Parallel Imports, Product Innovation and Market Structures

Transcription

1 Parallel Imports, Product Innovaton and Market Structures Hong Hwang a, Cheng-Hau Peng b, *, Pe-Cyuan Shh c a Department of Economcs, Natonal Tawan Unversty, 10055, Tawan and RCHSS, Academa Snca, 11529, Tawan b Department of Economcs, Fu Jen Catholc Unversty, 24205, Tawan c Department of Economcs, Natonal Tawan Unversty, 10055, Tawan (Ths verson: June 20, 2014) Abstract Ths paper sets up a two-country model n whch there s one domestc manufacturer authorzng ts product to a dstrbutor n foregn country to nvestgate the effect of parallel mports (PI) on product nnovaton of the former. The dstrbutor can sell the product not only to ts own market (.e., the foregn market) but also back to the domestc market f parallel mports are allowed by the domestc government. We fnd that f the manufacturer adopts a two-part tarff prcng scheme when sellng ts output to the foregn dstrbutor, permttng PI necessarly decreases the manufacturer s product nnovaton. Ths result however s very senstve to market structures. If the domestc market becomes duopolstc or olgopolstc, the above result s defntely reversed PI has a postve effect on the manufacturer s product nnovaton. Fnally, f there are more than one dstrbutor n the foregn market, parallel mports may ncrease or decrease product nnovaton dependng on the consumers qualty valuatons n the two countres. JEL classfcaton: F12, F13, L11, L13 Keywords: Parallel mports, Product nnovaton, Two-part tarff prcng, Market structure * Correspondng author at: Department of Economcs, Fu Jen Catholc Unversty, No. 510, Zhongzheng Rd., Xnzhuang Dst., New Tape Cty 24205, Tawan. Tel: ; fa: E-mal addresses: echong@ntu.edu.tw (H. Hwang), chpon@fju.edu.tw (C.H. Peng), f @ntu.edu.tw (P. C. Shh).

2 Parallel Imports, Product Innovaton and Market Structures 1. Introducton Parallel mport (PI) occurs when a genune product s sold back by lcensed foregn dstrbuters wthout the permsson of the domestc ntellectual property owner who, we call t the manufacturer hereafter, also serves the domestc market. PI has been popular and observed n many products snce 1980s. For eample, the value of PI n the US rose from 7 10 bllon USD n the md-1980s to 20 bllon USD n the 1990s (Cespedes et al. (1988); Computer Reseller News (2001)). The US s not the only country encounterng PI. Accordng to the House of Commons report (1999), the volume of PI n the UK s motorcycle market was around 25% of the sales n EU also suffers appromate $3 bllon sales per year owng to the occurrence of PI (Ganslandt and Maskus (2004)). Furthermore, accordng to the Frst Sale Doctrne of U.S. copyrght law, t was llegal to mport or resell the Amercan copyrght tems. However, not untl recently, the Supreme Court of the Unted States voted for the rule that tetbooks and other goods made and sold abroad can be re-sold onlne and n dscount stores wthout volatng U.S. copyrght law. 2 It means that the Frst Sale Doctrne s not applcable to PI and U.S.-made tems such as tetbooks, CDs, computer software purchased from foregn markets can be brought back to U.S. for resale. Besdes, there are numerous Amercan-made cars sold back from Canada and Meco every year. PI s also legal n other countres such as Australa, Chna, Japan, New Zealand, Sngapore, and Tawan. PI has attracted substantal attenton and been nvestgated etensvely n the lterature. The man focus along ths strand of research s on optmal PI polces (see, 1 Please refer to the followng webste for detals: 2 Please refer to the followng webste for detals: 1

