Knowledge sllover lensng and atent roteton Art Mukheree * YE Keele Unversty U.K. January 00 Abstrat: Ths aer nvestgates the effet of dfferent atent regmes on R&D nvestment and soal welfare n a duooly market wth unertan R&D roess. We fnd that strong atent roteton nreases R&D nvestment of at least one frm but whether both frms R&D nvestment wll be more under strong atent roteton s ambguous. Whle e-ante welfare s more lkely to be hgher under strong atent roteton e-ost welfare may be hgher under strong atent roteton. Whether the ossblty of lensng nreases both frms R&D nvestment s also ambguous. Lensng wth u-front fed-fee an nrease oly dlemma by nreasng the ossblty of hgher e-ante welfare under strong atent roteton but hgher e-ost welfare under weak atent roteton. However the results may be dfferent for lensng ontrat wth er-unt outut royalty. Key Words: Knowledge sllover Lensng Patent roteton Unertan R&D JEL Classfatons: D43 L13 O34 Corresondene to: Art Mukheree Deartment of Eonoms Keele Unversty Staffordshre ST5 5BG U.K. E-mal: a.mukheree@keele.a.uk ; Fa: +44-178-717577 * I would lke to thank Jong-Hee Hahn and Tarun Kabra for helful omments and suggestons. Ths aer s reared for the resentaton at the RES onferene 00. A relmnary verson of ths aer has been resented at the onferene enttled The future of nnovaton studes ECIS Endhoven. The usual dslamer ales. 1
1 Introduton Tehnologal rogress s an mortant fator for develoment and growth of an eonomy. An eonomy an nrease her tehnologal aablty through several ways. Two domnant ways to nrease tehnologal aablty are ndgenous researh and develoment R&D and tehnology lensng. Researhers workng on ndustral organzaton and nternatonal eonoms have already analyzed several ssues on R&D nvestments and otmal R&D organzatons n olgoolst ndustres see e.g. Renganum 1983 d Asremont and Jaquemn 1988 Mart 1991 Combs 199 Suzumura 199 Cho 1993 Beath et al. 1998 Poyago- Theotoky 1998 and Kabra and Mukheree 000. It has been found that knowledge sllover and unertanty n R&D are two maor onerns to the frms dong R&D. Whle the strategy on R&D nvestment may hel frms to overome the roblem of unertanty atent oly an nfluene knowledge sllover. However the above aers dd not ay attenton to eamne the role of dfferent atent oles on the nentves for R&D and soal welfare. There s another lterature eamnng the effets of dfferent atent systems on R&D see e.g. Glbert and Sharo 1990 Klemerer 1990 Galln 199 and Mukheree and Pennngs 001. But these aers gnored the ossblty of R&D by all the frms n the ndustry and onentrated on a re-defned sequene of R&D. However the abovementoned two sets of aers share a ommon feature vz. these aers more or less gnored the ossblty of other busness strateges suh as tehnology lensng whle analyzng R&D desons. 1 Hene whle the ossblty of tat knowledge or hgher ost assoated wth lensng an ustfy the revous works those works are not omletely relevant n those ndustres where lensng s not dffult. The resent aer starts off wth ths bakground and eamnes the mlatons of dfferent atent systems on R&D nvestment and soal welfare wth and wthout the ossblty of lensng e-ost R&D. In what follows seton onsders a duooly model of R&D ometton under dfferent atent systems. For smlty we onsder two dfferent atent systems alled
weak and strong atent rotetons. We assume that knowledge sllover s ossble only under weak atent roteton. We show that whether strong atent roteton nreases R&D nvestment of all frms omared to weak atent roteton s ambguous. If R&D funtons of these frms are suffently asymmetr then strong atent roteton an nrease R&D nvestment of one frm but an redue R&D nvestment of the other frm. But for more symmetr frms R&D nvestment of both frms s hgher under strong atent roteton omared to weak atent roteton. However there wll be no nfluene on R&D nvestment f n ase of unlateral suess n R&D the suessful frm beomes the monooly even under weak atent roteton. Usng a ross-ountry analyss wth aggregatve R&D data Varsakels 001 has shown that ountres wth a strong atent roteton nvest more n R&D. Hene the resent aer asks for frm level analyss and rovdes a testable hyothess regardng the nfluene of dfferent atent systems on R&D nvestment of ndvdual frms. 3 We show that the estene of unertanty n R&D an lead to a onflt between e-ante and e-ost soal welfare. If ost reduton from R&D s suffently small or the degree of knowledge sllover s suffently large then e-ost welfare wll be more under weak atent roteton. But for suffently large ost reduton and for suffently low knowledge sllover e-ost welfare wll be more under strong atent roteton. However as robablty of nnovaton nreases under strong atent roteton the e-ante welfare s lkely to be hgher under strong atent roteton when the effet of R&D nvestment on the robablty of suess s suffently strong. The ossblty of lensng e-ost R&D may enourage the frms to engage n tehnology lensng. We onsder ths ossblty n setons 3 and 4 by nororatng the ossblty of fed-fee lensng and lensng wth er-unt outut royalty resetvely. Wth fed-fee lensng we show that lensng s more lkely to our under weak atent 1 In a model of R&D ometton wth no unertanty n R&D Kultt and Takalo 1998 looked at the ossblty of ross lensng e-ost R&D. It s well known that atents do not always revent sllover of the researh results see e.g. Levn et al. 1987. Further the effeny of a atent system deends on the nature of ndustres. Though for smlty we assume that strong atent roteton does not enourage knowledge sllover our qualtatve results wll hold as long as one assumes hgher knowledge sllover under weak atent roteton omared to strong atent roteton. 3
