DISCUSSION PAPER SERIES

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1 DISCUSSION PAPE SEIES Dcuon paper No. 95 Strategc product &D nvetment polcy under nternatonal rvalry n the preence of demand pllover effect Tuyoh Tohmtu School of Economc Kwane Gakun Unverty September 0 SCHOOL O ECONOMICS KWANSEI GAKUIN UNIVESITY -55 Uegahara Ichban-cho Nhnomya Japan

2 Strategc product &D nvetment polcy under nternatonal rvalry n the preence of demand pllover effect Tuyoh TOSHIMITSU School of Economc Kwane Gakun Unverty Abtract Th paper frt preent the optmal condton for trategc &D nvetment polcy n the cae of noncooperatve and cooperatve &D nvetment polce wth nternatonal rvalry. Then we deal wth a model of trategc product (.e. ualty-mprovng) &D nvetment competton. In partcular we analye an optmal &D nvetment polcy wth regard to the two cae n the preence of demand pllover effect aocated wth mprovng the ualty of a product. We how how optmalty depend on the trength of demand pllover effect. We alo conder the ame problem aumng heterogeneou conumer and alternatve utlty functon. Keyword: trategc &D nvetment polcy; ualty choce; nternatonal rvalry; demand pllover effect JEL clafcaton: 3 L3 School of Economc Kwane Gakun Unverty -55 Nhnomya Japan Tel: ax: Emal: ttutomu@kwane.ac.p

3 . Introducton The purpoe of th paper to analye trategc product (.e. ualty-mprovng) &D nvetment polcy n a tandard framework of a thrd-country market. In partcular we ue a horontal product dfferentaton model that nclude endogenou ualty choce. urthermore aumng the preence of demand pllover effect aocated wth mprovng the ualty of a product we conder how demand pllover affect optmalty of &D nvetment polcy n the cae of a noncooperatve and a cooperatve polcy decon. Thu we how that the optmalty depend on the trength of demand pllover effect. Semnal paper that deal wth Cournot duopoly n a homogeneou product market and conder trategc proce (.e. cot-reducng) &D nvetment competton nclude Brander and Spencer (983) Spencer and Brander (983) and other. Thee author analye how &D nvetment affect the envronment for market competton. In addton they how that an &D nvetment ubdy an optmal polcy n the cae of nternatonal rvalry. Wth regard to the lterature that analye product &D nvetment competton.e. endogenou ualty choce baed on a model of vertcal product dfferentaton ome reearcher have analyed trategc product &D nvetment polcy wth nternatonal rvalry for example Park (00) Zhou et al. (00) and Jn (003). Thee reearcher mplctly aume the cae of partal market coverage n whch there are ome conumer who do not purchae any product. However n the cae of full market coverage n whch all conumer purchae ether any product a frm producng a low-ualty product chooe the lower lmt ualty level.e. a corner oluton. Thu the government &D nvetment polcy doe not affect the low-ualty frm actvty. However aumng a Hotellng model wth ualty choce (e.g. Sano 007; Ihbah and Kaneko 008) and a model of a horontally and vertcally dfferentated product market (e.g. André et al. 009) we examne the cae of