3 for eample, Maskus and Chen (2004); Chen and Maskus (2005); Kao and Peng (2009); Mueller Langer (2012); Mukherjee and Zhao (2012), among others). Maskus and Chen (2004) utlze a two-country and two-frm Cournot model wth a lnear demand to nvestgate the optmal quanttatve control of PI for an mport country. They show that restrctng parallel trade has an ambguous welfare effect, dependng on the trade cost of PI. Chen and Maskus (2005) reach a smlar result wth a general demand functon. Mueller Langer (2012) etends Maskus and Chen (2004) by assumng that products are heterogeneous and the manufacturer adopts one-part tarff prcng. He shows that permttng PI has a postve effect on the global welfare f the dfference of the market szes between the two countres s large and trade costs are low. Furthermore, Mukherjee and Zhao (2012) fnd that PI s proftable for the manufacturer f there s a labor unon n the domestc country. Kao and Peng (2009) construct a three-country model to dscuss the optmal quanttatve regulaton for PI. They show that f the manufacturer engages n prce dscrmnaton, the optmal PI polcy s that of partal regulaton and PI may decrease the global welfare f the manufacturer adopts two-part tarff prcng. Another strand of the lterature on PI shows that ts effect on the manufacturer s process nnovaton depends on the trade cost (L and Maskus (2006); L and Robles (2007)) or the degree of the horzontal product dfferentaton (L and Robles (2007)). Nevertheless, emprcal evdences have shown that process R&D can only represent a mnor part of the realty. 3 The effect of PI on product nnovaton remans an mportant ssue to be further addressed n the lterature. Matteucc and Reverber (2014) fnd that PI may stmulate the manufacturer s product nnovaton, dependng 3 For eample, Cohen et al. (1997) show that 51.5% of the nnovatons n the Amercan manufacturng sector between 1991 and 1993 are those of product nnovatons and only 33% are of process nnovatons. Arundel and Kabla (1998) also fnd that the percentage of nnovatons s made for product nnovatons s 35.9%, and t s 24.8% for process nnovatons n Europe s ndustral frms. 2

4 on consumers preferences for nnovaton between the two countres. Our paper complements the lterature n several ways. Frst, we consder the effect of PI on the manufacturer s product nnovaton by assumng the domestc manufacturer sells ts product to the foregn dstrbutor va two-part tarff prcng. Second, we eplore the effect of local rvals n the domestc market, whch s commonly observed n the real world but has been overlooked n ths lne of research. Thrd, we consder the case n whch the manufacturer has multple dstrbutors n the foregn market. It s found that permttng PI necessarly decreases the manufacturer s product R&D ncentve f the domestc market s monopolzed by the manufacturer. However, PI necessarly stmulates product nnovaton of the manufacturer f t faces local rvals. In addton, If the manufacturer can authorze ts product to multple foregn dstrbutors, t s found that the ncentve of product nnovaton can be ether postvely or negatvely affected by PI, dependng on consumers preferences for nnovaton n the domestc and the foregn markets. The remnder of ths paper s organzed as follows. Secton 2 ntroduces the basc model and eamnes the optmal product nnovaton wth no PI. Secton 3 nvestgates the effect of PI on the manufacturer s product nnovaton. Secton 4 eplores the product nnovaton of the manufacturer when t faces domestc rvals or authorzes ts product to multple dstrbutors. Secton 5 concludes the paper. 2. Product Innovaton wth no Parallel Imports Assume that there are two countres, a home country and a foregn country, hostng one frm each. A manufacturer, located n the home country, sells unts of ts product to ts own (.e., the home) market. The manufacturer also sells ts product to the foregn market va an authorzed foregn dstrbutor. The dstrbutor may engage n 3

