Technology Transfer in a Duopoly with Horizontal and Vertical Product Differentiation

Transcription

1 Dsusson Paer ERU/ November 008 Tehnology Transfer n a Duooly wh Horzonal and Veral Produ Dfferenaon Tarun Kabra Indan Sasal Insue, Kolkaa Chng Chy Lee The Chnese Unversy of Hong Kong Revsed Draf 008 Aknowledgemen: Ths s a revsed verson of he aer resened n a semnar a he dearmen of DSE, CUHK, Hong Kong. We would lke o hank Sukana Bhaaharya and Sudo Dasgua for helful suggesons and ommens. All remanng errors are ours. Corresond o: Tarun Kabra, Eonom Researh Un, Indan Sasal Insue, 0 B. T. Road, Kolkaa 70008, Inda. E-mal: arunkabra@homal.om; Fax:

2 Tehnology Transfer n a Duooly wh Horzonal and Veral Produ Dfferenaon Absra Ths aer dsusses lensng agreemens beween duools frms n a model of horzonal and veral rodu dfferenaon. I s shown ha a rofable ehnology ransfer deal under a fee onra an be sgned f and only f he qualy dfferenal s suffenly larger han he ehnology dfferenal. Tehnology ransfer under a royaly onra, however, does no requre suh a ondon. The aer also examnes he ossbly of radng a beer ehnology for a sueror qualy. Fnally, we show ha he exsene of a suffenly hgh radng os n an oen eonomy an always make a fee ransfer muually rofable. The aer also rovdes a welfare analyss. Key words: Tehnology ransfer, horzonal dfferenaon, veral dfferenaon, radng oss, lensng onras. JEL lassfaons: D4, F, L..

3 . Inroduon Tehnology ransfer beween wo frms whn a ounry or aross ounres s a ommon rae n almos all ndusres; by hs boh he ransferor and he ransferee an gan from he use of sueror roduon knowledge. Tehnology ransfer leraure s already vas and deals wh varous ssues. Bu he exsng analyss resumes ha he rodus are eher homogeneous or horzonally dfferenaed. No works so far have onsdered he ossbly of ehnology ransfer when he rodus are boh horzonally and verally dfferenaed. So he urose of he resen aer s o examne he ossbly of ehnology ransfer beween wo asymmer frms when he rodus have boh hese dmensons. Veral dfferenaon refles ha he omeng frms rodue dsn qualy levels, and onsumers erfely ereve he qualy dfferene and hene are wllng o ay a hgher re for he hgher qualy. And horzonal dfferenaon s haraerzed by dfferen loaons of he frms n a Hoellng 99 lnear y; also refles onsumers referenes for dfferen brands n he rodu sae. In suh a model, gven ha he onsumers are dsrbued along he y, a arular loaon of a onsumer refles he onsumer s hoe for an deal varan of he rodu, and o he exen hs aual hoe dffers from hs deal oson, he ereves a loss of uly. We resr o he senaro where boh he re-ransfer and he os-ransfer marke sruures are duooly of he omeng frms. By hs we fous our aenon on hose ehnology ransfer agreemens whh are self enforeable. So we don need any nsuonal assumon o enfore he onra. Perhas ould be omal for he ransferor o ransfer s sueror knowledge a an arorae re and leave he marke o he ransferee. Bu n he absene of an effeve nsuonal arrangemen, here s a ommmen roblem, beause he ransferor always has an nenve o ener he marke one he agreemen has been sgned. Hene n our analyss he os-ransfer marke sruure s duooly and he aenee s an nsder. Suh ssues are, for nsane, sraeg ehnology ransfer Galln 984, Roke 990a, obsolee ehnology ransfer Roke 990b, Kabra and Mar 99, ransfer under asymmer nformaon Galln and Wrgh 990, Beggs 99, Cho 00, omal lensng onras Kamen and Tauman 986, 00, Kaz and Sharo 986, Mukheree and Balasubramanan 00, Wang 998, 00, Kabra 005.