4 complete market coverage. A mentoned above ntroducng demand pllover effect nto a model of horontally dfferentated product wth ualty choce (e.g. Häckner 000; Symeond 003) we addre trategc product &D nvetment polcy. ormally our model mlar to d Apremont and Jacuemn (988) and De Bondt and Henrue (995) n whch they treat the pllover effect of cot-reducng &D nvetment on the margnal cot of producton.e. the technology-de pllover effect. Cloely related to our model dealng wth the pllover effect on the demand de aocated wth mprovng the ualty of horontally dfferentated product we have oro et al. (00) and Stühmeer (0) n whch they dcu the role of roamng endogenouly determned by compettve frm n a moble phone ndutry. oamng n ther model correpond to the parameter ndcatng demand pllover effect n our model. The remander of th paper tructured a follow. In Secton a prelmnary we preent the optmal condton wth repect to a noncooperatve and a cooperatve &D nvetment polcy. In Secton 3 we conder trategc product &D nvetment polcy n the preence of demand pllover effect and then examne the optmal polcy. urthermore n Secton 4 aumng heterogeneou conumer and alternatve utlty functon aocated wth a horontal product dfferentaton model wth ualty choce we addre the ame problem a n the prevou ecton. Secton 5 ummare our reult and rae remanng ue.. Prelmnary: The condton of an optmal &D nvetment polcy. &D nvetment competton wth nternatonal rvalry Symeond (003) deal wth the pllover effect of ualty-mprovng &D nvetment on the nvetment cot. 3

5 To conder a trategc product &D nvetment polcy we employ a tandard framework of the thrd-country market. That there are two countre home and foregn n whch one frm ext repectvely. The frm located n each country ell the product to the thrd-country market but t doe not ell t to the market n the home and foregn countre. Hereafter the frm located n the home (foregn) country denoted a frm (). The frm compete n a two-tage game. In tage each frm multaneouly chooe t nvetment level whch affect the market competton n the ubeuent tage. The nvetment can be nterpreted a &D. In tage each frm multaneouly chooe t market acton.e. ether prce or output. A analyed below the home and foregn government ether noncooperatvely or cooperatvely commt to an &D nvetment polcy n tage 0 pror to the game played by the frm. Throughout we retrct our attenton to pure-trategy eulbra and focu on the nteror oluton. We confne our attenton to ubgame-perfect eulbra n two tage by olvng the model backward. The Nah eulbrum outcome for frm n tage (.e. product market competton) expreed by the eulbrum revenue [ ] where frm actvty (e.g. nvetment and ualty level) and the rval frm actvty. urthermore the nvetment cot functon of frm gven by [ ] where [ 0] [0] 0 [ ] > 0 [ ] > 0 for > 0 lm [ ] ''' and [ ] 0. Thu the proft functon of frm n tage expreed a (< [ ] [ ] ( ) [ ] where ) an nvetment ubdy from the government of country. In addton negatve mple an nvetment tax. The frt-order condton (OC) to maxme the proft of frm gven by 4

6 5. 0 ) ( () or the followng analy takng e. () nto account we derve the effect of a ubdy on the actvte of the two frm a 0 > Δ () )0 ( )0 ( < < Δ (3) where. 0 > Δ It clear n e. () and e. (3) that a ubdy of government alway ncreae frm actvty wherea the effect on frm actvty depend on the gn of the cro effect of t proft functon.. The optmal &D nvetment polcy n the noncooperatve cae We conder the unlaterally et &D nvetment polcy at tage 0.e. noncooperatvely government chooe an nvetment ubdy/tax on t dometc frm to maxme dometc ocal welfare W whch gven by [ ] [ ] [ ] ] [ ] [ W where [ ]. Baed on the OC to maxme the ocal welfare of country.e. 0 W gven we derve the optmal &D nvetment polcy n the noncooperatve cae a

7 6. * (4) Baed on e. () and e. (3) e. (4) can be rewrtten a. * d d In th cae we obtan ( ). * d d gn gn (5) Becaue t hold that gn d d gn e. (5) can be rewrtten a ( ). * gn gn (6) Therefore a already hown n Spencer and Brander (983) Park (00) Tohmtu and Jn (008) and other n vew of e. (6) we ummare a follow. Lemma A noncooperatve optmal &D nvetment polcy by the home government depend on () the gn of the externalty of the foregn frm &D actvte toward the home frm.e. and

