Foreign Direct Investment and Technology Licensing in a Polluting Industry

Cao, Jiyun; Mukhe jee, A iji
A icle — Published Ve sion
Fo eign Di ec In es men and Technology Licensing in a
Pollu ing Indus y
En i onmen al and Resou ce Economics
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: Cao, Jiyun; Mukhe jee, A iji (2024) : Fo eign Di ec In es men and Technology
Licensing in a Pollu ing Indus y, En i onmen al and Resou ce Economics, ISSN 1573-1502, Sp inge
Ne he lands, Do d ech , Vol. 87, Iss. 9, pp. 2361-2399,
h ps://doi.o g/10.1007/s10640-024-00886-7
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/315260
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/4.0/
Vol.:(0123456789)
h ps://doi.o g/10.1007/s10640-024-00886-7
Fo eign Di ec In es men andTechnology Licensing
inaPollu ing Indus y
JiyunCao1,6· A iji Mukhe jee2,3,4,5
Accep ed: 22 May 2024
© The Au ho (s) 2024
Abs ac
We conside a i m’s incen i e o o eign di ec in es men (FDI) and in e na ional ech-
nology licensing in a pollu ing indus y. We explain he a ionale and he wel a e impli-
ca ions o complemen a i y be ween FDI and licensing, i.e., he i m’s s a egy o “FDI
and licensing” (FL), which is empi ically ele an bu igno ed in he li e a u e. When he
en i onmen al ax canno be commi ed, he i m adop s he licensing s a egy i he pol-
lu ion in ensi y is no high, and he licensing s a egy may c ea e lowe consume su plus
and wel a e compa ed o bo h FDI and FL. Howe e , i he pollu ion in ensi y is high, he
i m unde akes FL, which p o ide highe consume su plus and wel a e compa ed o bo h
licensing and FDI. When he go e nmen can commi o he en i onmen al ax, he i m
always p e e s FL. The hos -coun y wel a e is highe bu he consume su plus and wo ld
wel a e may be lowe unde he commi ed ax policy compa ed o he non-commi ed ax
policy. These esul s hold unde Cou no compe i ion and S ackelbe g compe i ion. We u -
he show ha FL can be he equilib ium s a egy o he o eign i m i he e is ixed- ee
licensing ins ead o a wo-pa a i licensing, which is conside ed in he main analysis.
Keywo ds Emission ee· Fo eign di ec in es men · Technology licensing· Wel a e
JEL Classi ica ion F18· F23· L13· L24· Q56· Q58
* A iji Mukhe jee
[email p o ec ed]
1 The School o Economics, Nankai Uni e si y, Tianjin, China
2 No ingham Uni e si y Business School, Jubilee Campus, Wolla on Road, No inghamNG81BB,
UK
3 INFER, Cologne, Ge many
4 CESi o, Munich, Ge many
5 GRU, Ci y Uni e si y o Hong Kong, Kowloon, HongKong
6 Collabo a i e Inno a ion Cen e o China Economy, Tianjin, China
En i onmen al and Resou ce Economics (2024) 87:2361–2399
/ Published online: 6 Augus 2024
J.Cao, A.Mukhe jee
1 In oduc ion
Many de eloping coun ies and ansi ional economies libe alized hei economies in las
ew decades, and o eign di ec in es men (FDI) and in e na ional echnology licensing
cons i u e wo impo an ways o se e he hos -coun y ma ke s by he o eign i ms.1
The e is a as li e a u e examining he p o i abili y and he implica ions o FDI and licens-
ing s a egies, which we e iew in he nex sec ion. Howe e , his li e a u e is es ic i e
o wo easons. Fi s , hey mos ly igno ed pollu ing indus ies. Howe e , gi en he cli-
ma e change p oblem a hand, i is impo an o in es iga e how en i onmen al policies
a ec hese s a egies and he co esponding wel a e. Secondly, he ex an li e a u e mos ly
conside ed FDI and licensing as subs i u es, while e idence shows ha o eign i ms o en
unde ake FDI and also license hei echnologies o he hos -coun y i ms in he same
ma ke . In o he wo ds, he e is a complemen a i y be ween FDI and licensing. We explain
his phenomenon and i s wel a e implica ions.
The e idence o “FDI and licensing” (FL o b e i y) in pollu ing indus ies, such as
pe ochemical and pha maceu ical indus ies, is abound. Fo example, BP (UK) has a
plan in China, and licensed i s la es gene a ion echnology o China’s Dongying Weilian
Chemical Co., L d.2 LyondellBasell is ope a ing h ee polyp opylene compounding plan s
in China,3 and also licensed i s polyp opylene echnology o Chinese companies, such as
Qingdao Jinneng New Ma e ial Co., L d,4 Shandong Chamb oad Sinopoly New Ma e ials
Co., L d.,5 and Wanhua Chemical G oup Co., L d.6 Belde bos (1998) illus a es ha Shell
has by a g own in o he hi d la ges ully in eg a ed oil company in Japan, and licensed
i s echnology o Japanese companies, such as Sumi omo Chemical, Seibu Oil, and Chi-
yoda Kako Ken e su om 1981 o 1986.
