Welfare Effects of Intellectual Property in a North-South Model of Endogenous Growth with Comparative Advantage

Sain -Paul, Gilles A icle Wel a e E ec s o In ellec ual P ope y in a No h- Sou h Model o Endogenous G ow h wi h Compa a i e Ad an age Economics: The Open-Access, Open-Assessmen E-Jou nal P o ided in Coope a ion wi h: Kiel Ins i u e o he Wo ld Economy – Leibniz Cen e o Resea ch on Global Economic Challenges Sugges ed Ci a ion: Sain -Paul, Gilles (2008) : Wel a e E ec s o In ellec ual P ope y in a No h-Sou h Model o Endogenous G ow h wi h Compa a i e Ad an age, Economics: The Open-Access, Open- Assessmen E-Jou nal, ISSN 1864-6042, Kiel Ins i u e o he Wo ld Economy (I W), Kiel, Vol. 2, Iss. 2008-5, pp. 1-24, h ps://doi.o g/10.5018/economics-ejou nal.ja.2008-5 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/18018 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h p://c ea i ecommons.o g/licenses/by-nc/2.0/de/deed.en Vol. 2, 2008-5 Feb ua y 13, 2008 Wel a e E ec s o In ellec ual P ope y in a No h-Sou h Model o Endogenous G ow h wi h Compa a i e Ad an age Gilles Sain -Paul Toulouse School o Economics and Bi kbeck College Abs ac : This pape de elops a model o analyzing he cos s and bene i s o in ellec ual p ope y en o cemen in LDCs. The No h is mo e p oduc i e han he Sou h and is he only sou ce o inno a o . The e a e wo ypes o goods, and each bloc has a compa a i e ad an age in p oducing a speci ic ype o good. I compa a i e ad an age is s ong enough, e en unde pi acy he e a e goods ha he Sou h will no p oduce. Pi acy will hen lead o a ealloca ion o inno a i e ac i i y in a o o hese goods. Tha may ha m consume s (including consume s in he Sou h) o he ex en ha hese goods ha e smalle dynamic lea ning ex e nali ies han he o he goods, and ha hei sha e in consump ion is small. Thus, whe he o no pi acy is in he in e es o he Sou h depends on how impo an a e he goods o which i has a compa a i e ad an age o i s consume s, and wha he g ow h po en ial o hese goods is. While, all else equal, he No h ends o lose mo e (o gain less) om pi acy han he Sou h, because monopoly p o i s e en ually acc ue o he No h, he Sou h may lose mo e han he No h i he e is a s ong enough home bias in a o o he goods o which i has a compa a i e ad an age. JEL: F12, F13, O30, O34 Keywo ds: Pi acy; in ellec ual p ope y; inno a ion; g ow h; compa a i e ad an age Co espondence: [email p o ec ed] www.economics-ejou nal.o g/economics/jou nala icles © Au ho (s) 2008. This wo k is licensed unde a C ea i e Commons License - A ibu ion-NonComme cial 2.0 Ge many Economics: The Open-Access, Open-Assessmen E-Jou nal 1 1 In oduc ion The ex en o which de eloping coun ies should en o ce in ellec ual p ope y igh s is a ho ly deba ed opic. I is o en hea d ha no doing so would allow a cheap access o impo an p oduc s such as d ugs. Some au ho s also poin ou ha in he nine een h cen u y, he US i sel did no ecognize o eign pa en s. While he a gumen ha a gi en small coun y can be made be e -o by ee- iding on in ellec ual p ope y in he es o he wo ld is s aigh o wa d, empi ically hings a e no so clea -cu : While Gould and G uben (1996) ind ha lowe en o ce- men o In ellec ual p ope y educes g ow h in a c oss-sec ion o coun ies, a numbe o au ho s ind ad e se e ec s on o eign di ec in es men , expo s and licensing by US high- ech i ms (See Lee and Mans ield (1996), Sma czynska (2002), Smi h, P. (1999), and Yang, G. and K. Maskus (1998)). This pape de elops a model o analyzing he cos s and bene i s o IP en o ce- men in LDCs. I is an