roteton. The ossblty of fed-fee lensng s lkely to nrease the dfferene of total R&D nvestment between these atent systems when lensng s rvately roftable under both atent systems. But f lensng s roftable only under weak atent roteton then the dfferene of total R&D nvestment redues between these atent systems. However when lensng s roftable under both atent systems then by reatng e-ost welfare lkely to be hgher under weak atent roteton and e-ante welfare lkely to be hgher under strong atent roteton the ossblty of lensng may nrease the oly dlemma. If lensng s roftable under weak atent roteton only then both e-ante and e-ost welfare are lkely to be hgher under weak atent roteton. If lensng onssts of er-unt outut royalty then royalty nome wll be hgher under weak atent roteton when ost reduton from R&D s suffently large. Therefore unlke fed-fee lensng lensng ontrat wth er-unt outut royalty an have hgher mat on R&D nvestment under weak atent roteton than strong atent roteton. The analyss on welfare shows that unlke fed-fee lensng ontrat e-ante welfare s lkely to be hgher under weak atent roteton when ost reduton from R&D s not suffently low. Thus ths aer shows the mortane of the tyes of lensng ontrat for our results. Ths aer an be related to the lterature on lensng also see e.g. Rokett 1990 Mart 1990 Kabra and Mart 1993 Mukheree 001. One ommon feature of these aers on lensng s the absene of R&D roess n ther framework. Contrary to ths the resent aer onsders the dynam effet of R&D and tehnology lensng. 4 The rest of the aer s organzed as follows. In the seond seton we onsder a two-stage game of R&D ometton n seton. Seton 3 etends ths two-stage game to a three-stage game by nororatng the ossblty of a lensng ontrat e-ost R&D. In ths seton we onentrate on fed-fee lensng ontrat. Then we eamne the mlaton of a lensng ontrat wth er-unt outut royalty n seton 4. Seton 5 onludes the aer. Due to the shortage of sae readers are requested to refer the 3 A reent overvew on the benefts and osts of atent roteton s gven by Mazzolen and Nelson 1998. 4 In totally dfferent ontet and framework Galln and Wnter 1985 and Katz and Sharo 1985 fous on the effet of lensng on R&D. Whle Galln and Wnter 1985 dentfy the ondtons for lensng n a searh-theoret model of R&D Katz and Sharo 1985 fous on the nentves to develo a roess when there s a ossblty of lensng by the atent holder to ts omettor. 4
workng aer Mukheree 00 for the dervatons of the results of ths aer or may be avalable from the author uon request. A two-stage game of R&D ometton Consder that there are two frms say 1 and n the ndustry ometng for an nnovaton. Suose the frms have a tehnology that orresonds to a onstant average ost of roduton > 0 and they are tryng to nvent a tehnology that orresonds to a onstant average ost of roduton where > 0. However the suess n R&D s robablst and the unondtonal robablty of suess n R&D =1 nreases wth R&D nvestment where s frm s R&D nvestment. We onsder that > 0 < 0 0 = and = 0 for =1. So we allow for the dfferene n robablty funtons between these frms. However for smlty we onsder that f the two robablty funtons are dfferent there s no ossblty of rossng of these funtons. Wthout loss of generalty we onsder that for same R&D nvestment robablty of suess n R&D for frm 1 s at least as good as that of for frm.e. 1 1 for 1 = and > 0 =1. Unertanty n the R&D roess an lead to unlateral suess n R&D and generates tehnologal dfferene e-ost R&D. We assume that knowledge sllover hels to redue the ost of roduton of the unsuessful frm n ase of tehnologal dfferene. Therefore f both frms sueed or fal n R&D then there s no ossblty of knowledge sllover. However knowledge sllover deends on the tye of atent roteton of the eonomy. In the followng analyss we wll onsder to dfferent atent rotetons weak atent roteton and strong atent roteton. A relatvely strong atent roteton redues knowledge sllover between the frms. For smlty here we assume that knowledge sllover s ossble only under weak atent roteton. Hene n ase of unlateral suess n R&D the effetve onstant average ost of roduton of the unsuessful frm s gven by α wth α [ 1] where α shows the degree of knowledge sllover. Whle α = mles erfet knowledge sllover α = 1 mles no knowledge sllover. Therefore strong atent roteton mles α = 1. 5
6 We assume that the nverse market demand funton s gven by q a P = 1 where the notatons have usual meanng wth a >..1 Weak atent roteton Frst onsder otmal R&D nvestments under weak atent roteton. Here the frms eerene a knowledge sllover n ase of unlateral suess n R&D and the effetve ost of the unsuessful frm s gven by α. Therefore the net eeted roft of the th frm are 1 1 1 + + π π π for a + α and 1 1 α π α π π + + + 1 1 π for a + α 3 where =1 the frst and seond argument of the π funton show the margnal ost of th and th frm resetvely and π shows the monooly roft of frm. The mamzaton of and 3 wth reset to gves us the followng frst order ondtons resetvely 1 1 1 = + π π π for a + α 4 and 1 α π α π π + 1 1 = π for a + α. 5 It s easy to hek that the seond order ondtons for mamzaton are satsfed. Equaton 4 and 5 mltly defne frm s reaton funtons * where =1