8 7 () the gn of the lope of the foregn frm &D nvetment reacton curve.e. d d n other word the gn of the cro effect of the foregn frm proft functon.e. where frm () the home (foregn) frm. Lemma () mple that the trategc relatonhp between frm ether ubttute or complement.e. 0 < d d or > 0 d d..3 The optmal &D nvetment polcy n the cooperatve cae In the cae of a cooperatve &D nvetment polcy by both government we aume that each government decde an &D nvetment polcy to maxme ont ocal welfare of both countre gven by [ ] [ ] [ ] [ ] [ ]. W W W + + That a hown n the euaton above the ont welfare the ame a the ont proft of both frm n the framework of the thrd-country market. Thu the OC to maxme the ont ocal welfare wth repect to the cooperatve &D nvetment polcy of the home government repreented a 0. + W (7) Smlarly for the cooperatve &D nvetment polcy of the foregn government we have

9 W + 0. (8) Takng e. () e. (3) e. (7) and e. (8) nto account an optmal cooperatve &D nvetment polcy gven by C (9) where upercrpt C denote the cooperatve cae. Therefore we um up the reult a follow. Lemma An optmal cooperatve &D nvetment polcy by the home government depend on the gn of the externalty of the home frm &D actvte toward the foregn frm.e. where frm () the home (foregn) frm. 3. Optmal &D nvetment polcy and ualty competton 3. Horontal product dfferentaton model wth ualty choce and demand pllover effect Here we employ the ame ettng a n Secton : that there are two countre home and foregn n whch one frm ext repectvely. The frm compete n a two-tage game. In tage a frm multaneouly chooe the ualty level hereafter. tage a frm multaneouly chooe the prce p. In We aume that the utlty of a repreentatve conumer n the thrd-market gven by a Th ecton baed on Tohmtu (0). 8

10 ualty-augmented veron of a tandard ualnear functon whch attached wth the term of demand pllover effect by mprovng ualty a V U + y U α ( x + x ) ( x + x ) θxx + {( + ε) x + ( + ε ) x} (0) where y the numeral good and p y. In addton α > 0 and > θ 0. θ a parameter ndcatng ubttutablty between the product. In partcular for the econd term compoed of ualty argument n e. (0) we aume that mple demand pllover effect of an ncreae n the ualty level of product 3. ε ( ε 0) The budget contrant gven by I px + px + x0 o that we obtan the optmal behavor of a repreentatve conumer a > U x α + + ε x θx p. Thu the demand functon of product gven by α( θ ) + ( θε) + ( ε θ ) p + θp x. ( θ )( + θ ) Gven e. () we have () x ( < )0 ε ( < ) θ. () A hown n e. () f the trength of demand pllover effect of product ualty larger (maller) than ubttutablty an ncreae n the ualty level ncreae (decreae) the demand of the rval frm. 3 If ε 0 the utlty functon formally mlar to that of Häckner (000). See alo the appendx n Symeond (003). 9

11 3. The analy In Stage frm decde the prce to maxme the proft.e. p x ( ) [ ]. The OC to maxme the proft of frm expreed by x Λp 0 p where Λ ( θ )( + θ ) > 0. Thu takng e. () nto account we have α ( θ ) + ( θε ) + ( ε θ ) p + θp 0. (3) Therefore the prce of product n the Nah eulbrum gven by Α + Φ + Γ p (4) ( θ )( + θ ) where Α ( θ )( + θ ) > 0 α Φ θε θ 0 > and Γ ( θ ) ε θ. Hereafter we omt the ndexe of the frm n each euaton.e. unle we refer to them pecfcally. In th cae t hold that [ ε ] ( < ) Γ ( < )0 Θ θ (5) + 8 ε where Θ[ ε ] < and [ ε ] > 0. ε Θ E. (5) how that f the parameter compoed of demand pllover wth product ualty.e. Θ [ ε ] larger (maller) than a certan value of the ubttutablty θ then ualty mprovement of product rae the prce of product a well a product. That frm rae (reduce) the prce becaue the potve effect by demand pllover larger (maller) than the negatve effect by ubttutablty between the product. In Stage frm decde the ualty level that maxme the proft whch gven by 0