endogenous g ow h model in he ashion o G ossman and Helpman (1991), wi h wo coun ies, No h and Sou h. Inno a ion only akes place in he No h. The No h is mo e p oduc i e han he Sou h. The e a e wo ypes o goods, and each bloc has a compa a i e ad an age in p oducing a speci ic ype o good. I he Sou h does no en o ce IP (pi acy), hen i is able o manu ac u e goods in en ed in he No h wi hou paying oyal ies. These goods a e sold a ma ginal cos ins ead o monopoly p ice, which bene i s wo ld consume s om a s a ic iew- poin . I compa a i e ad an age is s ong enough, e en unde pi acy he e a e goods ha he Sou h will no p oduce. Pi acy will hen lead o a ealloca ion o inno a i e ac i i y in a o o hese goods. Tha may ha m consume s (including consume s in he Sou h) o he ex en ha hese goods ha e smalle dynamic lea ning ex e - nali ies han he o he goods, and ha hei sha e in consump ion is small. Thus, whe he o no pi acy is in he in e es o he Sou h depends on how impo an a e he goods o which i has a compa a i e ad an age o i s consume s, and wha he g ow h po en ial o hese goods is. While, all else equal, he No h ends o lose mo e (o gain less) om pi acy han he Sou h, because monopoly p o i s e en ually acc ue o he No h, he Sou h may lose mo e han he No h i he e is a s ong enough home bias in a o o he goods o which i has a compa a i e ad an age. We also p o ide some nume ical esul s on how he monopoly ma kup a ec s he gains o losses om pi acy o he No h and he Sou h. Casual in ui ion would sugges ha pi acy is mo e bene icial o wel a e i ma kups a e lowe , since pi acy elimina es he ma kup and b ings p ices down o ma ginal cos s. Howe e , his igno es he ac ha he ma kup depends on he p ice-elas ici y o demand, i.e. on how new goods a e complemen a y wi h exis ing goods. When he elas ici y alls, i means ha complemen a i ies a e s onge , so ha in oducing new goods is mo e alued. This e ec ends o magni y he wel a e losses om ha ing less inno a ion in one sec o because o pi acy. We show ha unde ce ain pa ame e alues, a la ge ma kup makes he Sou h mo e likely o lose om i s own pi acy. Ou esul s a e eminiscen o h ee ela ed pape s: Diwan and Rod ik (1991) conside he bene i s o IPR in he Sou h when he e exis s a ange o p oduc s ha i speci ically consumes. G ea e speci ici y o hese p oduc s make i mo e cos ly o he Sou h o op o pi acy, as i will ge less inno a ion o he p oduc s ha i needs. Thei pape , howe e , is s a ic and does no conside endogenous g ow h o compa a i e ad an age. Thoenig and Ve die (2003) a gue ha he h ea o pi acy www.economics-ejou nal.o g 2Economics: The Open-Access, Open-Assessmen E-Jou nal will induce he No h o in es in mo e complex, skill-in ensi e echnologies ha a e ha de o imi a e; he a gumen es s on a di ec link be ween complexi y and imi a ion, while he e ec s discussed he e a e ela i e p ice e ec s.1Finally, he pape which is closes o he p esen one is Gancia and Bon iglioli (2007). Thei model ca ies a simila message, bu using a Do nbusch-Fische -Samuelson (1997) - ype model. Fu he mo e, hei model assumes ha imi a o s in he Sou h ge monopoly en s, which changes he analysis o he ade-o be ween s a ic and dynamic gains. 