The e a e also e idences whe e he o eign i ms only license o he hos -coun y i ms.7
As Sikimic e al. (2013) documen ed, se e al leading I alian pha maceu ical and bio ech
companies adop ed echnology licensing as he o eign ma ke -en y mode.
Gi en his backg ound, we examine a o eign monopolis ’s decision on FDI, licensing,
and FL, in a pollu ing indus y and show he co esponding wel a e implica ions. Since he
o eign monopolis needs o in e nalize he e ec s o i s s a egies on he emission ee (o
he en i onmen al ax) imposed by he hos -coun y go e nmen , whe he he hos -coun y
go e nmen can commi o i s policies may play impo an oles.
1 FDI s ock in de eloping economies is o e US$12 illion in 2020 (UNCTAD Handbook o S a is ics,
2021).
2 h ps:// gul o iland gas. com/ webp o1/ main/ mainn ews. asp? id= 901043.
3 h ps:// cen. acs. o g/ busin ess/ pe o chemi cals/ Lyond ellBa sell- in es - Chine se- p oje c / 97/ web/ 2019/ 09.
4 h ps:// gul o iland gas. com/ webp o1/ main/ mainn ews. asp? id= 66206.
5 h ps:// gul o iland gas. com/ webp o1/ main/ mainn ews. asp? id= 70993.
6 h ps:// gul o iland gas. com/ webp o1/ main/ mainn ews. asp? id= 67044.
7 Fo example, No h Ca olina-based T The apeu ics signed an exclusi e licensing ag eemen wi h
Hangzhou Zhongmei Huadong Pha maceu ical Co., L d., in China, o he igh s o de elop and comme -
cialize T The apeu ics’ GLP-1 agonis p og am in China and o he Paci ic Rim coun ies (See h ps://
www. busin esswi e. com/ news/ home/ 20171 22100 5238/ en/ T - The a peu i cs- Annou nces- Licen sing- Ag ee
men - wi h- Hangz hou- Zhong mei- Huado ng- Pha m aceu ical- Co.- o- Righ s- o - T % E2% 80% 99s- GLP- 1 -
Agoni s % C2% A0Dia be es- P og am- in- China- and- O he - Paci i c- Rim- Te i o ies). Huadong Medicine Co.,
L d., in China won he exclusi e igh s o wo au oimmune p oduc s, A calys ( ilonacep ) and ma ili-
mumab, o Kiniksa Pha maceu icals (UK) L d. in he Asia Paci ic egion (including China, Sou h Ko ea,
Aus alia and 18 o he coun ies, excluding Japan) (see h p:// www. pha m adj. com/ en/ cms/ de ail. h m? i em.
id= ecb84 5cca8 cb11e cbee6 a163 e4204 9a).
2362
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
In Sec ion 4, we ollow he li e a u e on non-commi ed go e nmen policies whe e
he go e nmen s canno commi o hei policies (o en because o he ime inconsis ency
p oblem) and adjus hei policies a e i ms’ decisions. Since licensing o FL by he o -
eign monopolis ans e s (pa o ) i s p oduc ion o he hos -coun y i m, i encou ages he
hos -coun y go e nmen o educe he emission ee. A highe ma ginal cos o he hos -
coun y licensee because o a posi i e oyal y a e cha ged by he o eign monopolis also
helps o educe he emission ee by educing pollu ion. Thus, a less s ingen emission ee
esul ed om licensing o FL makes he o eign monopolis be e o compa ed o FDI.8
When compa ing be ween licensing and FL, lowe compe i ion and less s ingen
emission ee unde licensing make he o eign monopolis be e o compa ed o FL i
he pollu ion in ensi y is no high. Hence, depending on he pollu ion in ensi y, he o eign
monopolis p e e s licensing only (FL) when he pollu ion in ensi ies a e mild (high).9
When looking a he wel a e implica ions, we ind ha licensing as a subs i u e o FDI
educes he hos -coun y wel a e, and may educe consume su plus and wo ld wel a e
(which is he hos -coun y wel a e plus he p o i o he o eign monopolis ) compa ed o
FDI, al hough he ma ke s uc u e is he same unde licensing and FDI. Howe e , i he
o eign monopolis does FL whe e licensing complemen s FDI, i inc eases consume su -
plus and wel a e in he hos coun y compa ed o FDI. FL also inc eases he hos -coun y
wel a e and wo ld wel a e compa ed o licensing, bu i educes consume su plus com-
pa ed o licensing when he pollu ion in ensi y is low. Hence, licensing educes (inc eases)
he hos -coun y wel a e compa ed o FDI i i subs i u es (complemen s) FDI.