5 parallel trade, sellng y to the foregn market and back to the home market, f the home government adopts the nternatonal ehauston rule (.e., allowng parallel trade). Contrarly, PI does not occur and 0 f the home government endorses the natonal ehauston rule. When producng the product, the manufacturer ncurs a constant margnal cost, c. Trade costs and retalng costs are assumed to be zero for smplfcaton. 4 The manufacturer charges two-part tarff prcng (.e., a fed fee, T plus a wholesale prce, w), when sellng the product to the foregn dstrbutor. Furthermore, the manufacturer engages n product nnovaton and ts R&D cost functon s specfed as V( ) wth V 0 and V 0. The nverse demand functons of the home and the foregn markets are assumed to be * p p, and p p y, wth p p * 0, p 0, p 0, * y * p 0 and the second dervatves of the demands are assumed to be zero. Subscrpts are used to denote dervatves. The game n queston conssts of three stages. In the frst stage, the manufacturer determnes ts optmal product nnovaton level. In the second stage, takng the product qualty as gven, the manufacturer chooses ts optmal prcng contract ( w plus T ) and offers t to the foregn dstrbutor. In the thrd stage, the manufacturer and the foregn dstrbutor determne ther optmal sales n the two markets wth or wth no PI. The sub-game perfect Nash equlbrum wll be solved va backward nducton. In ths secton, we shall nvestgate the case under natonal ehauston (.e., the no PI regme) and then, n Secton 3, eamne the nternatonal ehauston case (.e., the PI regme). Under the natonal ehauston regme, the foregn dstrbutor s not allowed to resell the product back to the home market. Under such a crcumstance, the home and the foregn markets are monopolzed respectvely by the manufacturer and the foregn dstrbutor. Accordngly, the proft functons of the manufacturer and the foregn dstrbuter can be respectvely epressed as follows: ( wt ;,, ) p, c ( wcy ) TV( ), (1) ( y ; wt,, ) ( p w) y T. (2) By dfferentatng (1) wth respect to and (2) respect to y, we can derve the 4 Ths s for mathematcal smplcty and does not change the qualtatve results of the paper. 4

6 frst-order condtons for the thrd stage of the game as follows: pc p 0, (3) p w p y (4) y * y* 0. The second-order and the stablty condtons are all satsfed gven the assumpton of lnear demands and constant margnal cost. Thus, we can derve the equlbrum outputs of the two frms as follows: ( c ) and y *( w ). By (3) and (4), we can further derve the comparatve statc effects as follows: p 2p 0, y p 2p 0, and y 1 2p 0. (5) * * y* w y* The above results show that an ncrease n product nnovaton rases the sales of the home and the foregn markets whereas ncreasng the wholesale prce w lowers the sales of the foregn dstrbutor to the foregn market. By substtutng the equlbrum outputs from the thrd stage nto (1), we can rewrte the proft functon of the manufacturer for the second-stage game as follows: Ma ( y, ( w), wt, ; ) ( pc ) ( wcy ) ( w) T V( ), (6) w Followng the lterature, we assume that the manufacturer can etract the entre proft from the foregn dstrbutor under two-part tarff prcng. Thus, the optmal fed fee charged by the manufacturer s defned as T ( p ( y ( w)) w) y ( w). By substtutng T nto (6) and then dfferentatng t wth respect to w, we can derve the frst-order condton for proft mamzaton of the manufacturer n the second stage as follows: d y T ( wc) yw 0. (7) dw y w w T w By solvng (7), we derve the optmal wholesale prce wth no PI as w c. By substtutng w nto T, we can further derve the optmal fed fee as T* ( p ( y ( c)) c) y ( c). Ths result mples that f the manufacturer adopts two-part tarff prcng, t wll set the wholesale prce at ts margnal cost and etract the monopoly rent from the foregn dstrbutor va the fed fee. Furthermore, product nnovaton has no effect on the wholesale prce as w 0 by (7). Gven the above results, we can establsh the frst proposton as follows. Proposton 1. If the manufacturer adopts two-part tarff prcng and parallel trade 5