2 The Model The e a e wo coun ies, deno ed by A and B, and wo ypes o goods, deno ed by 1 and 2. Wi hin each ype he e po en ially is a con inuum o goods. Each good is p oduced wi h a linea echnology which uses labo only. A each da e he e is a con inuum o goods, wi h a mass Nio goods o ype i. Goods o ei he ype a e indexed by k∈[0, Ni].Goods o ype 1 di e om goods o ype 2 in ha he ela i e p oduc i i y o coun y B is no he same. Speci ically, coun y A p oduces all goods wi h a uni p oduc i i y. Coun y B p oduces goods o ype 1 wi h p oduc i i y b and goods o ype 2 wi h p oduc i i y a. We assume ha coun y B is less de eloped han coun y A, and ha i has a compa a i e ad an age in p oducing 1-goods. Tha is, a < b < 1 Each coun y has a ep esen a i e consume . Times is con inuous. The ep esen a- i e consume in coun y jmaximizes Vj=Z+∞ 0 Uj e−ρ d , whe e Uj is in a empo al u ili y a da e . U ili y is allowed o di e be ween he wo coun ies, embodying he possibili y o home bias: UA=αln CA 1 + (1 −α) ln CA 2 −(αln α+ (1 −α) ln(1 −α)), UB=βln CB 1 + (1 −β) ln CB 2 −(βln β+ (1 −β) ln(1 −β)), whe e Cj i , i ∈ {1,2}, j ∈ {A, B},is he agg ega e consump ion index o goods o ype iin coun y j, gi en by Cj i =µZNi 0 cij (k)σ−1 σdk¶ σ σ−1 , whe e cij (k) is consume j0sconsump ion o he i-good indexed by ka da e .We assume α≤β, so ha he e will be home bias i his inequali y s ic ly holds. The demand unc ion o good ko ype icoming om coun y jis cij (k) = sij Yj ¯pi µpi (k) ¯pi ¶−σ , 1O he ela ed wo ks include Goh and Oli ie (2003) and G ossman and Lai (2001). www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 3 whe e Yj is agg ega e nominal income in coun y ja ;pi (k) is he p ice o he good conside ed; sij he app op ia e income sha e (s1A=α;s2A= 1 −α;s1B= β;s2B= 1 −β); and ¯pi he app op ia e p ice index o i−goods: ¯pi =µZNi 0 pi (k)1−σdk¶1 1−σ . Coun y jis endowed wi h Ljuni s o p oduc ion labo . Fu he mo e, coun y Ais endowed wi h a s ock LRo esea che s, who p oduce new bluep in s o ei he ype. Thus, R & D can only ake place in coun y A. The cos o p oducing a new good is he same i espec i e o he ype o he good. Once he good is in en ed, he in en o holds a monopoly igh o e e on he good. Resea che s decide ex- an e whe he o y and in en a 1-good o a 2-good. Thus, hey all specialize in he good ha yields he la ges p esen discoun ed alue (PDV), unless he wo PDVs a e equal, in which case hey a e indi e en . While hey ha e a ixed labo endowmen , hey ha e a small, in ini esimal disu ili y o labo , so ha hey would no wo k o a ze o income. The e o e, i p oducing a new bluep in in bo h ypes o goods yields a ze o o nega i e p esen discoun ed alue, esea che s do no wo k a all and no inno a ion akes place. To gua an ee sus ained long- un g ow h, I assume, as he li e a u e o en does, ha he cos o in en ing new bluep in s is p opo ional o he o al numbe o goods o he same ype Ni .Thus, i θ is he p opo ion o esea che s wo king on 1-goods, we ha e ˙ N1 =γ1θ N1 ,(1) ˙ N2 =γ2(1 −θ )N2 . No e ha he γs a e allowed o di e be ween he wo ypes o goods: one ype o good may ha e s onge dynamic lea ning ex e nali ies han he o he . We will cha ac e ize equilib ium in wo di e en cases: 1. Coun y B does no en o ce any in ellec ual p ope y by coun y A, and can expo he p oduc s i copies o coun y A. In such a case any good ican be p oduced by he pa en holde in coun y Aplus a inge o pe ec compe i o s in coun y B. 2. Coun y B ully en o ces in ellec ual p ope y igh s. In such a case only he pa en holde can p oduce a good. Pa en holde s can be loca ed in ei he coun y2, bu all monopoly p o i s acc ue o coun y A. We now desc ibe he main p ope ies o he solu ion unde di e en policy egimes, elega ing p oo s o he Appendix. We i s cha ac e ize he alloca ion o esou ces and p ices a a gi en da e, and hen s udy he de e minan s o inno- a ion and he e olu ion o he numbe o goods. We shall exp ess p ices in e ms o labo in coun y A. I s wage