The e o e, in e nalizing he o eign monopolis ’s en y decision, we ind ha i he pol-
lu ion in ensi y is no high, he o eign monopolis adop s he licensing s a egy, which may
c ea e lowe consume su plus and wel a e compa ed o bo h FDI and FL. Howe e , i he
pollu ion in ensi y is high, he o eign monopolis does FL, which c ea es highe consume
su plus and wel a e compa ed o bo h licensing and FDI.
Sec ion5 conside s he case o a commi ed go e nmen policy whe e he hos -coun-
y go e nmen can commi o an emission ee be o e he o eign monopolis ’s decision.
This may be due o he adminis a i e o poli ical di icul ies in policy adjus men ha may
a ec he epu a ion o he go e nmen . We ind ha he o eign monopolis is be e o
unde FL compa ed o licensing and FDI since FL helps o educe he o al ax paymen
compa ed o licensing and FDI. We also show ha he commi ed policy educes pollu -
an emission, inc eases domes ic wel a e, and may inc ease o dec ease consume su plus
compa ed o he non-commi ed policy.
We assume in Sec sion 4 and 5 ha i ms play Cou no compe i ion unde FL. Sec ion6
conside s S ackelbe g compe i ion unde FL. The abo e-men ioned esul s de i ed om
Cou no compe i ion s ill hold unde S ackelbe g compe i ion. In Sec ion7, we conside a
licensing con ac wi h ixed- ee only. In his si ua ion, he o eign monopolis p e e s FL
unde he non-commi ed policy when he pollu ion in ensi y is high and always p e e s i
unde he commi ed policy.
8 The e is a ecen li e a u e showing he e ec s o licensing o cleane echnologies (see, e.g., Sibailly
2013, Ha o i 2017, Kim e al. 2018 and Xia e al. 2019). In con as , we conside licensing he echnology
o a new p oduc .
9 The li e a u e on pollu ion ha en hypo hesis shows he e ec s o en i onmen al egula ion in he hos
coun ies on inwa d FDIs (see, e.g., Dijks a e al. 2011, Chung 2014 and Cai e al. 2016, o some ecen
con ibu ions, and he e e ences he ein). Zhao e al. (2019) compa e he wel a e e ec s o FDI in pollu ing
indus ies o ha unde closed pollu ing sec o s. In con as , we conside he choice be ween FDI, licensing,
and FL.
2363
J.Cao, A.Mukhe jee
Thus, we con ibu e o he li e a u e by p o iding a new amewo k ha conside s FDI
and licensing in a pollu ing indus y, explains en i onmen al ax as a a ionale o FL, and
shows he implica ions o commi ed and non-commi ed hos -coun y policies, Cou no
and S ackelbe g compe i ion unde FL, and wo-pa a i and ixed- ee licensing con ac s.
Hence, in con as o he exis ing li e a u e on FDI and licensing, we conside a pollu ing
indus y, and show he exis ence o FL (i.e., complemen a i y be ween FDI and licensing)
e en i he e is a monopolis inal good p oduce unde FDI o licensing. Ra he han he
business s ealing incen i e in he p oduc ma ke , he o eign i m has he incen i e o c e-
a e compe i ion in he p oduc ma ke h ough FL o manipula e he en i onmen al ax.
The emainde o he pape is o ganized as ollows. Sec ion2 e iews he ele an li e a-
u e. Sec ion3 desc ibes he model. Sec ion4 in es iga es he si ua ion whe e he go e n-
men canno commi o an emission ee be o e he o eign monopolis ’s ma ke -en y deci-
sion. Sec ion5 examines he si ua ion whe e he go e nmen can commi o he emission
ee be o e he o eign monopolis ’s ma ke -en y decision, and compa es he esul s unde
he commi ed and non-commi ed policies. While Sec ions4and 5conside Cou no com-
pe i ion unde FL, Sec . 6 ex ends he analysis by conside ing S ackelbe g compe i ion
unde FL. Sec ion7 conside a licensing con ac wi h ixed- ee only. Sec ion8 concludes.
2 Li e a u e Re iew
While he p oximi y-concen a ion hypo hesis explains he mul ina ional i ms’ incen i e
o FDI compa ed o expo (see, e.g., K ugman 1983, Ho s man and Ma kusen, 1992,
B aina d 1993 and 1997), he e is ano he li e a u e examining he mul ina ional i ms’
bene i s om he in e nalisa ion s a egies, such as FDI, compa ed o hei a m’s leng h
ansac ions, such as echnology licensing, which is he ocus o his pape .
S a ed wi h Dunning (1958), he li e a u e examining he mul ina ional i ms’ bene i s
om FDI compa ed o echnology licensing ocused on di e en ypes o ansac ion cos s
a ising om echnology licensing. Rugman (1986) p o ides a su ey o he ea lie li e a-
u e on he in e na ionalisa ion heo y ocusing ondi e en ypes o ansac ion cos s.