4 In our sudy we mosly fous our aenon on a fxed fee onra, alhough we also dsuss he queson of ehnology ransfer under royaly onras. One reason s ha under royaly onras veral rodu dfferenaon does no lay any seal role n our model. There are oher reasons. In a sa one erod model lke ours, ehnology lensng s equvalen o ehnology sale; hene only an ufron fee aymen should naurally arse. In a royaly onra royaly aymen ours only a he end of he roduon erod. Then whou any nsuonal assumon a royaly onra anno be mlemened redbly. Furher, n a model of duooly where aenee s an nsder, generally eher fee onras are no rofable or royaly onras srly domnaes fee onras, beause ehnology ransfer under a fee onra nreases omeveness of he ransferee, whereas under a royaly onra he ransferor an kee he omeveness of he rval under hek for nsane, see Kamen and Tauman 984, 986, 00, Kaz and Sharo 986, Kamen e al. 99, Wang 998, and Wang and Yang 999. Hene s an oen queson wheher a fxed fee onra s a all feasble n a model where rodus are verally and horzonally dfferenaed, and f feasble, under wha ondons. Fnally, n he emral leraure here s evdene o show ha ehnology ransfer agreemens nvolvng only fxed fee have been sgned e.g., Rosoker 984. One moran queson ha we lke o examne n hs onex s he followng. Can here be a ehnology ransfer agreemen beween wo frms f he same frm owns sueror roduon ehnology as well as sueror rodu qualy? Ths s a hyohess whh needs verfaon emrally. In our seng we show ha n a losed eonomy framework, or n an oen eonomy wh no rade or arff resrons, a hgh-qualy lowos frm has no nenve o share s ehnology wh a low-qualy hgh-os frm. The reason s ha he frm havng advanages n boh rodu qualy and ehnoloy already owns a large marke share; n suh a suaon ransfer of ehnology o he neffen rval wll erode he ransferor s marke share sgnfanly. Therefore, n our model s There s a leraure ha assumes ha lensng resuls n a shf of marke demand and when suh a shf s suffen, ehnology ransfer beomes rofable e.g., Sheard 987, and Bovn and Langner

5 neessary ha, gven ha one frm has ehnologal advanage, he oher frm mus have suerory n oher rese. In an oen eonomy when a foregn frm holds a sueror roduon ehnology, a arff or rade resron wll benef he loal frm and hene relax he ondon of ransfer. We show ha here always exss a rade os, suffenly hgh, ha makes ehnology ransfer muually rofable for boh frms, rreseve of her rodu quales. 4 The reason s ha by ransferrng a sueror ehnology o he loal frm, he foregn frm an oherwse aure a leas a ar of he radng oss of he onsumers n he form of ehnology ransfer fee. To he exen lberalzaon redues radng oss, also redues he ossbly of ransfer of sueror qualy or knowledge. In a duooly wh homogeneous goods Mar 990 has shown ha ehnology ransfer beween wo frms s rofable f and only f he frms are reasonably lose n erms of her nal ehnologes. Mukhoadhyay, e al. 999 reexamne he queson n he resene of rodu dfferenaon and behavoral neraons oher han Courno oneures. I s shown ha f he nal suaon s one of near olluson, or he rodus are suffenly horzonally dfferenaed, a rofable ehnology ransfer deal beween he frms always exss, whaever be he nal ehnologal ga. On he oher hand, f rodu dfferenaon s of Hoellng ye, as n Poddar and Snha 004, hen here wll be no ehnology ransfer under he fee onra. In onrary, n our model, wh rodus beng horzonally and verally dfferenaed, for ehnology ransfer o be rofable we need he qualy dfferenal o be suffenly large. Generally, a frm rodung a hgher qualy rodu has a larger un os of roduon, bu hs may no always be he ase for all rodus. For nsane, a frm may be an orgnal enran n a marke, and anoher frm may be an maor. The laer s aable o merfely mae he rodu and roess, so ends u wh hgher os and lower qualy. If a frm has onrol over some ral resoures or even `beer eole, hen s ossble o rodue a hgher qualy a a lower os. Therefore, o dsuss he queson of ehnology ransfer n our framework, we assume ha he qualy of he Bu suh a ondon s no neessary for ehnology ransfer o be rofable under royaly onras see he analyss n seon 4. 4 In a Courno duooly wh homogeneous goods Kabra and Mar 00 have shown ha a arff resron an be hosen sraegally suh ha ehnology ransfer beomes feasble and onsumers welfare goes u see also Mukheree and Pennngs

