δ 2) 2 (δ 2, 1)] q fx (δ) = 3γ(a c)[135γ2 3γ(16δ 2 67δ + 70) 16(δ 2) 2 (δ 2 1)] (9γ + 2δ 2 2δ 4)[108γ 2 39γ(δ 2) 2 10(δ 2) 2 (δ 2 1)], q fx j (δ) = 3γ(a c)[54γ2 3γ(4δ 2 19δ + 22) 4(δ 2) 2 (δ 2 1)] (9γ + 2δ 2 2δ 4)[108γ 2 39γ(δ 2) 2 10(δ 2) 2 (δ 2 1)], t fx (δ) = 9γ(a c)(3γ 2δ 2 + 6δ 4) 108γ 2 39γ(δ 2) 2 10(δ 2) 2 (δ 2 1), Π fx (δ) = [q fx (δ)]2 + [q fx j (δ)]2 γ[x fx (δ)] 2 ; π fx (δ) = t fx (δ)q fx j (δ). The equlbrum outcomes under the floatng-prce contract are x l (δ) = q l j(δ) = (a c)(43 14δ) 144γ + 14δ 2 29δ 43 ; ql (δ) = 24γ(a c) 144γ + 14δ 2 29δ 43 ; tl (δ) = 60γ(a c) 144γ + 14δ 2 29δ 43, 36γ(a c) 144γ + 14δ 2 29δ 43, Π l (δ) = [q l (δ)] 2 + [q l j(δ)] 2 γ[x l (δ)] 2 ; π l (δ) = t l (δ)q l j(δ). The equlbrum outcomes under the smultaneous move scenaro are x s (δ) = q s j(δ) = 7(a c)(2 δ) 36γ + 7 (δ 2 δ 2) ; qs (δ) = 6γ(a c) 36γ + 7 (δ 2 δ 2) ; ts (δ) = 15γ(a c) 36γ + 7 (δ 2 δ 2), 9γ(a c) 36γ + 7 (δ 2 δ 2), Π s (δ) = [q s (δ)] 2 + [q s j(δ)] 2 γ[x s (δ)] 2 ; π s (δ) = t s (δ)q s j(δ). Now, we can check the robustness of Proposton 1. Under our assumptons, 0 δ < ( )/44 and γ > 4/3, we compare equlbrum proft. By numercal calculaton, we have Π l (δ) > Πs change. (δ) > Πfx (δ). Thus, part () of Proposton 1 does not We next consder the proft rankng of carrer. Numercal calculaton yelds Fg. 17

20 5. In the lower left area, we have π s(δ) > πl (δ) > πfx (δ); n the other area, we obtan π s (δ) > πfx (δ) > π l (δ). Hence, part () of Proposton 1 does not change f the spllover rate s small. On the other hand, a hgh spllover rate yelds only the proft rankng π s (δ) > πfx (δ) > π l(δ). 2.0 γ π s (δ) > πfx (δ) > π l(δ) π s(δ) > πl (δ) > πfx (δ) δ Fgure 5: Proft rankng for carrer wth spllover Our results change for the followng reason. Under a postve spllover rate, an ncrease n R&D nvestment reduces the rval frm s margnal cost. Then, frms have a small ncentve to nvest. Ths case s smlar to that wth neffcent nvestment technology (.e., large γ). In other words, the effect of an ncrease n δ s smlar that of an ncrease n γ. In our model, the nvestment level plays an mportant role so we therefore obtan Fg