Ho s man and Ma kusen (1987) show ha he o eign i m’s isk o losing epu a ion
unde licensing due o a lowe quali y p oduc p o ided by he licensee may c ea e he
incen i e o FDI. Saggi (1996) shows ha a o eign i m’s incen i e o FDI and licensing
may depend on he ade-o c ea ed by he o eign i m’s loss o p o i unde FDI due o a
highe p oduc -ma ke compe i ion and i s loss o p o i in o he ma ke s due o he licen-
see’s oppo unis ic beha iou unde licensing.
Saggi (1999) conside s a wo pe iod model whe e a o eign i m chooses licensing o
FDI (bu no licensing and FDI) in each pe iod. In his se up, i explo es how he ade-o
be ween a lowe knowledge spillo e unde FDI and highe en dissipa ion unde FDI due
o an inc eased p oduc -ma ke compe i ion a ec s he o eign i m’s decision on FDI and
licensing.
W igh (1993) shows how he in o ma ion asymme y abou he echnology ype and
he cos o FDI in e ac o de e mine a o eign i m’s decision on expo , FDI, o licensing.
I shows ha he ma ke sha e es ic ions and pe -uni oyal ies can signal he echnology
ype and make licensing he mos a ac i e op ion o he o eign i m.
Vishwas ao (1994) conside s he o eign i m’s decision on expo , FDI, o licensing
when he licensee has p i a e in o ma ion abou i s abili y o imi a e he echnology o he
o eign i m unde licensing. I conside s a sc eening amewo k whe e he o eign i m
2364

Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
uses he licensing con ac o gain in o ma ion abou he licensee’s abili y o imi a e he
echnology. I shows ha FDI domina es licensing i he p obabili y o imi a ion is high.
Conside ing a quali y ladde model o inno a ion, Glass and Saggi (2002) show he
e ec s o he o eign i m’s mode o ope a ion (licensing o FDI) on inno a ion by he
o eign i m. I he o eign i m needs o sac i ice mo e en o he licensee o he cos
disad an age o FDI educes, he o eign i m’s incen i e o FDI inc eases compa ed o
licensing. Fu he , he i m doing FDI chooses la ge inno a ion compa ed o he i m
unde aking licensing.
Yang and Maskus (2009) show he implica ions o he hos -coun y pa en p o ec ion on
a o eign i m’s decision on expo , FDI, o licensing. I shows ha a o eign i m p e e s
FDI in coun ies wi h weak pa en s and lowe cos s o se ing subsidia ies; s eng hening
he pa en p o ec ion in his si ua ion c ea es he incen i e o licensing by he o eign i m.
While he abo e men ioned pape s p o ide se e al impo an insigh s, unlike his pape ,
hey conside FDI and licensing as subs i u es.
Sinha (2010) conside s a amewo k whe e a o eign i m, compe ing wi h a hos -coun-
y i m, decides on FDI o expo a e aking a decision on licensing i s echnology o
he hos -coun y compe i o . I shows ha licensing educes he possibili y o FDI. How-
e e , i he ixed cos o FDI is no high, he o eign i m unde akes FDI a e licensing.
Wang e al. (2016a) ex end Sinha (2010) o show he implica ions o be e in o ma ion
acquisi ion unde FDI abou he ma ke condi ion. In con as o Sinha (2010), i shows
ha , due o he bene i o be e in o ma ion acquisi ion unde FDI, licensing may inc ease
he incen i e o FDI.10 Al hough hese pape s conside he possibili y o FDI a e o e -
ing he licensing con ac , we di e om hem in some impo an ways. Fi s , unlike ou
pape , hose pape s did no conside a pollu ing indus y. Second, he incen i e o FDI
a e licensing occu s in hose pape s due o he o eign i m’s incen i e o s ealing ma ke
sha e om he hos -coun y licensee, since, unlike ou pape , licensing does no c ea e a
monopoly ma ke s uc u e in hose pape s.
Mukhe jee (2000) and Mukhe jee and Pennings (2006) show ha s a egic hos -coun y
ax policy and s a egic a i imposed by he impo ing coun ies may encou age o eign
inno a o s o license hei echnologies o hos -coun y i ms. Howe e , hese pape s nei-
he looked a he en i onmen al p oblems no conside ed he s a egy o FL.
While Mukhe jee (2000) and Mukhe jee and Pennings (2006) showed he implica ions
o s a egic go e nmen policies, A ya and Mi endo (2006) and Mukhe jee e al. (2008)
showed a monopolis inal goods p oduce ’s incen i e o c ea ing compe i ion h ough
licensing when he e is s a egic inpu p ice de e mina ion. Shepa d (1987) and Fa ell and
Gallini (1988) showed a monopolis inpu supplie ’s incen i e o echnology licensing o
ano he inpu supplie o educe he hold-up p oblem aced by he inal goods p oduce s.