6 rodu and he un os of roduon are ndeenden. To be more rese, here s a frm whh holds an nferor ehnology of rodung a hgher qualy rodu omared o a frm whh holds a beer roduon roess bu rodues a relavely nferor qualy. Suh a senaro s obvously ossble f we assume ha rodu nnovaons and roess nnovaons are ndeenden. In arular, assume ha he qualy of a rodu deends on he hoe of a veor X, whereas he un os of roduon deends on he hoe of a veor Y, where X onans relevan nformaon relaed o nnovaon of he rodu, and Y onans nformaon for roess nnovaon. Noe ha he os of nnovang a hgher rodu qualy should always be larger, bu hs does no maer o us beause we are no modelng nnovaon n hs aer. We sar wh he suaon where rodu quales are already gven o he reseve frms, and assume ha a gven qualy rodu an be rodued by dfferen roesses. In he onex of ehnology ransfer, nnovaon os s sunk. Sne we assume ha he qualy of he rodu s ndeenden of he un os of roduon, hs also erms us o dsuss he ossbly of ransfer of knowledge assoaed wh he hgher qualy o dsngush from he ehnology ransfer we all hs ransfer of rodu knowledge, and n arular, o examne wheher ross lensng of advanages beween he frms wll be rofable. As far as rodu knowledge ransfer s onerned, our bas resul s he same, ha s, for a rofable knowledge ransfer n a suaon of zero rade resron s neessary ha he frm whh owns a sueror rodu qualy does no, a he same me, hold he low-os roduon ehnology. Gven ha eah frm has advanage n one dreon, here are suaons where only ehnology ransfer or only knowledge ransfer s rofable. And agan here are suaons where ransfer of eah of hese s rofable. Bu n our model he frms have no nenve o rade a beer ehnology for a beer qualy. We have also suded welfare mlaons of ehnology ransfer and knowledge ransfer assoaed wh roduon of a beer qualy. A rofable ransfer mles ha no frm s worse off and a leas one frm omes u wh a hgher rof. Therefore, roduers surlus as a whole mus go u. Consumers also benef, beause n ase of 6

7 ehnology ransfer boh frms use he low-os ehnology, and gven re omeon, res of all rodus fall; moreover, some onsumers an now buy a beer qualy rodu; and n ase of rodu knowledge ransfer, he beer qualy resuls n a hgher onsumer welfare. The seu of he aer s he followng. In he seond seon we rovde he model: n subseon. and. we examne he ossbly of ehnology ransfer and rodu qualy ransfer resevely; subseon. examnes wheher ross-lensng of eah oher s advanages an be muually rofable; and subseon.4 sudes he welfare effe of suh a ransfer. Seon derves an mlaon of he exsene of a rade os n he onex of ehnology ransfer beween wo frms aross borders. In seon 4 we dsuss ehnology ransfer under royaly onras. Seon 5 onludes he aer.. Model Consder a dfferenaed duooly where wo frms, all frm and, are omeng n res. The rodus have wo dmensons: rodus are verally as well as horzonally dfferenaed. 5 Veral dfferenaon s aured by he onsderaon ha he frms rodue wo dsn rodu quales, exogenously sefed and denoed by and ; 0. Obvously, means ha boh he frms rodue he same qualy rodus. And h > mles ha he frm rodues he sueror qualy rodu. 6 The quales are erfely ereved by he onsumers. 5 Here we follow he framework of Garella 00 haraerzng a duooly wh rodus dfferenaed horzonally and verally. The aer develos an R&D model and shows ha ha he mlemenaon of a mnmum qualy sandard ndues he hgh qualy roduer o lower s qualy level f he onsumers have srong horzonal referenes. 6 In he Hoellng sruure veral rodu dfferenaon may be nrodued n erms of dfferenal ransor os see, for nsane, Ferrera and Thsse

8 Horzonal dfferenaon s haraerzed by he dfferen loaons of he frms n a Hoellng lnear y. To nerre oherwse, mles dsrbuon of onsumers referene for hese wo rodus n he rodu sae. We assume ha he lengh of he y s uny and he frms are loaed a he oose end ons; n arular frm s loaed a x 0 and frm a x. Consumers are assumed o be unformly dsrbued over he lengh of he y, and eah onsumer has an address or deal varan haraerzed by x [0,]. Then a onsumer a an address x, who fals o oban hs deal varan, faes a os of x when he buys from frm, and x when buys from frm. Therefore, > 0 s us lke a ransor os of ravel er un dsane. We furher assume ha eah onsumer buys exaly one un of he rodus and ha he marke s fully overed. He buys he rodu of he frm whh brngs hm he larges ne uly, ha s, gross uly mnus he oss of aqurng. The oss omrse of he rodu re and he loss of uly ha s, ravel os for no buyng he deal varan. Toal number of onsumers s normalzed o be. We assume ha he ne uly of onsumng one un of he rodu s addvely searable n he veral and horzonal dmensons, and hs s gven by: v x u v x f o buyfromfrm f o buyfromfrm where v > 0 denoes he bas uly, same for all onsumers, and s he un re harged by frm. Then for a onsumer, x, who s ndfferen beween frm and frm s rodus, we have u, u,. Ths gves x [ ] Therefore, demand for frm s rodu s D, x and ha for frm s rodu s D, x. 8