12 [ ] [ ] ) ( where [ ]. p Λ Thu the OC gven by 0. ) ( ) )( ( + Φ Λ p θ θ In addton the econd-order condton gven by 0. ) ( ) )( ( < + Φ Λ θ θ urthermore wth repect to the cro effect we obtan. ) )( ( ) )( ( + Γ + Φ Λ θ θ θ θ (6) Thu t hold that )0. ( )0 ( < Γ < (7) E. (7) mple that the lope of reacton functon n other word the trategc relatonhp between the frm depend on the trength of a demand pllover effect of the rval frm. urthermore the external effect on the proft (revenue) gven by. ) )( ( θ +θ Γ Λ p (8) Thu we obtan )0. ( )0 ( < Γ < (9) E. (9) llutrate the external effect on the frm revenue. The gn depend on the trength of demand pllover effect of the rval frm only rrepectve of the mode of market competton. or the followng analy we aume a follow.

13 Aumpton : Aymmetrc demand pllover effect If the demand pllover effect of product larger than that of product.e. ε > ε then t hold that Θ Θ[ ε ] > Θ Θ[ ]. ε lemma. Takng nto account e. (5) e. (7) e. (9) and Aumpton I derve the followng Lemma 3 () If Θ > Θ > θ each frm reacton curve lopng upward. Hence an ncreae n the ualty of product () ncreae the revenue of frm (). () If θ > Θ > Θ each frm reacton curve lopng downward. Hence an ncreae n the ualty of product () decreae the revenue of frm (). (3) If > > Θ Θ θ frm reacton curve lopng downward wherea frm lopng upward. Hence an ncreae n the ualty of product () decreae (ncreae) the revenue of frm (). or Lemma 3 () (Lemma 3 ()) f the trength of demand pllover of both frm product larger (maller) than a certan value of ubttutablty an ncreae n the ualty level of one frm expand (reduce) the rval frm demand and th n turn ncreae (decreae) the rval frm prce and ualty. Thu the rval frm proft ncreae (decreae). Smlarly the frm proft ncreae (decreae) wth an ncreae n the rval frm ualty. Therefore the trategc complementary (ubttutonary) relatonhp between the frm hold. See gure (gure ).

14 Place gure and approxmately here urthermore for Lemma 3 (3) when the trength of demand pllover aymmetrc between the frm.e. the trength of a demand pllover effect of product larger and that of product maller than a certan value of ubttutablty an ncreae n product expand frm demand whle an ncreae n product reduce frm demand. In th cae frm ncreae t prce and ualty whle frm decreae t prce and ualty. A a reult frm proft ncreae whle frm fall. Thu the trategc ubttutonary relatonhp utan for frm whle the trategc complementary relatonhp utan for frm. See gure 3. Place gure 3 approxmately here 3.3 The optmal &D nvetment polcy n the noncooperatve cae An optmal &D nvetment polcy n the noncooperatve cae one n whch the government make the dometc frm a leader n a Stackelberg game. Th apect ha already been addreed n the context of trategc trade and ndutral polce. Therefore baed on Lemma and 3 we ealy derve the followng reult. Propoton () If ether Θ > Θ > θ or θ > Θ > Θ then a noncooperatve &D nvetment ubdy optmal.e. () If > > Θ * > 0. * Θ θ then a noncooperatve &D nvetment tax optmal.e. < 0 3