Unlike hese pape s, we conside an open economy wi h ma ke en y whe e he hos -coun-
y en i onmen al policy is he eason o encou aging he o eign monopolis o license i s
echnology.11
10 Wang e al. (2016b) ex end Wang e al. (2016a) o show he implica ions o pa en p o ec ion in he hos -
coun y.
11 The e is a ela ed li e a u e whe e exogenous en y o a new inal goods p oduce may inc ease he p o -
i s o he incumben i ms o he indus y p o i in he absence o s a egic go e nmen policies. See, e.g.,
Tyagi (1999), Naylo (2002a, b), Mukhe jee e al. (2009), Ma sushima (2006) and Mukhe jee (2019) o
s a egic inpu p ice de e mina ion, Pal and Sa ka (2001) and Mukhe jee and Zhao (2017) o S ackelbe g
compe i ion, Ishibashi and Ma sushima (2009) o e ical p oduc di e en ia ion and he e ogeneous con-
sume g oups, Ishida e al. (2011) o inno a ion by asymme ic cos i ms, and Fan i and Buccella (2017)
o ne wo k ex e nali y wi h co po a e social esponsibili y.
2365
J.Cao, A.Mukhe jee
In con as o he as li e a u e conside ing exogenously gi en ou side inno a o s,
which do no compe e wi h he licensees, o inside inno a o s, which compe e wi h he
licensees (see, e.g., Ros oke 1984, Kamien 1992, Saggi 2002 and Mukhe jee 2009, o
su eys o his li e a u e), he endogenous decision on licensing and FL in ou analysis
makes he o eign monopolis an ou side inno a o (in he case o licensing only) o inside
inno a o (in he case o FL) endogenously.
Ou pape also con ibu es o he g owing li e a u e on wel a e educing echnology
licensing. Licensing may educe wel a e by c ea ing collusi e ou come (Faulí-Olle and
Sandonis 2002; E kal 2005), a ec ing he R&D o ganiza ion (Mukhe jee 2005), c ea -
ing excessi e en y (Mukhe jee and Mukhe jee 2008), a ec ing he mode o en y o he
o eign i m (Sinha 2010), educing R&D incen i e (Chang e al. 2013), and inc easing
(dec easing) he go e nmen ’s subsidy bill ( ax e enues) (Ghosh and Saha 2015). In con-
as , we show he wel a e educing licensing in a pollu ing indus y. Fu he , when he
go e nmen canno commi o an emission ee, licensing educes wel a e in ou analysis i
i ac s as a subs i u e o FDI bu inc eases wel a e i i complemen s FDI.
In ou analysis, licensing only gi es he hos -coun y licensee he exclusi e igh o use
he echnology, since only he licensee uses he echnology in his si ua ion. On he o he
hand, FL gi es he hos -coun y licensee he non-exclusi e igh o use he echnology,
since bo h i ms use he echnology in his si ua ion. Hence, ou pape can also be ela ed
o he li e a u e on exclusi e con ac s.12 In ha li e a u e, he buye s and selle s, which
decide on exclusi e con as s, a e no compe i o s in he p oduc ma ke . In con as , we
conside whe he a o eign monopolis p e e s o gi e a hos -coun y i m he exclusi e
igh o use i s echnology o p e e s o o e a non-exclusi e igh whe e i compe es wi h
he licensee. Fu he , unlike ha li e a u e, we conside a pollu ing indus y wi h emission
ee.13
3 The Model
Conside a o eign inno a o , called i m 1, which holds pa en o a new p oduc ha has
no subs i u es. Fi m 1 wan s o sell he p oduc in a hos -coun y, called domes ic coun y.
Fi m 1 can se e he domes ic coun y h ough FDI o licensing o “FDI and licensing”
(FL).
FDI Unde FDI, only i m 1 p oduces and sells he p oduc in he domes ic coun y. Fi m 1
can p oduce he good a a cons an ma ginal cos ,
c
.
Licensing Unde licensing, i m 1 licenses i s echnology o a domes ic i m exclusi ely,
called i m 2. Hence, only i m 2 p oduces and sells he p oduc in he domes ic coun y.
Fi m 2 can also p oduce he good a he cons an ma ginal cos , c.
12 See, e.g., Calzola i and Denicolò (2013, 2015), G a z and Reisinge (2013), Ki amu a e  al. (2018,
2022), Calzola i e al. (2020), Chen and Sha e (2019), Ulsake (2020) and he e e ences he ein.
13 Bane jee and Podda (2019) and Niu (2019) conside ed exclusi e e sus non-exclusi e licensing in a
closed economy and in a non-pollu ing indus y. Hence, unlike ou pape , hose pape s nei he conside ed
FDI and licensing, no conside ed a pollu ing indus y. Saggi (1996) compa ed he incen i e o FDI and
licensing wi h he possibili y o exclusi e and non-exclusi e licensing. Howe e , unlike ou pape , he nei-
he conside ed a pollu ing indus y no conside ed he possibili y o FDI and licensing as complemen .