9 We assume ha he un os of roduon s onsan and ndeenden of he qualy level, and he os assoaed wh he qualy s already sunk. 7 Le be frm s un roduon os. Ths gves he rof funon of frm as:,, D Π, The orresondng wo reaon funons n res are: We assume ha hese reaon funons nerse n he osve quadran. Therefore, he re-ehnology ransfer res are obaned by solvng hese reaon funons smulaneously 8 seond order ondons are also sasfed. These are [ ] [ ] 4 The orresondng marke shares and re-ransfer rof levels n equlbrum are: [ ] [ ] 6 6 x D x D 5 [ ] [ ] 8 8 Π Π 6 I s assumed ha under he gven arameers boh and are osve D D 9. The rof exressons ell ha eah frm s rof s nversely relaed o s un os bu drely relaed o he rval s un os. Therefore f ehnology ransfer ours from he low os o he hgh os frm, he ayoff of he low os frm wll fall whereas ha of he hgh os 7 We have already dsussed hs n he nroduon. If roduon of a hgher qualy rodu nvolves a larger un os, hen our hyohess s ha here wll be no ehnology ransfer f he ransferor and he ransferee omee n he same marke. Prooson learly roves he resul. 8 d Asremon e al. 979 have shown he roblem of non-exsene of equlbrum n Hoellng model wh lnear ransor os when boh res and loaon of frms are varable. 9 In arular, we assume } /, / max{ >. 9

10 frm wll go u. Hene he queson s: Can here be a rofable ehnology ransfer agreemen beween he frms? In he nex seon we dsuss he queson under a fxed fee onra, ha s, wheher here exss a fee L > 0 suh ha a muually rofable ehnology ransfer deal an be sgned. We shall also sudy he welfare mlaon of suh a ransfer.. Tehnology Transfer under he Fee Conra Le us assume and onsder he ossbly of ehnology ransfer from he low os frm o he hgh os frm under a fee onra. The desons of he frms are he followng. Frs, he mos effen frm dedes wheher o ransfer s ehnology o he less effen frm, gven he rodu quales of he frms. Seond, he frms omee n res. Hene f ehnology ransfer ours, he marke sruure wll reman o be duooly wh symmer roduon ehnology wh eah frm havng low un os of roduon. Then he marke-oeraed rofs of he frms wll be: ~ Π ~ Π 8 8 [ ] [ ] Immedaely, we have he followng resuls. 7 Prooson : a There wll be no ehnology ransfer agreemen under he fee onra f he mos effen frm also ossesses he sueror qualy of he rodu. Formally, here does no exs L > 0 f smulaneously < and > hold. b A ehnology ransfer agreemen s rofable under he fee onra f and only f her rodu qualy dfferenal s suffenly larger han he ehnology dfferenal. Formally, f >, L > 0 ff >. Proof: Par a s learly roved f he ondon underlyng ar b holds. 0

11 To rove ar b, whou loss of generaly assume <. Then ehnology ransfer under he fxed fee onra s muually rofable f and only f he followng wo ondons hold smulaneously, ha s, ~ ~ L Π > Π and Π L > Π Therefore, ~ ~ L > 8 0 ff Π Π > Π Π Gven he ayoffs, as defned n 6 and 7, he ondon an be smlfed o ge >. 9 Frs noe ha he ehnology ransfer agreemen under he fxed fee onra s muually rofable f and only f he os-ransfer ndusry ayoff s larger han he reransfer ndusry ayoff hs s ondon 8. Ths s naurally requred beause oherwse he ransferee wll no be n a oson o omensae he loss of he ransferor. Then 9 ells ha a ehnology ransfer agreemen wh a fxed fee onra s never muually rofable f he frm ossessng sueror ehnology also rodues sueror qualy rodus. One mlaon of he resul s he followng. If a frm omees n a marke wh a sueror qualy rodu and a he same me ossesses a sueror roduon roess, hen has no nenve o ransfer s ehnology o s rval, beause already oues a large marke share. Thus our model rovdes a esable hyohess: Wll a frm, whh omees wh a sueror qualy rodu and ossesses a beer mehod of roduon, ransfer s roduon ehnology o s rval? To exlan he ondon furher, gven he ehnologal dfferene beween he frms, ehnology ransfer s muually rofable f and only f s suffenly large, ha s, he rodus are suffenly verally dfferenaed. On he oher hand, f he rodus are no suffenly dfferenaed, he ehnology ransfer deal s rofable f and only f he nal ehnologal dfferenes beween he frms are no oo large. Therefore, wha we really need s ha he dfferene beween quales of rodus s suffenly larger han he dfferene beween ehnologes. Poddar and Snha 004 show ha f he rodu dfferenaon s of Hoellng ye, ehnology ransfer under a