and. These reaton funtons show the roft mamzng levels of gven. Solvng these reaton funtons we get the otmal R&D nvestments for these frms. We onsder that the robablty funtons are suh that we get unque equlbrum for R&D nvestment. Prooston 1: a The reaton funtons are negatvely sloed and the absolute sloe of the reaton funtons s less than 1. b If R&D rodutvty 5 of frm s more than frm =1 and.e. > then equlbrum R&D nvestment of frm s more than frm. The equlbrum robablty of suess n R&D s also hgher for frm than frm.e. > n equlbrum. See Mukheree 00 for the dervaton of the above rooston.. Strong atent roteton Now we onsder the R&D game under strong atent roteton where knowledge sllover s not ossble. Therefore here the net eeted rofts of the th frm are gven by π + 1 π + 1 1 π for and a + 6 π + 1 π + 1 π a + + 1 1 π for 7 where =1. Mamzng 6 and 7 we get the resetve frst order ondtons for otmal R&D nvestment of the th frm =1 : 5 Here by R&D rodutvty we mean the effet of R&D nvestment on the robablty of suess. Hene hgher rodutvty mles that same R&D nvestment an lead to hgher robablty of suess n R&D. 7
π + 1 π 1 π = 1 a + for 8 and π + 1 π π a + 1 π = 1 for. 9 Seond order ondtons for mamzaton are satsfed. Further we an have the fndng smlar to Prooston 1 even for strong atent roteton..3 Comarson between weak and strong atent rotetons.3.1 Effet on R&D nvestments It s lear that f ost reduton from R&D s suffently large and knowledge sllover s suffently small then n ase of unlateral suess n R&D the suessful frm beomes a monooly under both atent systems see 4 and 8. Hene here atent rotetons do not have any nfluene on the R&D nvestments of these frms. Now onsder the stuaton where n ase of unlateral suess n R&D the unsuessful frm an omete n the market under both weak and strong atent rotetons. Therefore here 5 and 9 are the relevant frst order ondtons for otmal R&D nvestments. From these eressons we see that gven frm wll nvest more n R&D under strong atent roteton than weak atent roteton. Therefore the reaton funtons for both the frms wll shft outward under strong atent roteton omared to weak atent roteton. However whether the equlbrum R&D nvestment of both frms wll be hgher under strong atent roteton omared to weak atent roteton deends on the relatonsh between the robablty of suess n R&D and R&D nvestment. The outward movement of a frm s reaton funton wll be more when the margnal roftablty of her R&D nvestment redues slowly. Therefore f a frm s nremental gan from hgher R&D nvestment s more then t gves that frm hgher nentve for R&D nvestment. So f the robablty funtons of these frms dffer sgnfantly then t s more lkely that the equlbrum R&D nvestment of one frm other frm wll be more less 8
under strong atent roteton omared to weak atent roteton. But for frms wth more symmetr R&D rodutvty the smlar outward movement of both the reaton funtons wll lead to hgher R&D nvestment by both frms under strong atent roteton. Fgure 1 shows the effet of dfferent atent systems on the reaton funtons for a+ R&D nvestments wth <. The fgure shows frm 1 s and s reaton funtons as NN and HH resetvely under weak atent roteton and Y shows the equlbrum R&D nvestments. Strong atent roteton shfts the reaton funtons of both frms towards rght. If new equlbrum of R&D nvestments does not our n the range XYZ then one frm s R&D nvestment nreases under strong atent roteton whle the other frm s R&D nvestment dereases under strong atent roteton. In ths fgure we show that MM and GG are the reaton funtons of frm 1 and resetvely under strong atent roteton. Therefore new equlbrum s at K and frm 1 s frm s equlbrum R&D s more less under strong atent roteton omared to weak atent roteton. Fgure 1 If n ase of unlateral suess n R&D the unsuessful frm an omete n the market under weak atent roteton only then the relevant frst order ondtons are 5 and 8. The omarson of 5 and 8 shows that gven the R&D nvestment of the omettor t s always better for a frm to nvest more n R&D under strong atent roteton omared to weak atent roteton. However lke the revous stuaton whether equlbrum R&D nvestment of both frms wll be more under strong atent roteton s ambguous smlar to Fgure 1. The followng rooston summarzes the above dsusson. Prooston : a If knowledge sllover s not large enough and ost reduton from a+ suessful R&D s suffently large.e. α then R&D nvestments under weak and strong atent rotetons are same. a+ b If ether ost reduton from R&D s not suffently large.e. < or knowledge a+ sllover s suffently large.e. α < then R&D nvestment of at least one frm s more under strong atent roteton omared to weak atent roteton. 9
It has been argued n the lterature that strong atent roteton nreases R&D nvestment n a ountry see e.g. Varsakels 001. But above result shows that the effet of atent systems on the frm level needs more nvestgaton..3. Imat on soal welfare Now we would lke to nvestgate how dfferent atent systems affet soal welfare. Here by soal welfare we mean the summaton of ndustry roft net of R&D nvestment and onsumers surlus. We wll show that the estene of unertanty n R&D may lead to dfferenes n e-ante and e-ost welfare..3..1 E-ost welfare under weak and strong atent rotetons We start our analyss by lookng at the e-ost soal welfare under both atent regmes. If both frms sueed or fal n R&D then both frms ost of roduton wll be same rresetve of the atent roteton. The analyss n subseton.3.1 shows that R&D nvestment wll hange under these atent systems when the unsuessful frm ometes at least under weak atent roteton n ase of unlateral suess n R&D. Therefore gven a duooly market struture under unlateral suess n R&D f both frms sueed or fal n R&D we an say that wth hgher total R&D nvestment under strong atent roteton 6 e-ost welfare wll be hgher under weak atent roteton relatve to strong atent roteton. 7 Now we eamne what wll haen f there s an unlateral suess n R&D. If n ase of unlateral suess n R&D the suessful frm beomes a monoolst under weak and strong atent rotetons then the effetve ost of roduton and R&D nvestments of these frms are same under both atent systems. Hene here e-ost soal welfare remans same under these two atent systems. 6 Total R&D nvestment nreases under strong atent roteton omared to weak atent roteton f the absolute sloe of the reaton funtons for R&D nvestment s less than 1 whh has been satsfed for ths analyss Prooston 1a. 7 E-ost welfare wll be same when the suessful frm beomes a monooly n ase of unlateral suess n R&D as n ths stuaton R&D nvestments wll not be nfluened by the atent systems. 10