21 4.2 Dfferentated products We consder the effects of product dfferentaton here. To exclude the effect of market expanson by product dfferentaton (Sngh and Vves, 1984), we employ the Shubk (1980)-type utlty functon: 11 ( u = a (q + q j ) (1 β) ( ) q 2 + qj 2 ) β + 2 (q + q j ) 2, j. β [0, 1] s nterpreted as the degree of product dfferentaton. That s, products are homogeneous at β = 1 and are ndependent at β = 0. Moreover, under ths utlty functon, the aggregate demand n country H or F, q + q j, does not depend on the degree of product dfferentaton. In partcular, we have q + q j = a (p + p j )/2. Hence, we can exclude the market expanson effect. Solvng the utlty maxmzaton problem, we have the nverse demand p = a (2 β)q βq j and p j = a (2 β)q j βq jj. Then, frm s proft s Π (β) = (a (2 β)q βq j (c x ))q + (a (2 β)q j βq jj (c x ) t )q j γx 2 and carrer s proft s π (β) = t q j. We consder the same contract schemes and the same tmng of the game. The equlbrum outcomes under the fxed-prce contract are x fx (β) = (a c)(2 β)φ 3 2Φ 1 Φ 2 ; q fx (β) = (a c)(16 16β + 3β2 )Φ 4 4(2 β)φ 1 Φ 2, q fx j (β) = (a c)(16 16β + 3β 2 )γφ 5 2Φ 1 [9β 4 γ + β 3 (6 96γ) + 8β 2 ( γ)β(88 512γ) + 64( 1 + 4γ)], t fx (β) = (a c)(16 16β + 3β2 ) 2 γφ 6 4(2 β)φ 2, Π fx (β) = (2 β) ( [q fx (β)]2 + [q fx j (β)]2) γ[x fx (β)] 2 ; π fx (β) = t fx (β)q fx j (β), 11 Our qualtatve results do not change when usng the utlty functon proposed by Sngh and Vves (1984). 19

22 where we defne Φ m (m = 1,..., 6) as n the appendx. The equlbrum outcomes under the floatng-prce contract are x l (β) = (a c)( β+200β2 29β 3 ) Ψ 1 ; q l (β) = 4(a c)(8 3β)(16 16β+3β2 )γ Ψ 1, qj(β) l = 8(a c)(2 β)(16 16β + 3β2 )γ ; t l Ψ (β) = 4(a c)(16 16β + 3β2 ) 2 γ, 1 Ψ 1 ( Π l (β) = (2 β) [q(β)] l 2 + [qj(β)] l 2) γ[x l (β)] 2 ; π(β) l = t l (β)qj(β), l where Ψ 1 48β 4 γ + β 3 (29 544γ) + 8β 2 (272γ 25) 448β(8γ 1) + 64(32γ 5). The equlbrum outcomes under the smultaneous move scenaro are x s (β) = (a c)(2 β)(12 5β) Ψ 2 ; q s (β) = (a c)(8 3β)(16 16β + 3β2 )γ 2(2 β)ψ 2, qj(β) s = (a c)(16 16β + 3β2 )γ ; t s (β) = (a c)(4 3β)2 ( 4 + β) 2 γ, Ψ 2 2(2 β)ψ 2 ( Π s (β) = (2 β) [q(β)] s 2 + [qj(β)] s 2) γ[x s (β)] 2 ; π s (β) = t s (β)qj(β), s where Ψ 2 6β 3 γ + β 2 (56γ 5) + β(22 160γ) + 8(16γ 3). Here, we consder the robustness of Proposton 1. Under our assumptons, 0 β 1 and γ > 4/3, we compare equlbrum proft. By numercal calculaton, we depct the proft rankng of frm n Fg. 6. On the rght, we fnd Π l (β) > Πs (β) > Πfx (β); n the mddle, we have Π l (β) > Πfx (β) > Π s (β); and on the left, we obtan Πfx (β) > Π l(β) > Πs (β). That s, n the case wth hgher product dfferentaton, the frms wth fxed-prce contracts earn larger profts. The reason s as follows. When products are hghly dfferentated, compettons between frms become less mportant. Then, the frms profts depend on vertcal relatonshps between the frms and carrers. Hence, a commtment toward aggressve 20

23 γ 10 Π fx (β) > Π l (β) > Πs (β) Π l (β) > Πs (β) > Πfx (β) β Π l (β) > Πfx (β) > Π s (β) Fgure 6: Proft rankng for frm wth product dfferentaton nvestment wll ncrease proft n a channel. Therefore, product dfferentaton brngs hgher profts to the frms. Next, we consder the proft rankng of carrer. Fg. 7 depcts the numercal calculaton. In the lower rght area, we have π s (β) > πl we fnd π s (β) > πfx (β); n the mddle, (β) > πfx (β) > π l (β); and on the left, we obtan πfx (β) > π s(β) > πl (β). Hence, under hgher product dfferentaton, carrers prefer fxed-prce contracts. The ntuton behnd ths result s smlar as n the case of frms. 21