12 fxed fee s never rofable. Noe ha Poddar and Snha model s a seal ase of our model when boh frms have he same qualy rodus. 0 Wh boh horzonal and veral dfferenaons, our model shows ha muually rofable ehnology ransfer wh fxed fee an our. Inuon of he resul s he followng. If ehnology ransfer ours n a Courno duooly wh homogeneous goods, he ransferee gans from he use of sueror roduon ehnology and he ransferor suffers a loss due o nreased omeon. However, he exen of loss and gan deends on he re-ransfer marke shares of he frms, whh, n urn, deends on he asymmery of ehnologes. If he ehnologal asymmery s oo large, he effen frm wll have a larger marke share omared o he neffen frm. Then ransfer of ehnology means ha he ransferor wll have a greaer amoun of loss han he nreased rof of he ransferee. Under hs suaon ransfer s no rofable under he fxed fee onra. Bu f he frms are lose n erms of her ehnologes, he effeny effe wll domnae he omeve effe and he osransfer ndusry ayoff wll go u makng suh a ransfer muually rofable. On he oher hand, when he frms omee wh dfferenaed rodus, omeon beomes relaxed, and as a resul ehnology ransfer an be rofable even f her ehnologes are no lose enough, rovded ha he degree of rodu dfferenaon s suffenly large. Obvously, here wll be no ehnology ransfer under re omeon wh homogeneous goods. 0 The Poddar and Snha model, lke he resen model, assumes unform dsrbuon of onsumers over he lengh of he y. We may generalze he dsrbuon assumon. Le Fx be he dsrbuon over [0,] nerval. Then he rof funons of he frms are: π F and π F x x where x s he ndfferen onsumer. Now f <, hen ehnology ransfer from low os frm o hgh < π / F x f x x / / f x x / / os frm wll be rofable only f π π / 0. Bu π In Hoellng model wh unform F, he las wo erms domnae he frs erm and hene ehnology ransfer s no rofable. However, wh non-unform dsrbuon, here an be suaons where he frs erm wll domnae he las wo erms, and he ehnology ransfer an be rofable. In our model we have nrodued veral dfferenaon ha nreases x and hene F x, gvng he ossbly of ehnology ransfer..

13 Now onsder re omeon wh rodus horzonally dfferenaed n Hoellng sense rodus are oherwse hysally denal. In suh a suaon boh he frms wll have a osve rof even f hey would have denal ehnologes. So nal asymmery n ehnologes means ha he sueror ehnology ownng frm wll have a larger marke share, gven re omeon. Now, f ehnology ransfer would ake lae, boh frms would omee on equal foong and re omeon means ha he ransferor anno exra a large enough rof from he ransferee so as o overomensae he loss of s ayoff due o omeon. Thus under saal dfferenaon wh re omeon, ehnology ransfer s no rofable. Bu f he hgh os frm rodues sueror qualy rodus, an overome o some exen he dsadvanage of havng an neffen ehnology and hereby mrove s marke share. Then when ehnology ransfer ours, f he ransferee has nally a suffenly hgh rodu qualy and so subsanally a large marke share, ransferee s oeraed ayoff goes u subsanally n he os-ransfer suaon and hene he ransferor an exra a larger ayoff from he ransferee by means of a fxed fee. Thus when he ransferee rodues suffenly hgh qualy relave o ha of he ransferor, ehnology ransfer beomes muually rofable.. Produ Knowledge Transfer In hs aer he un roduon os and he qualy of he rodu are ndeenden. Moreover, eah frm s rof s drely relaed o s own rodu qualy and nversely relaed o he rval s rodu qualy see 6. Therefore, we may hnk of he ossbly of ransferrng he assoaed knowledge of rodung he hgh qualy from he hgh qualy rodung frm o he low qualy rodung frm. In he os-ransfer suaon, boh he frms wll oerae wh he hgh qualy rodus. So when, our queson s: Wll suh knowledge ransfer be rofable o he frms under he fee onra? The os-ransfer ayoffs of he frms wll be