15 . rt a to Propoton () f the trength of demand pllover of both frm ether larger or maller than a certan value of ubttutablty of the product each government gve t dometc frm a ubdy to upgrade t ualty level. Incdentally n the cae of a large enough demand pllover effect ubdng the dometc frm ncreae the foregn frm ualty level a well a that of the dometc frm. Th n turn lead to an ncreae n the proft of both frm and thu the welfare of both countre (ee pont S n gure ). However n the cae of a maller demand pllover effect ubdng the dometc frm reduce the foregn frm ualty level but ncreae that of the dometc frm. Th n turn lead to a decreae n the foregn frm proft and an ncreae n that of the dometc frm (ee pont S n gure ). Th cae mlar to that of Spencer and Brander (983) n whch they conder the cot-reducng (.e. proce) &D nvetment polcy n a Cournot competton. In the cae of a large demand pllover effect becaue the market e ncreae through ualty mprovement of the product both government wll ubde the dometc frm. On the other hand n the cae of a mall demand pllover effect becaue market e doe not ncreae through ualty mprovement of the product but the frm hare reduce by an ncreae n the ualty level of the rval frm product both government wll ubde the dometc frm to expand t market hare. Second a to Propoton () n the cae of aymmetrc demand pllover each government taxe the dometc frm to reduce t ualty level. That a decreae n the ualty level of frm () reduce (ncreae) the ualty level of frm (). In th cae the proft of frm () ncreae by the negatve (potve) externalty effect on the revenue of 4

16 frm (). However a country &D nvetment tax polcy n whch the frm produce the product aocated wth a larger (maller) demand pllover effect reduce (ncreae) the proft of the other frm and thu the welfare of the other country. See pont S ) ( S n gure 3. Taxng frm producng a large demand pllover product reduce the ualty level of the rval frm a well a t ualty. Th mtgate the degree of a fall of the prce of frm and expand t hare. Accordngly &D tax polcy ncreae the proft of frm and thu the welfare of the government although t reduce the proft of the rval frm. On the contrary taxng frm producng a mall demand pllover product reduce t ualty level but ncreae the ualty level of the rval frm. or frm th mtgate the degree of a fall of the prce of frm and expand t demand. In addton the proft of frm ncreae. Accordngly the &D tax polcy ncreae the proft of both frm and thu the welfare of both countre. Th mple that the &D tax on the frm producng a mall demand pllover product Pareto mprovng. 3.4 The optmal &D nvetment polcy n the cooperatve cae An optmal cooperatve &D nvetment polcy of the government determned by ont welfare maxmaton. Th mple that both frm colluvely determne ther ualty level to maxme ther ont proft; however they noncooperatvely compete n prce n the product market 4. Therefore both frm chooe the ualty level extng n Pareto uperor et whch are the haded area urrounded by the o-proft curve of both frm.e. N. or example n the cae of large demand pllover effect.e. 4 Th tuaton llutrate emcolluon mlar to the cooperatve &D nvetment condered by d Apremont and Jacuemn (988) and other. 5

17 Θ > Θ > both frm chooe hgher ualty level than the level n the Nah θ eulbrum. In other word each government ubde t dometc frm (ee gure ). Wth repect to the other cae of demand pllover effect we can mlarly explan the optmal cooperatve &D nvetment polcy. Therefore baed on Lemma and 3 we ealy derve the followng propoton. Propoton () If Θ > Θ > θ ( > Θ > Θ ) C polcy a ubdy (tax).e. > 0 () If > > Θ θ then an optmal cooperatve &D nvetment C ( < 0).. Θ θ then a cooperatve &D nvetment ubdy on frm and tax on frm C are optmal.e. > 0 C and < 0. Note that upercrpt C denote the cooperatve cae. We have an nteretng cae n whch there are aymmetrc demand pllover preented by Propoton (). In the model of vertcal product dfferentaton Propoton 3 n Zhou et al. (00) that ontly optmal polce nvolve an nvetment ubdy n the developed country and an nvetment tax n the le-developed country. In ther model the frm producng the hgh- (low-) ualty product locate n the developed (le-developed) country. That the ontly optmal polce expand the dfference n ualty level and thu mtgate prce competton. Th n turn ncreae the ont proft of the frm and thu the ont welfare of ther countre. or our model f we can aume that a frm producng the product aocated wth large (mall) demand pllover locate n the developed (le-developed) country by the ame reaon derved n the reult of Zhou et al. (00) we tate that cooperatve &D polcy a mx of an nvetment ubdy n the developed country and an nvetment tax n the 6