7 s prohbted, product nnovaton has no effect on the wholesale prce. The above result dffers from those n L and Maskus (2006) and Matteucc and Reverber (2014). The former assumes that the manufacturer adopts two-part tarff prcng, and shows that process nnovaton decreases the wholesale prce whle the latter assumes that the manufacturer employs one-part tarff prcng and fnds that product nnovaton ncreases the wholesale prce. Makng use of the results n the prevous two stages, the proft functon of the manufacturer n the frst-stage game can be epressed as follows: Ma ( ( ), y ( ), T( ), ) ( p( ( ), ) c) ( ) T( y ( ), ) V( ). (8) By dfferentatng (8) wth respect to and usng the envelope theorem, we can derve the frst-order condton for proft mamzaton as follows: d dt py p V 0. (9) d T d * * * * where dt d ( T y )( y ) ( T ) p y. From (9), we can derve the optmal product nnovaton level regme. We shall compare followng secton. N N under the no PI wth that under the PI regme to be eamned n the 3. Product Innovaton wth Parallel Imports Under the PI regme, the foregn dstrbutor can engage n PI f t s proftable. All the assumptons and model settngs are the same as those n the prevous secton, ecept that the foregn dstrbutor now sells part of the goods acqured from the manufacturer back to the home market and competes wth the manufacturer n Cournot fashon. Thus, the proft functons for the manufacturer and the foregn dstrbutor can be respectvely wrtten as follows: (,, y ; wt,, ) p, c ( w c ) y TV ( ), (,, y ; w, T, ) p Q, w p y, w y T, (11) where * as defned before s the goods sold back to the home market by the foregn dstrbutor. By dfferentatng (10) wth respect to and (11) wth respect to 6 (10)

8 * and y *, we can derve the frst-order condtons for proft mamzaton as follows: pc p 0, (12) pw p* 0. (13) p w p y (14) y * y* 0. The three equatons can be dvded nto two segments. By solvng (12) and (13), we can derve the equlbrum outputs and prce of the home market whle by solvng (13) alone, we can derve the counterparts of the foregn market. The second-order and the stablty condtons are all satsfed as 2p * 0, 2p 0, and 0, gven the lnear demand and constant margnal cost assumptons. From the above frst-order condtons, we can derve the comparatve statc effects as follows: * y* p 3p 0, p 3p 0, and y p 2p 0. (15) 1 3p 0, 2 3p 0, and y 1 2 p 0. (16) * w w w y* The ntuton for the above results s qute straghtforward. Each frm s equlbrum output ncreases wth product nnovaton and ts rval s margnal cost (.e., the wholesale prce) but decreases wth ts own margnal cost. By substtutng the equlbrum nto (10), the proft functon of the manufacturer for the second-stage game can be epressed as follows: Ma ( w ( ), ( w), y( w), wt, ; ) w ( pqw ( ( )) cw ) ( ) ( wc) ( w) y( w) TV ( ). (17) By dfferentatng (17) wth respect to w and applyng the envelope theorem, we can derve the frst-order condton for proft mamzaton of the manufacturer as follows: d y dt dw w y w w T dw p w ( wc) yw w p w 0. (18) The second-order condton s satsfed as y 2p 0. ww w w w w 7

9 By utlzng (16), we can derve from (18) that w p c, * ( ) 2 (2 ) 5 whch s necessarly greater than the margnal cost of the manufacturer as *. By substtutng w( ) nto T, we can derve that the optmal fee as T T( ). By totally dfferentatng (18), we can derve the comparatve statc effect as follows: 0, where p 9p 0. Ths result stands n lne w w ww w wth the fndng n Matteucc and Reverber (2014) but runs aganst that n L and Maskus (2006). It mples that the wholesale prce defntely ncreases wth product nnovaton under the PI regme. Ths result s also n sharp contrast to the one derved under the no PI regme. If there s no PI, the wholesale prce as we concluded n Proposton 1 s always set at the margnal cost of the manufacturer and s not affected by product nnovaton. Contrarly, the wholesale prce necessarly ncreases wth product nnovaton f PI s allowed. Ths s because product nnovaton shfts the demands outwards, ncreasng the volume of PI. Ths hurts the profts of the manufacturer from the home market, gvng the manufacturer an ncentve to rase the wholesale prce to mtgate PI from the foregn dstrbutor. Gven the above dscussons, we can construct the proposton as follows. Proposton 2. If the manufacturer adopts two-part tarff prcng and parallel mports are permtted, the wholesale prce s necessarly hgher than ts margnal cost and s postvely related to the product nnovaton level. We can now move to the frst-stage of the game to solve the optmal nnovaton level of the manufacturer. The proft functon of the manufacture frm s defned as follows: Ma ( ( w( ), ), ( w( ), ), y ( w( ), ), w( ), T( w( ), ), ; t) 8