24 γ 3.0 π fx (β) > π s(β) > πl (β) π s (β) > πfx (β) > π l(β) β π s(β) > πl (β) > πfx (β) Fgure 7: Proft rankng for carrer wth product dfferentaton 5 Concluson In a vertcal producton relatonshp, upstream tradng frms lkely hold up downstream R&D nvestment. If these upstream frms set a hgher nput prce after observng downstream nvestment, then they can extract the downstream R&D beneft, and such opportunstc behavor reduces downstream nnovaton ncentves. The prevous lterature emphaszes that a fxed-prce contract for the nput prce s requred to overcome ths hold-up problem. In the fxed-prce contract, upstream frms commt to an nput prce level and downstream frms subsequently nvest n cost-reducng R&D. By employng the fxed-prce contract, upstream frms set a lower nput prce to promote downstream 22

25 nvestment. Snce ths lower-prce commtment ncreases outputs and demand for nputs through nvestment expanson, all frms become better off. In contrast to ths standard theory, we show that the fxed-prce contract can harm all frms. We consder a two-country, two-way trade model wth two frm-specfc carrers upstream, and two exporters downstream. Each country has a carrer and an exportng frm. Whle each country s exportng frm freely supples to the domestc market, t uses a local carrer to export ts product. Each carrer charges a transport prce and conveys ts domestc exportng frm s product. In ths settng, exporters can create a stuaton close to a domestc monopoly when the transport prce s hgh enough. Although the domestc monopoly s most proftable for exporters, the fxed-prce contract lowers the transport prce and encourages frms to nvest and export aggressvely, creatng a market furthest from a domestc monopoly. Ths makes exporters worse off. Furthermore, f R&D effcency s hgh enough, carrers set consderably low transport prces n the fxed-prce contract. Ths also makes carrers worse off. Moreover, we examne the robustness of the man result n two dfferent stuatons: a case wth postve R&D spllover and a case wth product dfferentaton. We fnd that n these extended cases, our man result holds. Ths study shows that a fxed-prce transportaton contract can harm all frms n both upstream and downstream markets when downstream (exportng) frms engage n cost-reducng R&D. Therefore, t would be nterestng to nvestgate other forms of R&D, such as product nnovaton and product qualty mprovement to determne whether our result holds. However, ths ssue s beyond the scope of ths study, and we 23

26 thus leave t to future research. Acknowledgments We thank Norak Matsushma for hs helpful comments. Any remanng errors are our own. Appendx Proof of Lemma 1. () Comparng nvestments, we get x fx x s = 9γ(15γ 8)(a c) 2(3γ 1)(9γ 10)(9γ 4)(18γ 7) > 0; xs x l = () Dfferentatng (3), (7), and (12) w.r.t. γ, we obtan 234γ(a c) (18γ 7)(144γ 43) > 0. x fx γ = 27(1701γ4 4968γ γ γ + 320)(a c) 2(9γ 4) 2 (9γ 10) 2 (3γ 1) 2 < 0, x l γ 6192(a c) = (144γ 43) 2 < 0; x s γ 126(a c) = < 0. Q.E.D. (18γ 7) 2 Proof of Lemma 2. () Comparng transport prces, we get t s t l = 117γ(a c) 2(18γ 7)(144γ 43) > 0; tl t fx = () Dfferentatng (2), (8), and (11) w.r.t. γ, we have 27γ(27γ 4)(a c) 4(3γ 1)(9γ 10)(144γ 43) > 0. t s γ = 1548(a c) (144γ 43) 2 < 0; t l γ = 63(a c) 2(18γ 7) 2 < 0; t fx γ = 9(9γ2 60γ+40)(a c) 4(9γ 10) 2 (3γ 1) 2. From the last equaton, t fx / γ < ( ) 0 f γ > ( ) 2 ( ) / Q.E.D. Proof of Lemma 3. () Comparng exports, we get q fx j qs j = 9γ(15γ 8)(a c) 2(9γ 10)(9γ 4)(18γ 7) > 0; qs j q l j = 39γ(a c) (18γ 7)(144γ 43) > 0. 24