18 le-developed country. 4. Dcuon: Alternatve utlty functon and heterogeneou conumer 4. A Hotellng model wth ualty choce In the prevou ecton we aumed a homogeneou conumer wth a tandard ualnear utlty functon nvolved wth ualty argument. Here we frt aume heterogeneou conumer and ue a tandard Hotellng patal model of duopoly aocated wth ualty choce (e.g. Sano 007; Ihbah and Kaneko 008). There a contnuum of conumer unformly dtrbuted on the [ 0 ] nterval. The denty of conumer aumed to be one. rm ( 0) upple product at a product ualty wth prce. purchae at mot one unt of a product. A conumer located at [ 0] U v + 0 p0 tx p Each conumer x ha net utlty 0 when he or he purchae product 0. Smlarly when purchang product the net utlty U v + p ( x) t. Here (> 0) v v the utlty obtaned from conumng a ngle unt of the product rrepectve of the ualty level. In addton the parameter t (> 0) mple the tranportaton cot. Comparng net utlte.e. U the demand functon of product gven by x + ( p + p ) 0. t (0) To mplfy we aume no producton cot. Thu we derve the eulbrum prce n Stage a p t () 7

19 Therefore the revenue functon of frm n Stage gven by [ ] t () 3 Baed on () we obtan the externalty of frm toward the revenue of frm and the factor decdng the trategc relatonhp between frm (.e. the lope of the reacton functon). That wth regard to thee factor we have 6t t + t < 0 3 (3) 9t < 0 (4) where 0. In vew of (3) and (4) and takng Lemma and nto account we derve the followng reult. Corollary () An optmal noncooperatve &D nvetment polcy a ubdy.e. C () An optmal cooperatve &D nvetment polcy a tax.e. < 0 * > Thee reult are mlar to thoe of Spencer and Brander (983 Propoton ) and the cae of a mall demand pllover effect a n Propoton () and () of our model. Although we do not aume demand pllover effect even wth the preence of demand pllover effect the reult do not change (ee Appendx A). 8

20 4. A horontal and vertcal product dfferentaton model We explot the utlty functon compoed of horontally and vertcally dfferentated product preented by André et al. (009 Secton 6). That there a contnuum of conumer unformly dtrbuted on the [ 0 ] nterval. The denty of conumer aumed to be one. rm ( 0) upple product at ualty wth prce. mot one unt of a product. A conumer located at [ 0] U p Each conumer purchae at x ha net utlty 0 ( x) 0 p0 when he or he purchae product 0. Smlarly when purchang product the net utlty gven by U x p. Therefore we derve the demand functon of frm x p + p x x 0. + (5) To mplfy we aume no producton cot. In th cae we derve the eulbrum prce n Stage a follow. p (6) Thu baed on e. (5) and e. (6) frm revenue functon of ualte n Stage gven by + + [ ] 3 0. (7) 3( ) + Baed on e. (7) we obtan the externalty of frm toward the revenue of frm and the factor decdng the trategc relatonhp between frm. That wth regard to thee factor we have a ( + ) 0 9( + ) > (8) 9