10 * p ( ) c w( ) c y T( ) V( ). (19) By dfferentatng the above equaton wth respect to, applyng the envelope theorem and utlzng (15), (16) and w w ww, we can derve the frst-order condton for proft mamzaton as follows: d w y T T d w y T T ( wc) y p p p y p V ( wc) 2( ) ( wc) p p y V 0 * 3p 3. (20) 2p y* The second-order condton for the proft mamzaton requres that 2 ** p 2p w 9p p 2p V 0 whch s assumed to be satsfed. From y (20), we can derve the optmal nnovaton under the PI regme. We now compare the product nnovaton levels under the two regmes. By evaluatng (20) at the product nnovaton level derved under the no-pi regme (.e., (9)), we obtan: d ( wc) 2( ) N ( wc) N p p y y * d N 3p 3 2py* (21) If we further assume that the nverse demand functons of the home and the foregn markets take respectvely the followng lnear forms as p a( ) b( ) and p a ( ) b y, we can derve that d p a( ) c0. d N 2(4b 9 b) It shows that PI defntely decreases the product nnovaton of the manufacturer. The ntuton of ths result s as follows. The manufacturer s capable of makng monopoly rent from both markets f there s no PI. Ths s the frst-best soluton from the vewpont of the manufacturer. Wth PI, two effects take place. Frst, the domestc 9

11 market becomes duopolstc. Second, n order to lower the competton from the dstrbutor, the manufacturer tends to rase ts wholesale prce whch devates from ts frst-best soluton. Both of the effects reduce the profts of the manufacturer, causng a lower ncentve to engage n product nnovaton. Therefore, we can arrve at the proposton as follows. Proposton 3. If the manufacturer adopts two-part tarff prcng, parallel mport defntely reduces product nnovaton of the manufacturer. Ths result s n sharp contrast to the fndng by Matteucc and Reverber (2014). They assume the manufacturer adopts one-part tarff prcng and conclude that PI lkely rases ts product nnovaton. It s also worth mentonng that ths result s smlar to the fndng of L and Maskus (2006). They assume the manufacturer adopts, lke that n our model, two-part tarff prcng and conclude that the openness of parallel trade nhbts the manufacturer s process nnovaton. 4. Product Innovaton and Market Structures In the estng lterature on PI, t s commonly assumed that there are only two frmsone manufacturer and one dstrbutor- n the models. Ths assumpton smplfes the analyss, but makes the model less general and realstc. In ths secton, we shall rela ths assumpton to nvestgate the effect of PI on the manufacturer s product nnovaton f the domestc or the foregn market becomes olgopolstc. We wll frst eplore the case n whch there are many rvals n the domestc market followed by the case wth multple dstrbutors n the foregn market. 4.1 The estence of domestc rvals 10

12 All the model settngs are the same as those n the prevous sectons ecept that now there are n homogeneous rvals n the domestc market whose product nnovaton s predetermned and whose outputs are sold to the home market only. The nverse demand functons for the home and the foregn markets under the PI regme are n and p p y, a ( ) y 1 p a( ), and 0 f there s no PI. We shall frst nvestgate the equlbrum under the no PI regme followed by that under the PI regme. Gven ths specfcaton, the proft functons of the manufacturer, the domestc rval frms and the foregn dstrbutor under the no PI regme can be respectvely epressed as follows: (, ; wt,, ) pq, c ( wcy ) TV( ), (, ; ) p Q, c, for 1,..., n. ( y ; wt,, ) p y, w y T. where denotes the output of the th domestc rval. The frst-order condtons for proft mamzaton for the thrd-stage game are dervable as follows: pc p 0, pc p 0, 1,..., n, * y* 0. y p w p y The proft functon of the manufacturer n the second-stage game can be epressed as follows: Ma (,, y ( w), wt, ; ) ( pq ( )) c ) ( wcy ) ( w) T V( ), w subject to T ( p ( y ( w)) w) y ( w). Proceedng as before, we can derve the optmal wholesale prce as w c. The economc eplanaton s as follows. In the absence of PI, the markets n the two countres are ndependent. As a result, the equlbrum n the foregn market s that of monopoly, not affected by the estence of the domestc rvals. It s optmal for the manufacturer to set the wholesale prce equal to the margnal cost and to etract the monopoly rent from the foregn dstrbutor va the fed fee. Makng use of these results, we can rewrte the proft functon of the 11