27 Comparng domestc supples, we have From q fx q s q l = 195γ(a c) 2(18γ 7)(144γ 43) > 0; qs q fx = q fx q l = 3γ(675γ2 1434γ+448)(a c) 4(3γ 1)(9γ 10)(9γ 4)(144γ 43). 9γ(3γ 2)(15γ 8)(a c) 4(3γ 1)(9γ 10)(9γ 4)(18γ 7) > 0, q l, solvng 675γ2 1434γ w.r.t. γ, we have q fx < ( ) q l f γ < ( ) ( )/ () From (4), (9), and (13), we get q l j γ 1032(a c) = (144γ 43) 2 < 0; qj s γ fx j 21(a c) = (18γ 7) 2 < 0; q γ = 3(243γ2 360γ+160)(a c) (9γ 4) 2 (9γ 10) 2 < 0, q l γ = 2580(a c) (144γ 43) 2 < 0; q fx γ q s γ = 105(a c) 2(18γ 7) 2 < 0, = 3(10935γ γ γ γ+2560)(a c) 4(3γ 1) 2 (9γ 10) 2 (9γ 4) 2. From the last equaton, q fx / γ > ( ) 0 f γ < ( ) ˆγ Q.E.D. Proof of Proposton 1. () Comparng the frm s profts, we get Π l Π s = 117γ2 (5904γ 1945)(a c) 2 4(18γ 7) 2 (144γ 43) 2 > 0, Π s Π fx = 9γ2 (15γ 8)(8748γ γ 3 864γ γ 1024)(a c) 2 16(3γ 1) 2 (9γ 10) 2 (9γ 4) 2 (18γ 7) 2 > 0. () Comparng the carrer s profts, we have π s π l = 3159γ2 (32γ 11)(a c) 2 2(18γ 7) 2 (144γ 43) 2 > 0, π s π fx = 27γ2 (15γ 8)(27γ 4)(a c) 2 8(3γ 1)(9γ 10) 2 (9γ 4)(18γ 7) 2 > 0, and π fx π l = 27γ2 (101088γ γ γ 43232)(a c) 2. From the last equaton, we 8(3γ 1)(9γ 10) 2 (9γ 4)(144γ 43) 2 fnd that π fx π l (>) 0 f γ (>) γ These mply Proposton 1. Q.E.D. Proof of Proposton 2. () From (15), we have CS fx CS s = 81γ3 (15γ 8)(6804γ γ γ 1120)(a c) 2 32(3γ 1) 2 (9γ 10) 2 (9γ 4) 2 (18γ 7) 2 > 0 25

28 and CS s CSl = 51597γ2 (32γ 11)(a c) 2 8(18γ 7) 2 (144γ 43) 2 W fx > 0. From (16), we have W s = 9γ2 (15γ 8)(4860γ γ γ 560)(a c) 2 32(3γ 1) 2 (9γ 10) 2 (9γ 4)(18γ 7) 2 > 0 and W s W l = 117γ2 (5760γ 2149)(a c) 2 8(18γ 7) 2 (144γ 43) 2 > 0. () Dfferentatng eqs. (15) amd (16) w.r.t. γ, we get CS fx γ = 9γ(189γ2 276γ+80)(19683γ γ γ γ+3200)(a c) 2 16(3γ 1) 3 (9γ 10) 3 (9γ 4) 3 < 0, CS l γ W fx γ W l γ Q.E.D. c)2 CS s 3087γ(a c)2 = γ(a (144γ 43) 3 < 0, = γ 4(18γ 7) 3 < 0, ( ) γ γ γ γ 3 (a c) γ γ = 16(9γ 4) 2 (3γ 1) 3 (9γ 10) 3 < 0, = 43(10944γ 1849)(a c)2 (144γ 43) 3 < 0, and W s γ = 49(81γ 28)(a c)2 4(18γ 7) 3 < 0. Defnton of Φ m. We defne Φ m (m = 1,..., 6) as follows: Φ 1 3β 3 γ +β 2 (4 28γ)+ 16β(5γ 1) 64γ +16, Φ 2 27β 6 γ 2 +27β 5 (1 16γ)γ +6β 4 (1 55γ +456γ 2 ) 4β 3 (13 386γ +2176γ 2 )+24β 2 (7 144γ +608γ 2 ) 16β(15 232γ +768γ 2 )+128(1 12γ +32γ 2 ), Φ 3 135β 7 γ 2 36β 6 γ(69γ 5) + 48β 5 (1 53γ + 393γ 2 ) 16β 4 (32 909γ γ 2 ) + 128β 3 (17 337γ+1386γ 2 ) 512β 2 (9 137γ+462γ 2 )+256β(19 232γ+656γ 2 ) 2048(1 10γ +24γ 2 ), Φ 4 81β 7 γ 2 6β 6 γ(252γ 19)+8β 5 (4 205γ +1458γ 2 ) 8β 4 ( γ γ 2 )+128β 3 (12 225γ+886γ 2 ) 256β 2 (13 186γ+600γ 2 )+512β(7 80γ+216γ 2 ) 512(3 28γ+64γ 2 ), Φ 5 9β 4 γ β 3 (8 96γ) 16β 2 (22γ 3) β(96 512γ) 64(4γ 1), and Φ 6 9β 3 γ β 2 (4 60γ) 16β(7γ 1) + 64γ