wAis he e o e no malized o wA= 1.We will also deno e by µ=σ σ−1 he monopoly ma kup. 3 The In a-Pe iod Equilib ium This sec ion discusses how he in a-pe iod equilib ium is de e mined. I desc ibes i s main economic p ope ies and spells ou he solu ion o all he endogenous 2O , equi alen ly, ex ac all he en s by licensing o a monopoly based in coun y B. www.economics-ejou nal.o g 4Economics: The Open-Access, Open-Assessmen E-Jou nal a iables in all he speci ic egimes. The p ecise equilib ium condi ions, ha a e s anda d, and associa ed ma hema ical de i a ions a e le o he appendix. 3.1 Full Pi acy Le us i s analyze equilib ium in he case o ull pi acy. Tha means ha any i m in coun y B can p oduce and expo any exis ing good. Howe e , only he pa en holde can p oduce a good in coun y A. Depending on he model’s pa ame e s – in pa icula he coun ies’ ela i e sizes, hei ela i e p oduc i i y le el, and he le el o he monopoly ma kup – he econ- omy can be in one o ou di e en egimes. The p ope ies o hese egimes a e summa ized in Table 1 and g aphically ep esen ed in Figu e 1. Fo each coun y j=A, B and each good ype i= 1,2,we deno e he nominal wage le els by wj, he wo ld p ice by pi,employmen in coun y jand good ype iby Lij,GNP–which is equal o GDP unde pi acy bu no unde en o cemen –by Yj,and he p o i s o he pa en holde should i decide o p oduce a j−good in coun y A by πj. I coun y A is la ge enough (Regimes P1, P2, and P3), coun y B will only p oduce good 1. In such a case, p oduce s o 2-goods in coun y A ha e s ic ly posi i e p o i s: a he han copying 2-goods, coun y B ocuses on 1-goods in which i has a compa a i e ad an age. Consequen ly, he e is an incen i e o inno a e in hese goods. In egime P1, coun y A only p oduces 2-goods; a p oduce o 1-goods would make s ic ly nega i e p o i s. The condi ion o his egime o p e ail is deno ed by (CP1). In egime P2, i p oduces bo h ypes o goods, and cha ges a monopoly p ice on he 2-goods, while i makes ze o p o i s in he 1-goods. The same occu s in egime P3 excep ha , in ha egime, p oduce s o 2-goods cha ge a limi p ice equal o he p oduc i i y gap be ween he wo coun ies. In con as , i coun y A is no la ge enough ela i e o coun y B, he la e p oduces bo h ypes o goods, and i is impossible o i ms in coun y A o cha ge mo e han hei cos . Thus p o i s a e ze o e en o 2-goods p oduce s, and he e is no incen i e o inno a ion. Table 1 – Equilib ium Cha ac e iza ion unde Full Pi acy Regime P1 P2 P3 P4 Condi ion on aµ < z < b aµ < b < z b < aµ < z z < aµ z=αµLA (1−β)LB(CP1) wA1 1 1 1 wBz b b a p1z/b 1 1 a/b p2µ µ b/a 1 L2ALA(1−α)LA+b(1−β)LB αµ+1−α (1−α)LA+b(1−β)LB αb/a+1−αLA L1BLBLBLBαLA+aβLB a YAµLA(µ−1)L2A+LA(b/a −1)L2A+LALA YBzLBbLBbLBaLB π2>0>0>0 =0 π1<0 =0 =0 <0 www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 5 Figu e 1 – Specializa ion and P icing Regimes, Pi acy LA/LB µ P4 P3 P2 P1 LA/LB µ P4 P3 P2 P1 3.2 Full En o cemen We now u n o he second case, whe e in ellec ual p ope y is ully en o ced wo ld- wide. The e a e h ee possible egimes, ha a e summa ized in Table 2 below. Again, depending on he ela i e size o coun y A, we ha e di e en specializa ion egimes. In all o hem, pa en -holde s ge posi i e p o i s, since p ope y igh s a e en o ced. F om a s a ic poin o iew, i is clea ha en o cemen edis ibu es income om coun y B o coun y A, in he o m o monopoly p o i s o pa en holde s in coun y A. Figu e 2 illus a es he zone whe e each egime p e ails. In egime E1, coun y A only p oduces 2-goods and coun y B only p oduces 1-goods. The associa ed condi ion is deno