Net onsder the stuaton where under unlateral suess n R&D the unsuessful frm an omete n the market at least under weak atent roteton. Hene n ths stuaton t s lear that the ost asymmetry beomes more under strong atent roteton than weak atent roteton. Gven the demand and ost sefatons n ase of unlateral suess n R&D ndustry roft n the rodut market and onsumer surlus under weak atent roteton s gven by a + α a α + a α W w e = + +. 10 9 9 18 But under strong atent roteton the ndustry roft and onsumer surlus s ether W s e or W s e a + a + a a+ = + + for 11 9 9 18 a a a+ = + for. 1 4 8 Prooston 3: a If n ase of unlateral suess n R&D the suessful frm beomes a monooly under weak atent roteton then e-ost soal welfare s same under weak and strong atent rotetons rresetve of the number of suessful frm n R&D. b Suose that n ase of unlateral suess n R&D the suessful frm annot be the monooly. Then f ether both frms sueed or nether frm sueeds n R&D e-ost welfare s hgher under weak atent roteton. Suose n ase of unlateral suess n R&D the unsuessful frm an omete n the rodut market at least for weak atent roteton. Then e-ost welfare s more under weak atent roteton than that of under strong atent roteton when ether ost reduton from R&D s suffently small or knowledge sllover s suffently large. But for suffent large ost reduton from R&D and wth suffently low knowledge sllover e-ost welfare s more under strong atent roteton than weak atent roteton rovded the dfferene between total R&D nvestments under these atent systems s not suffently large. See Mukheree 00 for the roof of the above rooston. Ths result shows that even f weak atent roteton ndues knowledge sllover soal welfare may be more under strong atent roteton f the degree of knowledge sllover s suffently small. 11
Knowledge sllover hels to rase onsumer surlus by redung the effetve ost of the unsuessful frm but at the same tme t redues the roft of the suessful frm who has relatvely better tehnology than the unsuessful frm. Ths loss n roduton effeny may be larger than the gan n onsumer surlus. 8.3.. E-ante welfare under weak and strong atent rotetons Whle e-ost soal welfare deends only on the outomes of R&D and R&D nvestment robablty of suess s also mortant for e-ante soal welfare. For eamle lower ometton due to relatvely hgher ost of roduton of the unsuessful frm under strong atent roteton an redue e-ost welfare under strong atent roteton omared to weak atent roteton. But suffently hgher R&D nvestment under strong atent roteton an redue the hane of lower ometton under strong atent roteton sgnfantly and an rovde hgher e-ante welfare under strong atent roteton omared to weak atent roteton. It s easy to understand that e-ante welfare s same under these atent systems when n ase of unlateral suess n R&D the suessful frm beomes monooly under weak atent roteton. Ths s beause here R&D nvestments are same under both atent rotetons. Now onsder that even under unlateral suess n R&D the market beomes duooly under weak atent roteton. Hene e-ante welfare under weak atent roteton wll be W w ea = w w w w 1 1 We + [ 1 1 1 w + 1 α. 13 w w w w w w w w 1 1 ] We + 1 1 1 1 We 1 But e-ante welfare under strong atent roteton wll be ether W or s ea = s s s s s s s s 1 1 W + [ 1 1 1 + 1 1 1 ] W e s s s s s a+ + 1 1 1 1 We 1 for 14 e 8 The ossblty of welfare of loss due to ost reduton n a Cournot olgooly has also addressed n Lahr and Ono 1988. 1
W s ea = s s s s s s s s 1 1 W + [ 1 1 1 + 1 1 1 ] W e s s s s s a+ + 1 1 1 1 We 1 for e 15 where W s e shows e-ost welfare under strong atent roteton when only the suessful frm rodues n the market. Consder the followng lemma whh wll hel us n the followng analyss. Lemma 1: We have a W > W W b W > W W e e > a+ where and W W e > e α. e e e > e See Mukheree 00 for the dervaton of the above lemma. Now we are n a oston to eamne the effets of dfferent atent systems on eante welfare. Frst onsder a stuaton where n ase of unlateral suess n R&D the summaton of onsumer surlus and total roft n the rodut market s more under weak w s w s atent roteton.e. W α W and W α W. Then from the e > e e > eressons 13 15 t s lear that e-ante welfare an be more under strong atent roteton than weak atent roteton only f the robablty of at least one suess n R&D.e. β = + 1 + 1 whh s the 1 1 1 1 1 1 summaton of both-suess n R&D.e. γ = and only one suess n R&D 1 1.e. δ = 1 + 1 nreases under strong atent 1 1 1 1 roteton. It s easy to hek that the robablty of at least one suess nreases under strong atent roteton. 9 Net onsder the stuaton where e-ost welfare s more under strong atent w s roteton under unlateral suess n R&D.e. W α W. Sne e e < robablty of at least one suess s hgher under strong atent roteton n ths stuaton e-ante welfare wll be more under strong atent roteton. e 9 d d We have dβ = 1 11 d1 + 1 1 1 d = d γ and 1 1 d1 + 1 1 = d δ. 1 1 1 d1 + 1 1 1 13