13 manufacturer for the frst-stage game as follows: Ma ( ( ), ( ), y ( ), w, T( w, ), ) ( pq ( ( ), ) c ) ( ) ( p( y( ), ) cy ) ( ) V( ). By dfferentatng the above proft functon wth respect to and applyng the envelope theorem, we can derve the frst-order condton for proft mamzaton as follows: d y n np p y p V 0. (22) d y We now turn to the PI regme. In the thrd stage, the proft functons for the manufacturer, the domestc rval frms and the foregn dstrbutor can be respectvely epressed as follows: (,,, y ; wt,, ) pq, c ( wc) y TV( ), (,, ; w, T, ) p Q, c, 1,..., n. (,,, y ; w, T, ) p Q, w p y, w y T. The frst-order condtons for proft mamzaton are as follows: pc p 0, pc p I 0, 1,..., n, pw p 0, y y p w p y 0. Proceedng as before, we can derve the optmal wholesale prce as follows: w2 2 ( c) ( n1) ( w) (3n7) c. It shows that the optmal wholesale prce s equal to (lower than) c f n ( )1. 5 Thus, we can establsh the proposton as follows. Proposton 4. If the manufacturer encounters local rvals n the home market, parallel mport reduces the wholesale prce of the manufacturer. If there s only one local rval, PI has no effect on the wholesale prce. 5 Ths s derved by evaluatng the frst dervatve of the manufacturer s proft functon at w c: d dw (1 n) ( n 3) 0, f n 1. wc 12

14 The ntuton behnd ths result s qute straghtforward. If there are local rvals n the home market, the manufacturer can use PI to ncrease ts effectve market share (.e., ts own sale plus the sale va the dstrbutor) and to move the output equlbrum n the home market from Cournot to what would be the Stackelberg leader equlbrum wth the manufacturer as the leader. If there s only one local rval, the optmal wholesale prce s equal to the margnal cost as at ths prce, the effectve output of the manufacturer s dentcal to that of the Stackelberg leader. 6 If there are more than one local rval, the Stackelberg leader s output s hgher. It mples that the manufacturer should set a lower wholesale prce (.e., lower than the margnal cost). In the frst stage, the manufacturer faces the followng mamzaton problem: Ma ( w ( ( ), ), ( w( ), ), y ( w( ), ), ( w( ), ), w( ), Tw ( ( ), ), ) pqw ( ( ( ), ) c w ( ( ), ) w( ) c y( w( ), ) ( w( ), ) T( w( ), ) V( ) By dfferentatng the above equaton wth respect to, and utlzng the equlbrum n the last two stages and the envelope theorem, we can derve the frst-order condton for proft mamzaton of the manufacturer as follows: d w y T T T n n d w y T ( wc) y p np p y p ( ) V ( wc) 2( ) ( wc) p p y V 0 ( n 3) ( n 3) 2. By evaluatng the above equaton at the product qualty level derved under the no PI regme (.e., (22)), we can derve that d 2 p ( n2) ( n1) d N ( n1)( n2) 2 2 p a( ) c (2n 2n1) ( n2) ( n 10n13) The above equaton shows that the parallel mport necessarly rases the product N 6 If there s only one local rval n the domestc market, the manufacturer wll set w c and ts effectve output s * 2( p c)/ p whch s eactly the output of the Stackelberg leader under the no PI regme. 13