ed by (CE1). In egime E2, coun y A p oduces bo h goods, and coun y B only p oduces 1-goods. Finally, in egime E4, coun y B p oduces bo h goods and coun y A only p oduces 2-goods. No e ha he zones whe e hese pa e ns o p oduc ion p e ail a e subs an ially di e en om he en- o cemen egime. Also, p o i s can be w i en πi=qi/Ni,whe e qiis a cons an which only depends on he egime being conside ed. www.economics-ejou nal.o g 6Economics: The Open-Access, Open-Assessmen E-Jou nal Table 2 – Equilib ium Cha ac e iza ion unde Full En o cemen Regime E1 E2 E4 Condi ion on a<z0< b z0> b z0< a z0=αµLA [(1−β)+(1−α)(µ−1)]LB(CE1) wA1 1 1 wBz0b a p1µz0/b µ µa/b p2µ µ µ L2ALAz0LBL2 L1BLBLB(αµ+1−α)aLB−(1−β)aLB+αµLA µa YAµLA+ (µ−1)LBz0µLA+ (µ−1)bLBµLA+ (µ−1)aLB YBz0LBbLBaLB π2(µ−1)LA N2(µ−1)L2A N2(µ−1)LA+a(LB−L1B) N2 π1(µ−1)LB N1z0(µ−1)bLB+LA−L2A N1(µ−1)aL1B N1 Figu e 2 – Specializa ion and P icing Regimes, En o cemen LA/LB µ P4 P3 P2 P1 LA/LB µ P4 P3 P2 P1 4 Inno a ion To comple e he model’s cha ac e iza ion, we need o desc ibe how he numbe o a ie ies in each ype o good e ol es. We do so by in oducing inno a ion using he s anda d ools de eloped by he li e a u e. The R and D sec o is compe i i e. All agen s can bo ow and lend a a ixed nominal a e . I Videno es he alue o a pa en associa ed wi h an i−good, hen Vi=πi+˙ Vi(2) In equilib ium, esea che s alloca e hemsel es be ween he wo ypes o inno a ion. The labo ma ke o esea che s is pe ec ly compe i i e, so ha hey ea n he same wage in each sec o . www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 7 Le us i s conside he ull en o cemen case. I θis in e io , and we con ine he analysis o his case, he expec ed alue om one uni o esea ch mus be he same in bo h sec o s, implying γ1N1V1=γ2N2V2.(3) Subs i u ing (1) in o (2), in eg a ing o wa d and using (3), we ge he equilib ium alue o θ: θ=( γ1+γ1γ2)q1− γ2q2 γ1γ2(q1+q2). No e ha θdoes no depend on N1and N2,and is cons an h ough ime. I is inc easing in he p oduc i i y o esea ch o 1-goods γ1and he p o i abili y o hese goods q1,and dec easing in γ2and q2.Finally o θ o be in e io , we need ha γ1q1 γ2+γ1γ2 ≤q2≤( γ1+γ1γ2)q1 γ2 .(4) We can hen compu e he g ow h a e o he mass o goods o each a ie y ˙ N1 N1 =( γ1+γ1γ2)q1− γ2q2 γ2(q1+q2)=g1. ˙ N2 N2 =( γ2+γ1γ2)q2− γ1q1 γ1(q1+q2)=g2. In he no en o cemen case, π1≤0 always. I π2>0, hen θ= 0 and g2=γ2,while g1= 0.I π2= 0, hen esea che s a e ‘unemployed’ and g1=g2=π1=π2= 0. 5 Wel a e The egimes cha ac e ized in Tables 1 and 2 a e alid a a poin in ime, bu no e ha he condi ions do no depend on he alues o N1and N2(Tha is because p e e ences a e Cobb-Douglas be ween he wo agg ega es). The e o e, i he economy is in a gi en egime a = 0,i will s ay in ha egime. I om ime = 0 on, N1and N2g ow a cons an a es g1and g2,i is hen easy o exp ess he wel a e o bo h coun ies as a unc ion o hei nominal na ional income, he p ice le els, he ini ial numbe o goods and hei g ow h a es. We ge UA =α σ−1ln N1 +1−α σ−1ln N2 + ln YA−αln p1−(1 −α) ln p2, whe e ime indices ha e been d opped om piand YA,because hey a e cons an h oughou i one emains in he same egime. Simila ly, UB =β σ−1ln N1 +1−β σ−1ln N2 + ln YB−βln p1−(1 −β) ln p2. www.economics-ejou nal.o g 14 Economics: The Open-Access, Open-Assessmen E-Jou nal Appendix A: De i a ion o Analy ical Resul s De i a ion o he Fou Pi acy Regimes Coun y B Only P oduces 1-Goods Le us i s cha ac e ize an equilib ium whe e coun y B only p oduces 1-goods. We will no malize he wage o wo ke s in coun y A o wA= 1.Coun y B can p oduce any good compe i i ely. The e o e, i