2366
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
FL Unde FL, i m 1 licenses i s echnology o i m 2, and bo h i ms 1 and 2 p oduce and
sell he p oduc in he domes ic coun y like Cou no duopolis s.14 Bo h i ms p oduce he
p oduc s a he cons an ma ginal cos , c.
As men ioned in he in oduc ion, ou pape ollows he li e a u e examining he p e e -
ence o and consequences o FDI and licensing. Hence, we assume away i m 1’s choice
o expo ing o he hos -coun y. High in e na ional anspo a ion cos , lowe cos o p o-
duc ion in he domes ic coun y, a i imposed by he domes ic coun y and en i onmen al
ax imposed by he home coun y o i m 1 p o ide some easons o exclude expo ing as
an op ion o i m 1. The absence o expo ing also helps us o ocus on he e ec s o he
domes ic en i onmen al policy by igno ing he e ec s o he ade policies, which a e dis-
cussed in Kabi aj and Ma ji (2003) and Mukhe jee and Pennings (2006).
We assume ha pollu ion is a by-p oduc o he p oduc ion p ocess. Wi hou loss o
gene ali y, we no malize he emission- o-ou pu a io o one. The p oduce s can aba e pol-
lu ion by in es ing in pollu ion aba emen echnologies. I i m
i
(
i=1, 2
) p oduces
qi
uni s
o ou pu and chooses he amoun o pollu ion aba emen as
ai
(
0≤ai≤qi
),15 he pollu an
emission le el is
qi
−ai
. Howe e , pollu ion aba emen is cos ly and he cos o pollu ion
aba emen
ai
is
CA
=
1
2
a
2
i
, o he i h i m whe e
i=1, 2
.
In line wi h he exis ing li e a u e (see, e.g., Ulph 1996, Ba cena-Ruiz and Ga zon 2002,
Long and Soubey an 2005, An elo and Lou ei o 2009 and Pal 2012), we conside ha he
en i onmen al damage om pollu ion is
ED
=
1
2
d(q−a)
2
, whe e
q=q1+q2
is he o al
ou pu ,
a=a1+a2
is he o al pollu ion aba emen , and
d>0
shows he pollu ion in ensi y
in he domes ic coun y.
We assume ha he domes ic go e nmen imposes an emission ee,
(
≥0
), pe -uni o
pollu an emi ed. In o he wo ds, we assume away he possibili y o ou pu subsidy, which,
e.g., may occu o educe he dis o ion c ea ed by he impe ec p oduc ma ke compe i-
ion. Howe e , gi en he clima e change p oblem a hand, i may be di icul o ge a public
suppo o ou pu subsidy in a pollu ing indus y. Hence, we con ine ou analysis o
d
>
1
3
so ha he emission ee unde licensing is posi i e.
Assume ha he in e se ma ke demand unc ion is
p=A−q
, which comes om
he u ili y unc ion
U
=Aq −
1
2
q2+𝜁 o a ep esen a i e consume , whe e
p
is he p ice,
𝜁
is he nume ai e good, and
A>c
. Gi en his u ili y unc ion, he consume su plus is
CS
=Aq −
1
2
q2−pq =Aq −
1
2
q2−(A−q)q=
1
2
q
2
.16
The domes ic go e nmen se s an emission ee o maximize wel a e o he domes ic
economy, which is he sum o he consume su plus, he p o i o he domes ic i m a e
deduc ing he cos o pollu ion aba emen
𝜋2
, and he ax e enue
T= (q−a)
, minus he
en i onmen al damage
ED
, i.e.:
As men ioned in he in oduc ion, we will conside he ollowing wo si ua ions in he
nex wo sec ions espec i ely. Sec ion4 will conside ha he go e nmen canno commi
(1)
W
=CS +𝜋2+T−ED =
1
2
q2+𝜋2+ (q−a)−
1
2
d(q−a)
2
14 We will conside S ackelbe g compe i ion unde FL in Sec ion6.
15 The pollu ion aba emen echnology can educe pollu an emission o ze o a mos . Hence, a p oduce
has no incen i e o choose an aba emen ha is g ea e han i s ou pu .
16 See Va ian (1992, p. 164–166) o a discussion on consume su plus o a quasilinea u ili y unc ion,
which is widely used in he pa ial equilib ium analysis like ou s.
2367
J.Cao, A.Mukhe jee
o an emission ee be o e i m 1’s ma ke -en y decision. This can be mo i a ed by he
obse a ion ha he go e nmen policies a e o en “ ime inconsis en ”, implying ha he
go e nmen has an incen i e o e e se he p eannounced policies. Acco ding o S aige
and Tabellini (1987), go e nmen s may ind i di icul o commi when i has some deg ee
o disc e iona y powe o decide i s policy. In he case o ene gy policy, Helm e al. (2003)
no iced ha no commi men by he go e nmen migh occu since he ene gy policy is used
o achie e mul iple objec i es, such as in e na ional compe i i eness, poli ical in e es s, and
lowe ene gy p ices.17 Thus, his si ua ion is in line wi h he pape s conside ing he e ec s
o he non-commi ed go e nmen policies.18 Sec ion5 will conside ha he go e nmen
can commi o i s policy be o e i m 1’s decision due o he adminis a i e o poli ical di -
icul ies in policy adjus men ha may a ec he epu a ion o he go e nmen .