Now we see how the analyss wll be affeted wth more asymmetr hanges n R&D nvestments. As one frm s R&D nvestment nreases say frm 1 s t redues the R&D nvestment of the other frm.e. frm. From Prooston 1 we know that frm 1 s R&D nvestment n equlbrum s more than the frm rovded frm 1 s R&D rodutvty s more than that of under frm.e. > and ths also mles that the 1 robablty of suess n equlbrum s hgher for frm 1 than frm.e. 1 >. So for hgher total R&D nvestment under strong atent roteton more asymmetr hanges n R&D nvestments nreases the robablty of at least one suess and robablty of only one suess n R&D. But whether ths wll nrease also the robablty of both-suess s ambguous. If 1 > 1 then more asymmetr hanges n R&D nvestment under strong atent roteton also nreases the robablty of both-suess. So f more asymmetr hanges n R&D nvestment does not redue the robablty of both-suess sgnfantly we an say that t s more lkely that more asymmetr hanges n R&D nvestment nreases the lkelhood of hgher e-ante welfare under strong atent roteton. Hene summarzng the above dsusson we an have the followng rooston. Prooston 4: a Sne robablty of at least one suess nreases under strong atent roteton t s more lkely that e-ante welfare s hgher under strong atent roteton. If summaton of onsumer surlus and ndustry roft n the rodut market s hgher under strong atent roteton then e-ante welfare s always hgher under strong atent roteton. b It s more lkely that e-ante welfare wll be hgher under strong atent roteton wth more asymmetr hanges n R&D nvestments. 3 A three-stage game of R&D ometton and lensng In ths seton we wll etend the analyss of the revous seton by allowng the ossblty of lensng e-ost R&D and wll eamne how the results are nfluened wth ths modfaton. We defne a tehnology by orresondng onstant average ost of roduton and lower onstant average ost of roduton mles better tehnology. 14
Tehnology lensng an take lae when there s a dfferene n tehnology. Hene lke knowledge sllover we assume that f both frms sueed or fal n R&D then there s no ossblty of lensng e-ost R&D. In ths seton followng Katz and Sharo 1985 Mart 1990 Mukheree 001 and many others we wll onsder that tehnology lensng takes lae aganst an u-front fed-fee. 10 Then n seton 4 we wll brefly onsder another oular lensng ontrat vz. lensng wth er-unt outut royalty and wll eamne how the results are affeted under ths lensng ontrat omared to fed-fee lensng ontrat. Sne tehnology lensng mles a delberate knowledge transmsson from the tehnologally sueror frm to the tehnologally nferor frm t s lkely that the amount of knowledge transmsson under lensng ould be more than that of under knowledge sllover. But the lenser may dede on the etent of knowledge transmsson. However as noted n Rokett 1990 the lenser wll ether transfer full knowledge or wll not lense at all when lensng onssts of u-front fed-fee. Hene here we onsder that n ase of lensng omlete knowledge transmsson wll take lae and hene eost lensng both frms wll rodue wth same tehnology. We onsder the followng game n ths seton. In stage one frm 1 and smultaneously nvest n R&D. Outome of R&D s realzed. Then n stage two the frms dede whether to do lensng. In our framework lensng wll be an oton e-ost R&D rovded only one frm sueeds n R&D. In stage three these frms omete lke Cournot duoolsts. We solve the game through bakward nduton. We wll onsder ths game under weak and strong atent rotetons. 10 It s often not ossble to montor a rval frm's outut as s neessary to enfore a royalty rovson n a atent lensng ontrat. Ths may be so for urely nformatonal reasons. Alternatvely ths an haen f after gettng the lensed tehnology the lensee an mtate or nvent around the tehnology easly and rodue outut wth the mtaton thereby avodng royalty ayments. Ths an be onsstent wth our assumton of weak and strong atent rotetons f one assumes that strong atent roteton elmnates knowledge sllover but does not revent non-nfrngng nventng around see Katz and Sharo 1985. 15
3.1 Tehnology lensng Sne lensng ats as a delberate way of sharng nformaton between the frms we have to fnd out when lensng s roftable. Lensng wll be roftable rovded ndustry roft under lensng s more than that of under no lensng. Prooston 5: Suose the lenser and the lensee have onstant average ost and resetvely wthout lensng and both of them have onstant average ost after a+ 3 lensng. Then lensng s roftable rovded <. 5 Sne ths result an be found n Mart 1990 also the readers may be referred to Mart 1990 for the roof of ths result. The above rooston shows that f the ntal tehnologes of these frms are suffently lose then tehnology lensng s roftable. When ntal tehnologes are suffently lose then under lensng the lenser does not fae muh hgher ometton from the lensee but lensng hels to nrease ost effeny n the ndustry. Hene the gan from ost reduton n lensee s frm outweghs the loss of roft of the lenser. So lensng nreases ndustry roft. But f ntal tehnologes are far away then the lenser beomes a near monooly wthout lensng. In ths stuaton the loss of roft to the lenser s frm due to hgher ometton from the lensee outweghs the gan from ost reduton n lensee s frm. Therefore f ntal tehnologes of these frms are far away then lensng s not otmal. From Prooston 5 t s lear that lensng wll take lae under weak atent a+ 3 roteton whenever α < but lensng an take lae under strong atent roteton 5 a+ 3 when <. Therefore under fed-fee lensng ontrat lensng s more lkely 5 outome under weak atent roteton than strong atent roteton. Though t looks slghtly aradoal the reason s very smle. Weak atent roteton ndues knowledge sllover and hene redues the beneft from atent roteton. Therefore ths nreases the nentve for ganng from nformaton sharng through lensng omared to a stuaton where hgher beneft from atent roteton redues the gans from lensng. 16