21 3 9( + ) < 0 (9) where 0. In vew of e. (8) and e. (9) and takng Lemma and nto account we derve the followng reult. Corollary * () An optmal noncooperatve &D nvetment polcy a tax.e. < 0 0. C () An optmal cooperatve &D nvetment polcy a ubdy.e. > 0 0. Thee reult are the revere of Corollary derved n the Hotellng model wth the ualty choce model analyed n Secton 4.. Th becaue the gn of the externalty are dfferent between e. (3) and e. (8) although the gn ndcatng the trategc relatonhp between the frm the ame (.e. trategc ubttute). That n vew of e. (0) and e. (5) an ncreae n the ualty level of the rval frm product reduce the demand of the other frm rrepectve of the type of the utlty functon. However a n e. () the ncreae reduce the prce of the other frm wherea a n e. (6) t converely ncreae the prce of the other frm. Hence the gn of the externalty negatve a n e. (3). On the other hand becaue the effect of an ncreae n the prce larger than that of a decreae n the demand the gn of the externalty potve a n e. (8). Although we do not allow for the demand pllover effect of the model n th ecton even wth the preence of demand pllover effect the reult do not change (ee Appendx B). 0

22 5. Concludng remark There no doubt that nternatonal prce and ualty competton among frm preval n many ndutre uch a thoe manufacturng electronc applance computer HDTV and other. There nternatonal rvalry not only among frm n advanced countre but alo between frm n advanced countre and thoe n newly ndutraled countre ncludng Chna and Inda. urthermore government upport ther dometc frm &D nvetment actvte n many way for example wth ubde tax credt and other regulaton although they cannot publcly promote thee frm export actvte under the WTO ytem. Ung a vertcal product dfferentaton model Zhou et al. (00) and other have condered an optmal product &D polcy n the cae of noncooperaton and cooperaton. In a ene they llutrate the dfference n the competton and trategc polce of an advanced and a newly ndutraled country. In contrat n th paper we have analyed the ame ue a n prevou tude baed on a horontal dfferentated model wth ualty choce. urthermore we have aumed demand pllover effect n our model. That an ncreae n the ualty level of the frm product may ncreae the other rval frm demand and proft. In other word by focung on both horontal product dfferentaton (e.g. brand name and locaton) and vertcal product dfferentaton (.e. ualty) n the preence of mlar demand pllover effect between the frm product we how the example of trategc polcy and competton between advanced countre uch a the U.S. the EU and Japan. In addton n the preence of aymmetrc demand pllover effect we llutrate the example of trategc polcy and competton between an advanced country (e.g. the U.S.) and a newly ndutraled country (e.g. Chna). Under the above aumpton we have found the followng. In the cae of large and

23 mall demand pllover wth repect to the frm product.e. the tuaton of mlar demand pllover effect between frm n advanced countre an &D nvetment ubdy an optmal polcy. However n the cae of aymmetrc demand pllover effect an &D nvetment tax an optmal polcy for the advanced country and the newly ndutraled country. In partcular a government n a newly ndutraled country rather reduce the dometc frm &D actvty to explot large demand pllover of the frm n the advanced country. urthermore we have condered optmalty of cooperatve &D nvetment polcy. In partcular n the cae of aymmetrc demand pllover we have hown the ame reult a n Zhou et al. (00). That f a frm producng the product aocated wth large (mall) demand pllover locate n the advanced (newly ndutraled) country then an optmal cooperatve &D nvetment polcy combne a ubdy by the advanced country wth a tax by the newly ndutraled country. We underlne a pecfcty of our model. or example we have exogenouly ntroduced demand pllover effect aocated wth ualte nto the ualnear tandard utlty functon. Thu n future work we need to reearch a general utlty functon that nclude demand-de pllover effect.

24 Appendx A Let u ntroduce a demand pllover effect by ualty upgrade nto a Hotellng model wth ualty. In th cae a conumer located at [ 0] x ha net utlty U0 v ε p0 tx when he or he purchae product 0. Smlarly when purchang product the net utlty U v + + ε 00 p ( x) t. The ε 0 parameter (< ) denote the margnal coeffcent of a demand pllover effect. Thu the demand functon of product gven by x + ( ε) ( ε ) t p + p 0. We derve the eulbrum prce n Stage a p ( ε) ( ε ) t Therefore the revenue functon of frm n Stage gven by [ ] where 0. t + ( ε) ( ε ) 3 + ( ε) ( ε ) 6 t Becaue 0 ε < 0 we derve the ame reult of the externalty on the frm revenue and cro effect a thoe n the cae of nondemand pllover effect. Appendx B In the cae of a horontal and vertcal product dfferentaton model a conumer located at [ 0] x ha net utlty U0 ( x)( 0 + ε ) p0 when he or he purchae product 0. Smlarly when purchang product the net utlty U x( + ε 00) p. The 3