4 Non‑Commi ed Policy
In his sec ion, we conside he ollowing h ee-s age game. In s age 1, i m 1 decides
whe he o do FDI, licensing o FL. In case o licensing, i m 1 makes a ake-i -o -lea e-i
o e o i m 2. Following he li e a u e on echnology licensing, we assume ha he licens-
ing con ac (unde licensing only o unde FL) consis s o a wo-pa a i wi h a non-
nega i e up- on ixed- ee (
L
) and a non-nega i e pe -uni ou pu oyal y (
), and i m 2
accep s he o e i i s payo unde licensing is no less han ha o unde no licensing,
which is no malized o ze o.
In s age 2, he go e nmen se s he emission ee (
) o maximize he domes ic wel a e
gi en by (1).
In s age 3, he p oduce s de e mine he amoun o pollu ion aba emen s
a1
,
a2
, and ou -
pu s
q1
,
q2
, and he p o i s a e ealized.
We sol e he game h ough backwa d induc ion.
4.1 FDI
Fi s , conside he case whe e i m 1 unde akes FDI. Fi m 2 is inac i e in his si ua ion,
and he maximiza ion p oblem o i m 1 in s age 3 is:
The equilib ium ou pu and he pollu ion aba emen by i m 1 a e
(2)
max
a1
,
q1
𝜋1=
(
A−q1−c
)
q1−
(
q1−a1
)
−
1
2
a
2
1
17 As men ioned in Iida and Mukhe jee (2020), “ he Aus alian go e nmen epealed he Clean Ene gy ac
2011 and abolished he ca bon p ice mechanism o lowe he cos o domes ic p oduc ion and consump ion
(see he websi e o he Aus alian Depa men o he En i onmen h p:// www. en i onmen . go . au/).” Helm
e al. (2003) also p o ide examples o ime inconsis ency p oblems o he ene gy policies.
18 Fo he e ec s o non-commi ed en i onmen al policies, one may look a Poyago-Theo oky (2007),
Golombek e al. (2010) and Ha o i (2013) o en i onmen al in es men s, Ee ola (2006), Dijks a e al.
(2011) and De San is and S ähle (2009) o i ms’ loca ion decisions, and Iida and Mukhe jee (2020) o
bi-sou cing. Fo he e ec s o non-commi ed non-en i onmen al policies, one may look a S aige and
Tabellini (1987), Al-Saadon and Das (1996), Mukhe jee (2000), Nea y and Leahy (2000), Mukhe jee and
Pennings (2006), Mukhe jee and Tsai (2013), Lee e al. (2018) and Basak and Mukhe jee (2022).
2368
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
On he one hand, FL inc eases he ou pu , bu on he o he hand, i inc eases he pollu-
ion aba emen . We ind ha he o me e ec o e weighs he la e , making he pollu an
emission unde FL highe compa ed o FDI, i.e.
qFL −aFL >qF−aF
.
FL (compa ed o FDI) inc eases he o al ou pu and consume su plus by inc easing
compe i ion and educing he emission ee. Al hough he p o i o i m 2 does no help o
inc ease he domes ic wel a e,28 highe consume su plus unde FL compa ed o FDI domi-
na es he nega i e e ec due o a highe en i onmen al damage and lowe ax e enue. As a
esul , compa ed o FDI, FL inc eases domes ic wel a e, and he wo ld wel a e, since i also
makes he o eign i m be e o .
4.4 Equilib ium Choice: Licensing o FL
We ha e shown ha i m 1 p e e s bo h licensing and FL compa ed o FDI. Now we de e -
mine i m 1’s op imal mode o en y by compa ing licensing wi h FL and see he co -
esponding wel a e implica ions. We a ain
𝜋L
1⋛
𝜋
FL
1
o
d⋚d
, whe e
d≈0.88753
.29
Hence, we ha e he ollowing p oposi ion immedia ely.
P oposi ion 1 Fi m 1 p e e s licensing compa ed o FL i and only i
d
≤
d(≈
0.88753
)
.
Licensing (compa ed o FL) no only c ea es lowe p oduc -ma ke compe i ion bu also
c ea es lowe emission ee o a low pollu ion in ensi y.30 Howe e , he e ec i e ma ginal
cos o p oduc ion unde licensing is highe han ha o i m 1 unde FL since i m 2 has o
pay a oyal y a e, which is low i he pollu ion in ensi y is no high. Hence, lowe compe i-
ion and lowe emission ee unde licensing make i m 1 be e o compa ed o FL i he
pollu ion in ensi y is no high.