14 Π Π We an easly show ha 8 8 [ ] Π [ ] Π > Π Π f and only f 0 > Therefore, for knowledge ransfer o be rofable s neessary ha he sueror qualy rodung frm has an neffen mehod of roduon. And hen we need ha he ehnology dfferenal mus be suffenly large omared o he rodu qualy dfferenal. Inerreaon of he resul s smlar o he revous ase. The rual requremen s ha he oenal ransferee should have suffenly large marke share n he re-ransfer suaon. Furher observe ha ondons 9 and may or may no hold smulaneously. Therefore s ossble o have a senaro where only knowledge ransfer s rofable bu ehnology ransfer s no. Ths s he ase when > /. Cross-Lensng In he las wo subseons we have noed ha for ehnology ransfer or for rodu knowledge ransfer s neessary ha f one frm has suerory n roduon ehnology, he oher frm mus rodue a beer qualy. Therefore, gven ha eah frm has some advanage over s rval eher n qualy or n ehnology, we may hen ask he queson: Can he frms gan by ombnng her reseve advanages, ha s, by sharng her sueror ehnology as well as knowledge of rodung sueror qualy? The frms generally rea ha benef by ross-lensng her reseve advanages. In our model, however, ross-lensng s no rofable o he frms. Le us wre he resul formally. 4

15 Prooson : Gven < and <, ross-lensng ehnology and qualy wll never be rofable. Under ross-lensng boh he frms beome denal. Then he resul follows beause under ross-lensng he ndusry rof derved usng 6 s /8[] < π π. The smle nuon of he resul s ha one he frms have he same qualy of goods, he fere re omeon wll drve her rofs o a low level..4 Welfare Imlaons We now dsuss welfare mlaons of ehnology ransfer and rodu knowledge ransfer n our model. Frs onsder ehnology ransfer. Le us assume < and > Under hs ondon, ehnology ransfer from frm o frm s muually rofable. Ths means, he ndusry rof s larger n he os ransfer suaon. Therefore, roduers surlus as a whole goes u. To see he effe on onsumers welfare, noe ha n he os-ransfer suaon he res and marke shares of he frms are: ~ ~ ~ D ~ D ~ [ ] [ ] ~ x 6 ~ x 6 [ ] [ ] Clearly, <,, and ~ x > x. The use of sueror roduon ehnology along wh re omeon neessarly redues res harged by he frms, and n he new equlbrum some onsumers shf from frm o frm. Thus, all onsumers n he nerval [0, x ] and [x ~, ] rean her reseve hoes of frms and qualy unhanged bu buy a a lower re han before. Bu he onsumers n he nerval [ x, ~ x ] who were buyng from frm n he re-ransfer suaon, has now oon o buy from frm a a 4 5 5

16 lower re, bu her omal deson has been o swh o frm and buy he hgh qualy rodu. Hene hey are also beer off n he os-ransfer suaon. Therefore, all onsumers wll be beer off f ehnology ransfer ours, and under ondon, ehnology ransfer wll our. Now onsder rodu knowledge ransfer. I s easy o see ha n he os-ransfer suaon ransferor s rodu re wll fall and ransferee s rodu re wll go u, beause afer ransfer, ransferor faes more omeon and ransferee sules a hgher qualy. Marke share of he ransferee wll also go u. For examle, f > along wh > s sasfed, hen rodu knowledge wll be ransferred from frm o frm, and n he os-ransfer suaon, <, > and x < x. Then onsumers n he nerval [ 0, x ] onnue o buy he hgher qualy rodu from frm, bu now a a lower re. Consumers n he nerval [ x, x ] buy he hgher qualy rodu from frm n he re-ransfer suaon a re, bu n he os-ransfer suaon hey buy he same qualy rodu from frm a re, whh s lower han, herefore, hey are also beer off. Fnally, onsumers n he nerval [ x,] nally buy he low qualy rodu from frm a re, bu n he os-ransfer suaon hey buy he hgh qualy rodu from he same frm a a re >. I an be easly shown ha hey are also geng hgher uly. Hene we have he followng resul. Prooson : Consumers welfare mus go u n he os-ransfer suaon.. Tehnology Transfer aross Counres Noe ha he onsumers n he nerval [, ~ x x] are ayng a hgher re ~ > n he os-ransfer suaon, sll hey are beer off beause hey are now buyng a hgher qualy rodu. We have [ u, u, ] dx > 0. x 6

17 In hs seon we exend he revous model o analyze he ossbly of ehnology ransfer beween wo frms aross he border. So onsder he suaon where he frms belong o wo dfferen ounres. Le us denfy frm as loal frm and frm as foregn frm. Inally boh are omeng n he loal or domes marke. Furher assume ha here s a radng os τ o be nurred by he onsumers f o buy foregn frm s rodu. Obvously, f τ 0, he dsnon beween foregn and loal frms beomes blurred, and n ha ase he resen model s redued o he revous model as far as he neraon beween hese frms s onerned. Wh τ > 0 we rewre he uly funon as, v x u v x The re-ransfer ayoffs of he frms are Π Π 8 8 and he os-ransfer ayoffs are: ~ Π ~ Π 0 0 -τ [ τ ] [ τ ] 8 8 [ τ ] [ τ ] f o buy from frm f o buyfrom frm We examne wheher τ s layng any dsn role n hs model Le us assume > and onsder he ossbly of ransfer of foregn ehnology o he loal frm. I s hen easy o ge ha suh a ransfer under he fee onra s muually rofable f and only f > 9 τ The followng rooson fouses on he morane of he exsene of a radng os n he onex of ehnology ransfer aross borders. 7