29 References [1] Abe, K., Hattor, K. and Kawagosh, Y. (2014). Trade lberalzaton and envronmental regulaton on nternatonal transportaton, Japanese Economc Revew, vol. 65, pp [2] Aghon, P., Bloom, N., Blundell, R., Grffth, R. and Howtt, P. (2005). Competton and nnovaton: an nverted-u relatonshp, Quarterly Journal of Economcs, vol. 120(2), pp [3] Aghon, P., Howtt, P., Blundell, R., Prantl, S. and Grffth, R. (2004). Entry and productvty growth: evdence from mcrolevel panel data, Journal of the European Economc Assocaton, vol. 2(2-3), pp [4] Anderson, J.E. and Van Wncoop, E. (2004). Trade costs, Journal of Economc Lterature, vol. 42(3), pp [5] Banerjee, S. and Ln, P. (2003). Downstream R&D, rasng rval s cost, and nput prce contracts, Internatonal Journal of Industral Organzaton, vol. 21(1), pp [6] Behrens, K., Gagné, C. and Thsse, J.-F. (2009). Industry locaton and welfare when transport costs are endogenous, Journal of Urban Economcs, vol. 65, pp [7] Brander, J.A. and Krugman, P.R. (1983). A recprocal dumpng model of nternatonal trade, Journal of Internatonal Economcs, vol. 15, pp

30 [8] d Aprémont, C. and Jacquemn, A. (1988). Cooperatve and noncooperatve R&D n duopoly wth spllovers, Amercan Economc Revew, vol. 78, pp [9] Francos, J.F. and Wooton, I. (2001). Trade n nternatonal transport servces: the role of competton, Revew of Internatonal Economcs, vol. 9, pp [10] Ghosh, A. and Lm, J. (2013). Cooperatve and non-cooperatve R&D and trade costs, Journal of Internatonal Trade & Economc Development, vol. 22(6), pp [11] Glbert, S.M. and Cvsa, V. (2003). Strategc commtment to prce to stmulate downstream nnovaton n a supply chan, European Journal of Operatonal Research, vol. 150, pp [12] Haaland, J.I. and Knd, H.J. (2008). R&D polces, trade and process nnovaton, Journal of Internatonal Economcs, vol. 74, pp [13] Hummels, D., Lugovskyy, V. and Skba, A. (2009). The trade reducng effects of market power n nternatonal shppng, Journal of Development Economcs, vol. 89(1), pp [14] Ishkawa, J. and Taru, N. (2015). Backfrng wth backhaul problem: trade and ndustral polces wth endogenous transport costs, Dscusson Paper, HIAS-E-12. [15] Kesavayuth, D. and Zkos, V. (2009). Endogenous contracts n unonzed olgopoly, LABOUR, vol. 23, pp

31 [16] Long, N.V., Raff, H. and Stähler, F. (2011). Innovaton and trade wth heterogeneous frms, Journal of Internatonal Economcs, vol. 84, pp [17] Matsushma, N. and Takauch, K. (2014). Port prvatzaton n an nternatonal olgopoly, Transportaton Research Part B: Methodologcal, vol. 67, pp [18] Shubk, M. wth Levtan, R. (1980). Market Structure and Behavor. Harvard Unversty Press, Cambrdge, MA. [19] Sngh, N. and Vves, X. (1984). Prce and quantty competton n a dfferentated duopoly, RAND Journal of Economcs, vol. 15, pp [20] Takauch, K. (2015a). Endogenous transport prce and nternatonal R&D rvalry, Economc Modellng, vol. 46, pp [21] Takauch, K. (2015b). Transport effcency, downstream R&D, and spllovers, MPRA Paper No [22] Zkos, V. and Kesavayuth, D. (2010). Downstream R&D, rasng rval s costs, and nput-prce contracts: a comment on the role of spllovers, Economcs Bulletn, vol. 30(4), pp