Further ths fndng rovdes a testable hyothess regardng the ossblty of lensng n an ndustry wth ometng lenser and lensee for dfferent atent systems. The above rooston has looked at the roftablty ondton for tehnology lensng but dd not onsder the rng of the tehnology. We assume that the re for the lensed tehnology wll be deded through a Nash barganng roess. Assume that the barganng ower of the lenser s gven by β and the barganng ower of the lensee s gven by 1 β. Further we wll assume that the barganng owers of the lenser and the lensee are ndeendent of the dentty of these frms.e. whether frm 1 or frm ats as lenser or lensee. Prooston 6: Assume that the barganng owers of the lenser and the lensee are β and 1 β resetvely. Denote the lensee s onstant average ost of roduton before lensng by z where z = under no knowledge sllover and z = α under knowledge sllover. Suose F shows the re of the tehnology. If frm lenses to frm where =1 and then re of the lensed tehnology s F = β π π z + 1 β π z π. 11 Refer to Mukheree 00 for the roof of the result. From Prooston 6 t s easy to hek that lense fee nreases wth large dfferene n ntal osts whenever lensng s otmal. Hgher ost of roduton of the lensee redues the reservaton ayoff of the lensee whh n turn hels the lenser to etrat more beneft from lensng through hgher lense fee. 3. Effet of lensng on R&D efforts Sne lensng wll our when the effetve ost of the unsuessful frm s greater than a+ 3 5 the analyss of the seton wll not be nfluened f ost reduton from R&D s suffently large and the degree of knowledge sllover s suffently small. In ths seton 11 The frst seond argument of the π funton stands for the onstant average ost of the th frm. 17
we onentrate on those osts and the degree of knowledge sllover suh that lensng s an otmal deson at least under weak atent roteton. Hene we an have the followng rooston. Prooston 7: a Consder that lensng s roftable only under weak atent roteton. Then the dfferene n total R&D nvestment as well as the asymmetry n R&D nvestment under weak and atent roteton delnes wth the resene of lensng omared to no lensng. b Consder that lensng s roftable under weak and strong atent systems. Then the dfferene n total R&D nvestment as well as the asymmetry n R&D nvestment under weak and atent roteton s lkely to nrease under lensng omared to no lensng. The roof of the above rooston s gven n Mukheree 00. From Prooston 6 t s lear that hgher barganng ower of the lenser nreases lense fee. Sne there s a ostve relatonsh between the lense fee and the amount of rghtward shft of the reaton funtons hgher barganng ower of the lenser s lkely to reate hgher asymmetry n equlbrum R&D nvestments. Hgher barganng ower nreases the gan from lensng and enourages both frms to nvest more n R&D. But ths wll hel a frm wth more R&D aablty to nvest more aggressvely n R&D omared to a frm wth low R&D aablty. As a result hgher barganng ower tends to nrease the asymmetry n equlbrum R&D nvestments. 3.3 Effet on welfare 3.3.1 Effet of lensng on e-ost welfare It s easy to understand that there wll be no effet when ether both frms sueed n R&D or nether frm sueeds n R&D. Further even under unlateral suess n R&D the ossblty of lensng may have an mat on e-ost welfare when lensng s a roftable oton. If lensng s roftable under both atent systems then t wll make both frms symmetr n the rodut market. Hene n ths stuaton the summaton of onsumer surlus and ndustry roft n the rodut market wll be same under both atent systems. 18
But hgher lense fee under strong atent roteton wll hel to nrease total R&D nvestment under strong atent roteton. So here e-ost welfare s more under weak atent roteton. If lensng s roftable only under weak atent roteton then the summaton of onsumer surlus and ndustry roft n the rodut market s gven by W e and W e for weak and strong atent roteton resetvely. Here W W e > see Lemma 1. Further t an be heked easly that here total R&D nvestment s more under strong atent roteton we an say that e-ost welfare s hgher under weak atent roteton. Hene the followng rooston s mmedate. e Prooston 8: Whenever lensng s rvately roftable for at least weak atent roteton e-ost welfare s hgher under weak atent roteton omared to strong atent roteton. 4a+ 7 In Prooston 3 we have seen that for > 11 and for suffently low knowledge sllover e-ost welfare beomes more under strong atent roteton omared to weak atent roteton. So ontrary to ths Prooston 9 shows that n ths stuaton the ossblty of lensng an hange our qualtatve onluson regardng eost welfare and an make hgher e-ost welfare under weak atent roteton. 3.3. Effet of lensng on e-ante welfare Frst onsder the stuaton where n ase of unlateral suess n R&D lensng s roftable under weak and strong atent systems. Hene n ths stuaton the summaton of onsumer surlus and ndustry roft n the rodut market s same under both atent systems. But hgher lense fee under strong atent roteton wll lead to hgher total R&D nvestment under strong atent roteton. Followng the log of the subseton.3.. we see that here the robablty of at least one suess nreases under strong atent roteton. Therefore f the dfferene n total R&D nvestment under weak and strong atent roteton s not suffently large then n ths stuaton e-ante welfare s always hgher under strong atent roteton. 19