s p oduce s will pin down he p ice o 1-goods: p1(k) = wB/b =p1,∀k. 2-goods can be p oduced in coun y B a cos wB/a. The e o e, p2(k) = p2= min ³wB a, µwA´, whe e µ=σ/(σ−1) is he monopoly ma kup one would obse e absen compe i ion om coun y B. In equilib ium, i mus be be e o buy goods om compe i i e p oduce s in coun y B han om he pa en holde in coun y A. The e o e, one mus ha e wB/b < µwA=µ. To compu e equilib ium quan i ies, no e ha na ional income in coun y B is YB=wBLB Coun y A po en ially p oduces bo h ypes o goods. Le LiA be he labo inpu in coun y A de o ed o i-goods. Then: YA=p2L2A+wB bL1A Tha equa ion is he GDP a ma ke p ices na ional income iden i y, saying ha GDP is he o al alue o inal goods being sold. Equilib ium o supply and demand o ei he ype o good leads o he ollowing equal- i y, which mus hold in equilib ium: αp2L2A=wB·1−α bL1A+ (1 −β)LB¸(A1) P1: Monopoly P icing, Coun y A Only P oduces 1-Goods Le us i s look o an equilib ium wi h monopoly p icing o he 2-goods, and no p o- duc ion o good 1 in coun y A. Then wBmus be such ha µ < wB/a, (A2) and wB/b < wA= 1.(A3) The i s condi ion s a es ha he monopoly p ice o 2-goods is lowe han hei p oduc ion cos in coun y B. The second condi ion says ha he cos o 1-goods in coun y A is highe han in coun y B, so ha no holde o a pa en o a 1-good in coun y A wan s o ac ually p oduce. www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 15 We hen ha e L1A= 0, L2A=LA.Consequen ly, equa ion (A1) implies wB=αµLA (1 −β)LB . Subs i u ing in o condi ions (A2) and (A3), we ind ha his egime holds i and only i a < αLA (1 −β)LB <b µ, which cha ac e izes egime (P1). No e ha his egime may only hold i b > aµ. P2: Monopoly P icing, Coun y A P oduces Bo h Goods Le us now look o a egime whe e coun y A p oduces some 1-goods, assuming again monopoly p icing in he 2-goods. This will be he case i (A2) holds and i wB≥b. (A4) Gi en ha p1=wB/b, i p1>1, hen i is p o i able o p oduce s o 1-goods in coun y A o co e he whole ma ke , lea ing no ou pu o p oduce s in coun y B ( he s anda d dominan i m esul ). Tha canno be ue in equilib ium, as i con adic s he ull employmen condi ion in coun y B and he assump ion ha coun y B only p oduces 2-goods. The e o e in such a egime i mus be ha wB=b. P o i s a e equal o ze o o p oduce s o 1-goods in coun y A. L2Ais hen de e mined by (A1), yielding L2A=(1 −α)LA+b(1 −β)LB αµ + 1 −α. Fo his egime o hold, i mus be ha (A2), holds, i.e. µ < b/a, and ha L2A≤LA, ha is b µ<αLA (1 −β)LB . This he e o e cha ac e izes egime P2. P’1: Limi P icing, Coun y A Only P oduces 2-Goods Now le us conside he possibili y o limi p icing in 2-goods, and no p oduc ion o 1-goods in coun y A. Tha co esponds o he ollowing condi ions: p2=wB a< µ and wB< b. One hen has L1A= 0, L2A=LAPlugging hese condi ions in o (A1), we ind ha his is a kni e-edge case which can only hold i αLA/a = (1 −β)LB.We shall he e o e igno e i . www.economics-ejou nal.o g 16 Economics: The Open-Access, Open-Assessmen E-Jou nal P3: Limi P icing, Coun y A P oduces Bo h Goods Now conside he case o limi p icing in 2-goods, and some p oduc ion o 1-goods in coun y A. We again ha e p2=wB a< µ and wB=b. Subs i u ing in o (A1) we ge L2A=(1 −α)LA+b(1 −β)LB αb/a + 1 −α. This egime holds i b/a < µ and L2A< LA,o equi alen ly a < αLA (1 −β)LB . Thus we ha e cha ac e ized egime P3. P4: Coun y B P oduces Bo h Goods Now le us look a an equilib ium whe e coun y B p oduces bo h goods. I mus be ha p1=wB/b and p2=wB/a. Fo coun y B o p oduce some o he 2-goods, i mus be ha p2≤wA= 1,o he wise monopolis s