18 Prooson 4: Gven a osve radng os, even f he loal frm rodues no-beer han foregn qualy rodu, a rofable ehnology rade s ossble f he radng os s suffenly large. Gven he radng os, by means of ransfer he foregn frm an save and herefore an aure as lense fee a ar of he radng os, beause a larger roduon wll now ake lae n he loal ounry. Obvously, he ondon beomes relaxed f he loal frm rodues sueror qualy rodus and/or he frms are lose n rese of her nal ehnologes. In hs onex one may hnk of a senaro where he loal frm ossesses a sueror ehnology, ha s, > rofable? The relevan ondon s:. Is ehnology ransfer from he loal frm o he foregn frm > 0 τ Clearly, for ehnology ransfer o be rofable, s now neessary ha τ >. Therefore, a more srngen ondon s needed o make he ransfer rofable for he loal frm. The reason s he followng. The foregn frm whh has a dsadvanage due o exsene of a arff or radng os, s now n a more omeve oson n he osransfer suaon. Bu unless s rodu qualy s suffenly large, wll no be able o omensae, as lense fee, he loss of ayoff of he loal frm. 4. Tehnology Transfer under Royaly Conras In hs seon we onsder royaly equlbrum under he assumon of `full marke overage. Le us assume <, and onsder ehnology ransfer from frm o frm under a royaly onra. Sne nally boh frms have osve marke shares, we have > max{ /, / } We shall ge he smlar resul f we onsder he ossbly of rodu knowledge ransfer n hs ase. If >, he relevan ondon for ransfer s τ >. 8

19 Now gven, le us assume <. Clearly, s a suffen, bu no neessary, ondon o sasfy he nequaly. Wh hs, havng a osve marke share of eah frm mles > Then, gven any royaly r, he equlbrum res are 4 ˆ ˆ r r r r The orresondng marke shares and rof levels of he frms are resevely: ˆ ˆ r D r D and r r r Π Π ˆ ˆ Noe ha any suh royaly onra s aeable o frm beause, gven >, we have. Furher noe ha, and are ndeenden of ˆ Π Π r ˆD ˆD ˆΠ r, bu, and are lnear and nreasng funon of ˆ ˆ ˆΠ r. Hene he aenee frm has an nenve o nrease r as muh as ossble sube o he resron of `full marke overage ; n resonse frm wll us rase s re lnearly whou losng s marke share. 4 The seond sage roblem of frm s:, max D r and frm s roblem s:.,, max rd D 9

20 v Now, gven v > 0 see Eqn., he onsumer loaed a x f he buys from frm, and v x x enoys a surlus f he buys from frm. Tha s, nrease n r only exras onsumer surlus by nreasng he res of he goods. Therefore, under he assumon of `full marke overage, r an be nreased as long as he xˆ -h onsumer araes n onsumon. We assume ha a onsumer araes n onsumon f he enoys a non-negave surlus.e., u xˆ 0 from onsumon. So he maxmum ossble royaly s deermned orresondng o u xˆ 0. Ths gves he royaly rae Clearly, We an furher hek ha r ˆ v 4 rˆ > 0 ff < v > beause we have. v >. Now onsder any,. Then he royaly onra on rˆ an be sgned f and only f Πˆ rˆ Π. Ths means, usng 6, and 4, v > The L.H.S. of 5 s lnear and fallng funon of, wh osve neres, and he R.H.S. of 5 s onvex and fallng bu never nerseng any axs. Furher, L. H. S. v and Then L. H. S. > R. H. S. f and only f v R. H. S. 6[ ] > 6 6 0