Now onsder that lensng s rvately roftable only under weak atent roteton. Here lensng wll hange the eresson for e-ante welfare from 13 to the followng eresson: W w ea = w w w w w w w 1 1 + 1 1 1 + 1 1 1 ] W [ e + 1. 16 w w w w w 1 1 1 We 1 But e-ante welfare under strong atent roteton s gven by 14 or 15. From Lemma 1 and Prooston 7a we fnd that W e s greater than W e α and and the dfferene n total R&D nvestment between weak and strong atent roteton redues under lensng omared to no lensng. Whle the former effet tends to nrease the eost welfare under weak atent roteton for gven robablty of at least one suess the latter effet redues the dfferene between the robablty of suess under weak and strong atent systems. Therefore t redues the lkelhood of hgher e-ante welfare under strong atent roteton omared to weak atent roteton. We summarze the above dsusson n the followng rooston. W e Prooston 9: a Consder lensng s roftable under both weak and strong atent rotetons. Then e-ante welfare s always hgher under strong atent roteton omared to weak atent roteton when the dfferene n total R&D nvestments s not suffently large between strong and weak atent rotetons. Hene here lensng nreases the lkelhood of hgher e-ante welfare under strong atent roteton omared to a stuaton wth no lensng. b Consder lensng s roftable only under weak atent roteton. Then e-ante welfare s more lkely to be hgher under weak atent roteton under lensng relatve to no lensng. So unlke the effet on e-ost welfare the effet of lensng on e-ante welfare s ambguous. If the ost reduton from R&D s not suffently hgher so that n ase of unlateral suess n R&D lensng s a roftable oton under both atent systems the ossblty of lensng hels to nrease the e-ante welfare under strong atent roteton. But the ossblty of lensng hels to nrease e-ante welfare under weak atent 0
roteton when the ost reduton from R&D as well as the degree of knowledge sllover s suffently large. Thus ost reduton from R&D beomes mortant to determne whether the ossblty of lensng nreases e-ante welfare under weak atent roteton. 4 Lensng wth er-unt outut royalty In ths subseton we wll brefly eamne the mortane of another domnant way of lensng vz. lensng wth er-unt outut royalty. In fat wthout any nformatonal roblem or the absene of oortunsm on the art of the lensee ths ould be the otmal lensng ontrat see Rokett 1990 and Mukheree and Balasubramanan 001. Further for smlty n ths seton we wll onsder that the lenser has full barganng ower whh s enough for our urose. Hene t s lear that n ths stuaton lensng a+ wll be rvately roftable for all values of < and the lenser wll harge an outut royalty r = z where z = α under weak atent roteton and z = under strong atent roteton. 1 Hene lensng does not nfluene the effetve ost of roduton of the lensee but hels the lenser to nrease her roft through royalty nome. a+ 3 Prooston 10: Royalty nome s mamum at = 4. Effet of lensng wth er-unt outut royalty on equlbrum R&D nvestment wll be more under strong atent roteton a+ 3 f the ost reduton from R&D s suffently low.e. < 4. But for not so low ost a+ reduton from R&D and not large degree of knowledge sllover.e. α > 4 3 the effet of lensng wth er-unt outut royalty wll be more under weak atent roteton. Otherwse t wll deend on the ost reduton from R&D and the degree of knowledge sllover. The roof of the above result an be found n Mukheree 00. As the effetve ost of the frms are same under both the atent systems t s lear that the summaton of onsumer surlus and ndustry roft n the rodut market eet 1 Ths assumes that u-front fed-fee annot be negatve see e.g. Rokett 1990 and Mukheree and Balasubramanan 001. 1
royalty nome wll be same under lensng and no lensng. The analyss wthout lensng see subseton.3..1 shows that e-ost welfare s always hgher under weak 4a+ 7 a + 3 4a+ 7 atent roteton for < 11 where 4 < 11. We know that royalty nome s more a+ 3 a+ 3 under strong atent roteton for < 4. Hene for < 4 hgher royalty nome under strong atent roteton redues the lkelhood of hgher e-ost welfare under weak atent roteton omared to a stuaton wth no lensng f lensng does not nrease suffently large asymmetry n total R&D nvestments under these atent systems. If ost reduton from R&D s suffently large and the degree of knowledge sllover s not suffently large then we have seen n subseton.3..1 that e-ost welfare an be hgher under strong atent roteton. However royalty nome s more a+ 3 a+ 3 under weak atent roteton for > 4. Hene for > 4 hgher royalty nome under weak atent roteton redues the lkelhood of hgher e-ost welfare under strong atent roteton omared to a stuaton wth no lensng f lensng does not nrease suffently large asymmetry n total R&D nvestments under these atent systems. Hene whether lensng wth er-unt outut royalty nreases or redues the lkelhood of hgher e-ost welfare under weak atent roteton may deend on the ost of reduton from R&D and the degree of knowledge sllover. a+ 3 When ost reduton from R&D s suffently low.e. < 4 then the effet of lensng on the R&D nvestment s more under strong atent roteton as here royalty nome s hgher under strong atent roteton. Ths tends to rase the robablty of suess n R&D under strong atent roteton omared to weak atent roteton. Further n ase of unlateral suess n R&D hgher royalty nome under strong atent roteton nreases the summaton of onsumer surlus and ndustry roft n the rodut market. Thus both these effets under lensng make e-ante welfare more lkely to be a+ 3 hgher under strong atent roteton omared to no lensng. But for > 4 royalty nome s hgher under weak atent roteton omared to strong atent roteton. Hene n ths stuaton the effet of lensng on R&D nvestment as well as the hgher summaton of onsumer surlus and ndustry roft n the rodut market nreases under weak atent roteton. Thus here e-ante welfare more lkely to be hgher under weak atent roteton wth lensng omared to no lensng.