15 nnovaton of the manufacturer f there are local rvals n the domestc market (.e., n 1). Ths result s of some nterest as t s n sharp contrast to that wth no domestc rvals. The ntuton s as follows. If there are local rvals n the domestc market, PI ncreases the market share of the manufacturer, rasng ts margnal beneft from the nnovaton nvestment. Consequently, PI ncreases the R&D nvestment of the manufacturer. Gven the above result, we can buld the proposton as follows. Proposton 5. If there are local rvals n the domestc market, parallel mport stmulates product nnovaton of the manufacturer. 4.2 Multple Dstrbutors We have so far assumed that there s only one dstrbutor n the foregn market. In ths sub-secton, we shall dscuss the case n whch the manufacturer can engage n multple authorzatons. 7 All the assumptons and model setups are smlar to those n Secton 3, ecept that the manufacturer now can authorze ts product to more than one dstrbutor. In addton, for smplcty, we assume that all the dstrbutors are symmetrc and can engage n PI f t s permtted by the home country. The nverse demand functons for country H and country F under the PI regme are pa( ), n 1 p a ( ) y, and n 1 n 1 0 f there s no PI. Agan, we shall frst nvestgate the equlbrum under the no PI regme followed by that under the PI regme. At stage three, the proft functons of the manufacturer and the dstrbutors under the no PI regme can be respectvely epressed as follows: ( y, ; wt,, ) p, c ( wc) yntv( ), ( ;,, ), y wt p Q w y T, n 1 1,..., n The thrd stage game s smlar to that n Secton 3. Proceedng as before, we can derve the optmal wholesale prce as follows: N N w ( n1) p y c wth w 0. * y* n 7 Multple authorzatons can be found n ndustres such as books, CDs, vdeo games, cars and ce cream. 14

16 It mples that the optmal wholesale prce ncreases wth the number of the dstrbutors. By substtutng N w nto the dstrbutors frst order condtons n the thrd stage and by symmetry, we can derve that p c p ny. By y * y* 0 comparng ths equaton wth (4), n whch w c, t s found that the total output sold to the foregn market s not affected by the number of dstrbutors. Hence, even wth multple dstrbutors n the foregn market, the manufacturer can stll earn the monopoly profts from both markets under the no PI regme. Of course, ths result hnges on the assumpton that the manufacturer can charge two-part tarff prcng when sellng ts output to the foregn dstrbutors. Based on these results, we can defne the proft functon of the manufacturer n the frst-stage game, as follows: Ma ( ( ), y ( ), w( ), T( w, ), ) ( p ( ( ), ) c ) ( ) ( p( y( ), ) cy ) ( ) V( ). The frst-order condton for proft mamzaton s dervable as follows: d a ( ) c p a( ) c p py p V V 0. d 2 By solvng the above equaton, we can derve the optmal R&D of the manufacturer, whch s dentcal to that solved by (9). Thus, we can arrve at the proposton as follows. Proposton 6. Wth no PI, the optmal wholesale prce ncreases wth the number of authorzed dstrbutors n the foregn market. However, the equlbrum outputs of the two markets, the optmal product R&D and the profts of the manufacturer are not affected by the number of the authorzed dstrbutors. We now dscuss the equlbrum under the PI regme. In the thrd stage, the proft functons of the manufacturer and the dstrbutors can be epressed respectvely as follows: (,, ;,, ), ( ) n n y wt pq c w c y ntv( ), 1 1 ( y ; wt,, ) p Q, w p Q, w y T, 1,..., n. 15

17 The thrd stage game s smlar to that n Secton 3. Proceedng as before, we can derve the optmal wholesale prce under the PI regme as follows: 2( n1) (2 n)( n1) ( n2)(1 n) y w (3n 4) c. We can further derve that w 0. That s to say, the wholesale prce ncreases wth product nnovaton. By utlzng the results from the prevous stages of the game, we can defne the objectve functon of the manufacturer for the frst stage game as follows: Ma ( w ( ( ), ), y ( w( ), ), ( w( ), ), w( ), Tw ( ( ), ), ) pc ( w( ), ) n w( ) c y ( w( ), ) ( w( ), ) nt( w( ), ) V( ). By dfferentatng the above equaton wth respect to and usng envelop theorem, we can derve the frst-order condton for proft mamzaton as follows. d w y dt n d w y T d np nw ( c) y n p ( n1)( p p y y ) p py pv * y* ( wc) n 2 2 n ( wc) 2y p np V 0. ( n2) ( n2) ( n2) ( n1) ( n1) By evaluatng the above frst-order condton at the product qualty level derved under the no-pi regme (.e., (22)), we can obtan: d ( wc) n 2 2 n N ( wc) 2y N p np y d N ( n2) ( n2) ( n2) ( n1) ( n1) a( ) na ( )(1 n) c( n1) p np 0 f ( n 1) p np. 2 2(2n 6n5) 8 Ths result shows that PI has an ambguous effect on the manufacturer s product nnovaton. The ntuton s as follows. PI affects the manufacturer s product R&D n two ways. Frst, there s a negatve effect, takng place n the domestc market. Wth no PI, the manufacturer earns a monopoly proft n the domestc market. When PI s 8 * Note that the frst bracket of the numerator s postve f PI s postve (.e., 0 ). 16