in coun y A would lood he ma ke . Assume p2<1, hen a o io i p1<1,as b > a. Then, no p oduce in coun y A would be p o i able, which con adic s he ull employmen condi ion he e. Thus we mus ha e p2= 1,implying wB=a. Then p1=a/b < 1,implying ha coun y A does no p oduce 1-goods. The equilib ium is hen easily cha ac e ized. P o i s in coun y A a e equal o ze o, GDP in coun y Ais YA=wAL2A=LA; and GDP in coun y B is gi en by YB=wBLB=aLB. Equilib ium in he goods ma ke s can be w i en αYA p1 +βYB p1 =bL1B, implying L1B=αLA+βaLB a. Fo his egime o hold we mus ha e L1B< LB,i.e. αLA (1 −β)LB < a. This he e o e cha ac e izes egime P4. De i a ion o he 3 En o cemen Regimes We now u n o he en o cemen egime. In his egime all p oduc ion uni s a e owned by he monopolis in coun y 2, ega dless o whe e hey a e loca ed. P ices a e hus always equal o he ma kup imes he wage in he coun y whe e he good is being p oduced. www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 17 E1: Coun y A Only P oduces 2-Goods and Coun y B Only P oduces 1-Goods Fi s conside he case whe e coun y A only p oduces 2-goods and coun y B only p o- duces 1-goods. We hen ha e p1=µwB/b; (A5) p2=µwA=µ. (A6) GNP o coun y A’s esiden s is YA=p2LA+ (µ−1)wBLB,(A7) whe e he second e m ep esen s p o i s epa ia ed om coun y B. GNP in coun y B is gi en by YB=wBLB.(A8) Equilib ium in goods ma ke s is gi en by (1 −α)YA p2 + (1 −β)YB p2 =LA.(A9) Subs i u ing (A5)-(A8) we ge wB=αµLA (1 −β)LB+ (1 −α)(µ−1)LB . Fo his egime o be an equilib ium, i mus be ha i ms do no wan o eloca e in he o he coun y. Conside i s a monopoly based in coun y A. I s p o i is gi en by π2= (µ−1)c2, whe e c2=LA/N2is he amoun sold o each 2-good. I i decides o eloca e in coun y B, i s uni cos is wB/a. I will cha ge p0 2=µwB/a, and sell a quan i y equal o c0 2=c2(p0 2/p2)−σ,so ha i s p o i s a e π0 2=c2(µ−1) (wB/a)1−σ. We mus ha e π0 2≤π2,i.e. wB/a > 1.Simila ly, o p oduce s o 1-goods no o wan o eloca e in coun y A, we need wB/b < 1.These wo inequali ies a e equi alen o a < αµLA [(1 −β) + (1 −α)(µ−1)]LB < b, and his cha ac e izes egime E1. I is hen s aigh o wa d o compu e p o i s. E4: Coun y B P oduces Bo h Goods, Coun y A Only 2-Goods Now conside an equilib ium whe e coun y B p oduces 1-goods and 2-goods, and coun y A p oduces only 2-goods. P oduce s o 2-goods mus be indi e en be ween loca ing in coun y A and loca ing in coun y B, he e o e we mus ha e wB/a =wA= 1.Hence wB=a. www.economics-ejou nal.o g 18 Economics: The Open-Access, Open-Assessmen E-Jou nal Consequen ly, p2=µand p1=µa/b. Equa ions (A7) and (A8) s ill hold, while (A9) mus be eplaced by (1 −α)YA p2 + (1 −β)YB p2 =LA+aL2B. Subs i u ing, his allows o compu e L2B: L2B=(1 −β)aLB+ (1 −α)(µ−1)aLB−αµLA µa . Fo his egime o be an equilib ium, one mus ha e 0 < L2B< LB,which, as he second inequali y L2B< LBis always sa is ied, is equi alen o αµLA [(1 −β) + (1 −α)(µ−1)]LB < a. This cha ac e izes egime E4. E2: Coun y A P oduces Bo h Goods, Coun y B Only 1-Goods Finally, conside a egime whe e coun y A p oduces 1-goods and 2-goods, and coun y B only p oduces 1-goods. Equali y o uni cos s ac oss coun ies o 1-goods implies wB=b. Hence, p1=p2=µ; and equilib ium in goods ma ke s can be ob ained by subs i u ing L2A o LAin o he RHS o (A9), yielding L2A= (1 −α)LA+bLB µ[(1 −β) + (1 −α)(µ−1)] . This egime holds i L2A< LA,o equi alen ly αµLA [(1 −β) + (1 −α)(µ−1)]LB > b. This he e o e cha ac e izes egime E2. www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 19 Appendix B: Figu es Figu e3:Gains oCoun y A -25 -20 -15 -10 -5 0 5 