21 Clearly, he nequaly 6 s sasfed rovded ha s no oo large. Ths means, ˆ, < ˆ < suh ha L. H. S. of 5 > R. H. S. of 5, ˆ. Hene we an wre he followng rooson. Prooson 5: Assume, ˆ and s no large enough. Then under royaly onras he omal royaly rae s rˆ. Sne Πˆ r Π, he ransferor an, n fa, enhane s rof by wrng a fee lus royaly onra, Lˆ, rˆ, where Lˆ Πˆ rˆ Π, and n hs ase he resron on s relaxed beause now ˆ wll have o sasfy he nequaly Πˆ rˆ Lˆ Π. Fnally, f we relax he assumon of `full marke overage and herefore assume ha eah onsumer buys a mos one un of he rodu, hen learly as r goes beyond he level of rˆ, he xˆ -h onsumer dros ou, and hen here s a rade off beween fall n demand and nrease n royaly. I may be observed ha he exsene of veral rodu dfferenaon has no muh role o lay n he ase of royaly equlbrum. For nsane, assume and hus resr o he ase of horzonal rodu dfferenaon only. 5 Then our resuls reman unhanged o be more rese, beome more shar. On he oher hand, ransor os whh does no lay any seal role n he analyss of fee lensng, lays an moran role n a royaly onra. 5. Conluson Ths aer analyzes ehnology ransfer agreemens beween wo asymmer frms whose rodus are boh verally and horzonally dfferenaed. Horzonal dfferenaon s due o he frms dfferng loaons on he Hoellng lne, and veral 5 Poddar and Snha 004 have red o derve royaly equlbrum under saal omeon bu her resuls seem o be norre see Kabra and Lee 008.

22 dfferenaon s n he form of dfferng rodu quales erfely ereved by he onsumers. A he ouse boh loaon and qualy are gven for eah frm. The effen frm frs dedes wheher o ransfer s sueror ehnology o he less effen frm. Then n he seond sage hey omee n re. The man queson dsussed n he aer s wheher and under wha rumsanes s ossble o have a ransfer of ehnology beween he frms when hey have dfferen roduon ehnologes and dfferen rodu quales. As far as royaly equlbrum s onerned, n our seng veral dfferenaon has no seal be; of ourse, ransor os lays an moran role. On he oher hand, he degree of veral rodu dfferenaon s rual for ransfer of ehnology under a fxed fee onra. In our model a hgh-qualy low-os frm has no nenve o share s ehnology wh a low-qualy hgh-os frm. Indeed, for denal gven res, and akng no aoun ha loaons are also gven, he hgh-qualy frm has a hgher demand as ges more onsumers. For gven denal quales, he low-os frm an se a lower re and herefore has also a more demand. Thus here s no gan o share s ehnology for a frm ha has a beer ehnology as well as a hgh qualy good. Hene, n hs model, only a low-qualy low-os frm may wan o share s ehnology wh a hgh-qualy hgh-os frm. One rual assumon made n he aer s ha he qualy of he rodu s ndeenden of he un os of roduon. Ths s no an absoluely unreals assumon. Qualy of a rodu deends on an nu-mx whereas he un os of roduon deends on he hoe of a roduon roess. Thus, gven a qualy of a rodu, he same qualy an be rodued by dfferen mehods of roduon and herefore has dfferen un oss of roduon. Of ourse, nnovang a hgher qualy nvolves a larger R&D os. Bu n he onex of our aer he R&D os s already sunk. Ths erms us dsuss he ossbly of ransferrng knowledge assoaed wh he sueror rodu qualy o he low-qualy frm and nqure wheher frms have an nenve o rade a beer ehnology for a beer qualy. In our aer ross-lensng of

23 he reseve advanages under a fee onra s never rofable. Then we have rovded a welfare analyss. We have shown ha when ehnology ransfer or knowledge ransfer ours, he welfare effe s osve. Consumers welfare as well as global welfare always goes u. We have exended he model o dsuss he queson of lensng n an oen eonomy. In arular, we have foused on he morane of a arff or radng os n hs onex. The exsene of suh a arff relaxes he ondon of ransfer. We have shown ha f here s a suffenly large radng os, ehnology ransfer beween wo frms wll always be rofable, rreseve of he dfferenes n quales and ehnologes. To onlude, noe he followng. In our aer he low-qualy low-os frm ransfers s roduon ehnology o he hgh-qualy hgh-os frm rovded ha suh a ransfer s rofable. As an alernave, he effen frm ould ossbly nves n mrovng s rodu qualy. Ths s beyond he soe of hs aer. In a model of veral rodu dfferenaon frms have an nenve o nrease he ga beween quales. Bu n our seng he low-qualy frm has an nenve o have a beer qualy and hus redue he ga beween quales, whereas he hgh qualy frm does no benef from a reduon n he qualy ga, and herefore, has no neres o see s omeor havng a beer qualy.

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26 Wang, X. H. 00, Fee versus Royaly Lensng n Dfferenaed Courno Olgooly, Journal of Eonoms and Busness 54, Wang, X. H. and B. Z. Yang 999, On Lensng under Berrand Comeon, Ausralan Eonom Paers 8,