18 permtted, the domestc market becomes olgopolstc whch dscourages product nnovaton of the manufacturer. Furthermore, there s a postve effect takng place n the foregn market. The manufacturer has an ncentve to do more product R&D as t can rase the wholesale prce, mtgatng the amount of PI. The optmal product R&D can ncrease or decrease wth PI, dependng on the magntudes of the two effects. Thus, we can arrve at the proposton as follows. Proposton 7. If the manufacturer authorzes ts product to multple dstrbutors n the foregn country, parallel mports may ncrease or decrease ts product nnovaton, dependng on the consumers qualty valuatons n the two countres. 5. Conclusons In the past two decades, more and more countres engage n deregulaton on PI. Ther man concern s that PI s pro-competton and thus benefcal to the domestc welfare. However, many studes have argued that permttng PI could be socally undesrable as t dscourages the R&D ncentve of the domestc manufacturer. In ths paper, we set out a two-country model to eamne how PI affects product nnovaton of the domestc manufacturer f t adopts two-part tarff prcng when sellng ts output to foregn dstrbutors. We also nvestgate the cases n whch the manufacturer faces rvals n ts domestc market and the manufacturer can authorze ts product to multple dstrbutors n the foregn market. It s found that product nnovaton of the manufacturer s defntely stfled by PI f the domestc market s monopolzed by the manufacturer. Contrarly, f there are rvals n the domestc market, permttng PI necessarly enhances the producton nnovaton. Fnally, f the manufacturer authorzes ts product to multple dstrbutors n the foregn country, PI may ncrease or decrease product nnovaton dependng on the consumers preferences for product nnovaton n the two countres. 17

19 Ths paper has assumed that the manufacturer s the only frm whch can carry out R&D nvestment. One possble etenson s to allow local rvals or dstrbutors to also engage n R&D. Furthermore, ths paper does not consder technology spllover and ntellectual property rght protecton a la Mathew and Mukherjee (2014) and Yang (2013). It s of some nterest to eamne effects of the two factors on parallel mports and the manufacturer s nnovaton ncentve. These etensons are reserved for our future study. Acknowledgements Ths paper was presented at the IREF workshop on Trade, Resources and Growth organzed by Insttute of Economcs, Academa Snca and College of Busness, Feng Cha Unversty on May 22, We would lke to thank the partcpants and n partcular Shn-Kun Peng for helpful comments and suggestons. References Arundel, A. & Kabla, I. (1998). What Percentage of Innovatons are Patented? Emprcal Estmates for European Frms. Research Polcy, 27, Cespedes, F. V., Corey, E. R. & Rangan, V. K. (1988). Gray Markets: Causes and Cures. Harvard Busness Revew, July-August, Chen, Y. & Maskus, K. E. (2005). Vertcal Prcng and Parallel Imports. Journal of Internatonal Trade and Economc Development, 14, Cohen, W., Nelson, R., & Walsh, J. (1997). Approprablty Condtons and Why Frms Patent and Why They Do Not n the Amercan Manufacturng Sector. Unpublshed Workng Paper, Carnege Mellon Unversty. Computer Reseller News. (2001). Vendors Am to Squash Gray Market. 963, September

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