25 ε 0 parameter (< ) denote the margnal coeffcent of a demand pllover effect. In th cae we derve the demand functon of frm a + ε p + p x 0. ( + ε) + ( + ε ) The eulbrum prce n Stage gven by ( + ε ) + ( + ε ) p 0. 3 Therefore the revenue functon of frm n Stage gven by [ ] {( + ε) + ( + ε ) } 9{ ( + ε ) + ( + ε ) } 0. Although we omt the tedou calculaton we obtan the ame reult of the externalty on the frm revenue and the cro effect a thoe n the cae of nondemand pllover effect. 4

26 eference André. J. P. Gonále and N. Portero 009 Strategc ualty competton and the Porter Hypothe Journal of Envronmental Economc and Management Brander J. A. and B. J. Spencer 983 Strategc commtment wth &D: The ymmetrc cae Bell Journal of Economc d Apremont C. and A. Jacuemn 988 Cooperatve and noncooperatve &D n duopoly wth pllover Amercan Economc evew De Bondt. and I. Henrue 995 Strategc nvetment wth aymmetrc pllover Canadan Journal of Economc oro Ø. B. Hanen and J. Y. Sand 00 Demand-de pllover and em-colluon n the moble communcaton market Journal of Indutry Competton and Trade 5978 Jn N. 003 Strategc polcy for product &D wth ymmetrc cot Canadan Journal of Economc Häckner J. 000 A note on prce and uantty competton n dfferentated olgopole Journal of Economc Theory Ihbah K. and T. Kaneko 008 Partal prvataton n mxed duopoly wth prce and ualty competton Journal of Economc Park J.-H. 00 Strategc &D polcy under vertcally dfferentated olgopoly Canadan Journal of Economc Sano Y. 007 Hotellng locaton model wth ualty choce n mxed duopoly Economc Bulletn 8 Spencer B. J. and J. A. Brander 983 Internatonal & D rvalry and ndutral trategy evew of Economc Stude Stühmeer T. 0 oamng and nvetment n the moble nternet market Telecommuncaton Polcy forthcomng. 5

27 Symeond G. 003 Comparng Cournot and Bertrand eulbra n a dfferentated duopoly wth product &D Internatonal Journal of Indutral Organaton Tohmtu T. 0 Qualty competton and a demand pllover effect: A cae of product dfferentated duopoly School of Economc Kwane Gakun Unverty Dcuon Paper Sere No. 89 Tohmtu T. and N. Jn 008 A note on trategc trade polcy and endogenou ualty choce evew of Internatonal Economc Zhou D. B. J. Spencer and I. Vertnky 00 Strategc trade polcy wth endogenou choce of ualty and aymmetrc cot Journal of Internatonal Economc

28 L N S S N N L 0 gure Θ > Θ > θ N : Nah Eulbrum S : Stackelberg Eulbrum n whch frm the leader k k L : The proft of frm beng k ( L : leader : follower) Shaded area llutrate Pareto uperor et 7

29 L S N N S 0 N gure θ > Θ > Θ N : Nah Eulbrum S : Stackelberg Eulbrum n whch frm the leader k k L : The proft of frm beng k ( L : leader : follower) Shaded area llutrate Pareto uperor et 8

30 T L S N N L N 0 S gure 3 T Θ > θ > Θ N : Nah Eulbrum S : Stackelberg Eulbrum n whch frm the leader k k L : The proft of frm beng k ( L : leader : follower) Shaded area llutrate Pareto uperor et 9