The followng rooston summarzes the above dsusson. Prooston 11: Consder lensng wth er-unt outut royalty omared to no lensng. a+ 3 For suffently not suffently low ost reduton from R&D.e. < > 4 e-ante and e-ost welfare are less more lkely to be hgher under weak atent roteton omared to strong atent roteton. From Proostons 8 11 we an have followng onluson showng the dfferene of these two lensng ontrats on R&D nvestment and soal welfare. Corollary 1: Effet of lensng on R&D nvestment and e-ante welfare deends on the tye of lensng ontrat and f the ost reduton from R&D s moderate.e. a+ 3 a+ 4 5 3. Here both hgher mat of lensng on R&D nvestment and the lkelhood of hgher e-ante welfare under strong weak atent roteton s more f lensng nvolves u-front fed-fee er-unt outut royalty. 5 Conluson In a Cournot duooly we take a fresh look on the effet of dfferent atent systems on R&D nvestments and soal welfare. Further we eamne how the results are nfluened wth the estene of dfferent tyes of lensng. Whether strong atent roteton nreases R&D nvestment of both frms s ambguous. However R&D nvestment of at least one frm s hgher under strong atent roteton than weak atent roteton. Thus ths aer rovdes a testable hyothess for eamnng the effets of dfferent atent systems on the frm level R&D nvestment. Wthout any ossblty of lensng whether e-ost welfare wll be more under weak and strong atent roteton s also ambguous. However n ths stuaton e-ante welfare s lkely to be hgher under strong atent roteton. If lensng ontrat e-ost R&D onssts of u-front fed-fee only then the effet of lensng on R&D nvestment s hgher under strong atent roteton whenever lensng s roftable under both atent systems. But f lensng s rvately roftable 3
only under weak atent roteton then t redues the dfferene n total R&D nvestment between weak and strong atent rotetons. Whle a roftable lensng ontrat makes the e-ost welfare more lkely to be hgher under weak atent roteton the ossblty of lensng makes e-ante welfare more lkely to be hgher under strong weak atent roteton whenever lensng s roftable under both atent systems under only weak atent system. The results ould be hanged f lensng onssts of er-unt outut royalty only. Whether royalty nome s hgher under weak atent roteton deends on the ost reduton from R&D as well as on the degree of knowledge sllover. Whle for suffently low ost reduton from R&D the effet of ths tye of lensng on R&D nvestment s more under strong atent roteton the effet of lensng wll be more under weak atent roteton when ost reduton from R&D s suffently large and the degree of knowledge sllover s suffently small. Unlke fed-fee lensng ontrat eost welfare s lkely to be hgher under strong atent roteton when ost reduton from R&D s suffently small but e-ante welfare s lkely to be hgher under weak atent roteton when ost reduton s not suffently small. Referenes 1. Beath J. J. Poyago-Theotoky and D. Ulh 198 Organzaton desgn and nformatonsharng n a researh ont venture wth sllovers Bulletn of Eonom Researh 50: 47 59.. Cho J.P. 1993 Cooeratve R&D wth rodut market ometton Internatonal Journal of Industral Organzaton 11: 553 71. 3. Combs K. L. 199 Cost sharng vs. multle researh roets n ooeratve R&D Eonoms Letters 39: 353 71. 4. d Asremont C. and A. Jaquemn 1988 Cooeratve and non-ooeratve R&D n duooly wth sllovers Ameran Eonom Revew 78: 1133 37. 5. Galln N. T. 199 Patent oly and ostly mtaton RAND Journal of Eonoms 3: 5 63. 6. Galln N T. and R. A. Wnter 1985 Lensng n the theory of nnovaton RAND Journal of Eonoms 16: 37 5. 4
7. Glbert R. and C. Sharo 1990 Otmal atent length and breadth RAND Journal of Eonoms 16: 37 5. 8. Kabra T. and S. Mart 1993 Internatonal tehnology transfer under otental threat of entry - A Cournot-Nash framework Journal of Develoment Eonoms 4: 75 88. 9. Kabra T. and A. Mukheree 000 Cooeraton n R&D and roduton: a three-frm analyss Journal of Eonoms Zetshrft fur Natonalokonome 71: 81 304. 10. Katz M.L. and C. Sharo 1985 On the lensng of nnovatons RAND Journal of Eonoms 16: 504 0. 11. Klemerer P. 1990 How broad should the soe of atent roteton be? RAND Journal of Eonoms 1: 113 30. 1. Kultt K. and T. Takalo 1998 R&D sllovers and nformaton ehange Eonoms Letters 61: 11 3. 13. Lahr S. and Y. Ono 1988 Helng mnor frms redues welfare The Eonom Journal 98: 1199 10. 14. Levn R. C. A. K. Klevork R. C. Nelson and S. G. Wnter 1987 Aroratng the returns from ndustral researh and develoment Brookngs Paers on Eonom Atvty Seal Issue on Mroeonoms: 783 80. 15. Mart S. 1990 On a non-ooeratve theory of tehnology transfer Eonoms Letters 33: 93 98. 16. Mart S. 1991 Inentves for ooeratve and non-ooeratve R&D n duooly Eonoms Letters 37: 187 91. 17. Mazzolen R. and R. Nelson 1998 The benefts and osts of strong atent roteton. a ontrbuton to the urrent debate Researh Poly 7: 73 84. 18. Mukheree A. 001 Tehnology transfer wth ommtment Eonom Theory 17: 345 69. 19. Mukheree A. and E. Pennngs 001 Imtaton atent roteton and welfare Workng aer No. 001/03 Deartment of Eonoms Keele Unversty. 0. Mukheree A. and N. Balasubramanan 001 Tehnology transfer n horzontally dfferentated rodut-market Researh n Eonoms Rherhe Eonomhe 55: 57 74. 5
1. Mukheree A. 00 R&D lensng and atent roteton Workng aer No.00/01 Deartment of Eonoms Keele Unversty.. Poyago-Theotoky 1998 R&D ometton n a med duooly under unertanty and easy mtaton Journal of Comaratve Eonoms 6: 415 8. 3. Renganum J. F. 1983 Unertan nnovaton and the ersstene of monooly The Ameran Eonom Revew 73: 741 48. 4. Rokett K. 1990 The qualty of lensed tehnology Internatonal Journal of Industral Organzaton 8: 559 574. 5. Suzumura K. 199 Cooeratve and non-ooeratve R&D n an olgooly wth sllovers The Ameran Eonom Revew 8: 1307 0. 6. Varsakels N. C. 001 The mat f atent roteton eonomy oenness and natonal ulture on R&D nvestment: a ross-ountry emral nvestgaton Researh Poly 30: 1059 1068. 6
Frm 's R&D nvestment M X N G H Y K Z 0 N H M G Frm 1's R&D nvestment Fgure 1 7