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
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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.
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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]
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© 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
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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).
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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.
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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
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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.
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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 .
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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.
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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.
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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 .
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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.
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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.
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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.
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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
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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
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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
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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
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Economics: The Open-Access, Open-Assessmen E-Jou nal
23
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