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 Ma kup Gain S a ic Dynamic Figu e4:Ne Gains,Coun yB -10 0 10 20 30 40 50 60 70 80 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 Ma kup Ne gain S a ic Dynamic www.economics-ejou nal.o g 20 Economics: The Open-Access, Open-Assessmen E-Jou nal Figu e5:C i icalDiscoun Ra e,Coun yB 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Ma kup C i icaldiscoun  a e C i ical o Figu e6:Coun y A'sGains omPi acy -25 -20 -15 -10 -5 0 5 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 Ma kup Gains S a ic Dynamic www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 21 Figu e7:C i icalDiscoun Ra e,Coun y A 0 0.001 0.002 0.003 0.004 0.005 0.006 1.05 1.15 1.25 1.35 1.45 1.55 1.65 1.75 Ma kup C i icaldiscou a e C i ical o Figu e8:Coun yB 0.000800 0.000850 0.000900 0.000950 0.001000 0.001050 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Ma kup C i icaldiscoun  a e C i ical o www.economics-ejou nal.o g 22 Economics: The Open-Access, Open-Assessmen E-Jou nal Figu e9:C i icalDiscoun Ra e,Coun yB 0.00086 0.00088 0.00090 0.00092 0.00094 0.00096 0.00098 0.00100 0.00102 0.00104 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 Ma kup C i ical discoun a e C i ical o www.economics-ejou nal.o g Economics: The Open-Access, Open-Assessmen E-Jou nal 23 Re e ences Benassy, J.-P.l. (1996), Tas e o a ie y and op imum p oduc ion pa e ns in monopolis ic compe i ion. Economics Le e s 52(1): 41-47, 7. h p://ideas. epec.o g/a/eee/ecole / 52y1996i1p41-47.h ml Diwan, I., and D. Rod ik (1991). Pa en s, app op ia e echnology, and No h-Sou h ade. Jou nal o In e na ional Economics 30: 27-47. h p://ideas. epec.o g/a/eee/inecon/ 30y1991i1-2p27-47.h ml Do nbusch, R., S. Fishe , and P. A. Samuelson (1977). Compa a i e Ad an age, T ade and Paymen s in a Rica dian Model wi h a Con inuum o Goods. Ame ican Economic Re iew 67: 823-839. Gancia, G., and A. Bon iglioli (2007). No h-Sou h ade and di ec ed echnical change. CREI Wo king pape , Sep embe 2007. h p://www.c ei.ca /people/gancia/pd _ iles/NS-DTC.pd Goh, A., and J. Oli ie (2002). F ee T ade and P o ec ion o In ellec ual P ope y Righ s: Can We Ha e One Wi hou he O he ? Mimeo, HEC. h p://ideas. epec.o g/p/cp /cep dp/3127.h ml Gould, D., and W. G uben (1996). The ole o in ellec ual p ope y igh s in economic g ow h. Jou nal o De elopmen Economics 48: 323-350. h p://ideas. epec.o g/p/ ip/ eddwp/94-09.h ml G ossman, G., and E. Helpman (1991). Inno a ion and g ow h in he global economy. MIT P ess. h p;//books.google.com G ossman, G., and E. Lai, (2001). In e na ional P o ec ion o In ellec ual P ope y. Discussion pape s in economics 215. P ince on Uni e si y. h p://ideas. epec.o g/p/ h/p iwpu/215.h ml Lee, J-Y., and E. Mans ield (1996). In ellec ual P ope y igh s p o ec ion and US o eign di ec in es men . Re iew o Economics and S a is ics 78: 181-186. h p://ideas. epec.o g/a/ p / es a / 78y1996i2p181-86.h ml McCalman, P. (2000). Reaping wha you sow: An empi ical analysis o in e na ional pa en ha moniza ion. Mimeo, Uni e si y o Cali o nia-San a C uz. h p://ideas. epec.o g/a/eee/inecon/ 55y2001i1p161-186.h ml Sain -Paul, G. (2005). To wha ex en should less de eloped coun ies en o ce In ellec ual P ope y? Wo ld Economics 6(3): 175-196. h p://ideas. epec.o g/p/cp /cep dp/4713.h ml Sma zynska, B. (2002). The Composi ion o Fo eign Di ec In es men and P o ec ion o In ellec ual P ope y Righ s: E idence om T ansi ion Economies. Wo ld Bank Wo king Pape . h p://ideas. epec.o g/p/wbk/wb wps/2786.h ml www.economics-ejou nal.o g