4.5 Wel a e Implica ions
Now look a he wel a e implica ions. While FL inc eases consume su plus, domes ic wel-
a e and wo ld wel a e compa e o FDI, he licensing s a egy educes domes ic wel a e
and may educe consume su plus and wo ld wel a e compa ed o FDI. By compa ing he
consume su plus and wel a e unde licensing wi h hose unde FL, we ge he ollowing
Lemma.
Lemma 5 Compa ed o licensing, FL.
28 The eason is ha i m 1 uses he ixed- ee o ex ac he p o i o i m 2.
29
d
is a solu ion o he equa ion
108d4+
396
d3+
389
d2−
202
d−
471
=0
, and is he cu o alue o he
pollu ion in ensi y o which he p o i o i m 1 unde FL is he same o ha o unde licensing. I inc eases
wi h S ackelbe g compe i ion unde FL, as shown in subSec ion6.1.2.
30 We ha e
L< FL
o
d<d0
, whe e
d0
(
d0≈1.57688
) is a solu ion o he equa ion
108d4+225d3−97d2−563d−421 =0
, and is he cu o alue o he pollu ion in ensi y o which he
emission ee unde FL is he same o ha o unde licensing.
2375

J.Cao, A.Mukhe jee
(i) inc eases ( educes) he consume su plus i , whe e 31
(ii) inc eases he domes ic wel a e and wo ld wel a e.
P oo Appendix 7.
We know om Lemmas 2 and 4 ha he consume su plus unde FL is always highe han
ha o unde FDI which is highe han ha o unde licensing o
d
>2
√
3−
1
3
. Howe e , he
consume su plus unde licensing is highe han ha o unde FDI o
d
<2
√
3−
1
3
.
On he one hand, highe compe i ion unde FL compa ed o licensing ends o c ea e
highe consume su plus unde he o me han he la e . On he o he hand, i he pol-
lu ion in ensi y is no high, highe oyal y a e and emission ee unde FL compa ed o
licensing end o educe consume su plus unde he o me han he la e . As a esul , he
consume su plus unde FL is lowe han ha o unde licensing o low pollu ion in ensi y,
i.e.
d<
.
Compa ed o FDI, licensing educes he domes ic wel a e while FL inc eases i . Hence, i is
ob ious ha he domes ic wel a e unde FL is highe han ha o unde licensing.
Compa ed o FL, licensing ends o inc ease he wo ld wel a e by making he o eign i m
be e o o
d≤d
, bu ends o dec ease he wo ld wel a e by educing he domes ic wel-
a e. The la e e ec domina es he o me e ec , hus making he wo ld wel a e lowe unde
licensing compa ed o FL.
To sum up, since
d
�=2
√
3−1
3
≈0.82137 <0.88753 ≈d , We ge he ollowing wo esul s
om Lemmas 2, 4 and 5, and P oposi ion 1.
P oposi ion 2 (i) Fo
d
≤
d(≈
0.88753
)
, i m 1 p e e s licensing. In his si ua ion, licensing
(a) inc eases he consume su plus compa ed o bo h FDI and FL i and only i
d
<

d
(≈ 0.354329)
,
(b) inc eases he consume su plus compa ed o FDI bu dec eases i compa ed o FL i
and only i
<d<d�(≈0.82137)
,
(c) dec eases he consume su plus compa ed o bo h FDI and FL i and only i
d
′
<d≤d
.
(ii) Fo
d>d
, i m 1 p e e s FL, which bene i s he consume s compa ed o bo h licens-
ing and FDI.
P oposi ion 3 (i) Fo
d
≤
d(≈ 0.88753)
, i m 1 p e e s licensing. In his si ua ion, licensing
(a) educes he domes ic wel a e compa ed o bo h FDI and FL,
(b) inc eases (dec eases) he wo ld wel a e compa ed o FDI o
d<�
d(≈ 0.64101)
(
�
d<d≤d
), bu always dec eases i compa ed o FL.
31 is he cu o alue o he pollu ion in ensi y o which he consume su plus is he same unde FL and
unde licensing. As shown in subSec ion6.1.2, i inc eases wi h S ackelbe g compe i ion unde FL.
2376
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
(ii)Fo
d>d
, i m 1 p e e s FL, which c ea es highe domes ic wel a e and wo ld wel-
a e compa ed o bo h licensing and FDI.
Figu e1 shows i m 1’s choice and he implica ions on he consume s, domes ic wel a e
and wo ld wel a e.
5 Commi ed Policy
Now we conside a si ua ion whe e he domes ic go e nmen can commi o i s policy
be o e i m 1’s ma ke -en y decision. Hence, in e ms o he game s uc u e, he o de o
s ages 1 and 2 in he p e ious sec ion is swi ched. To be speci ic, he go e nmen se s an
emission ee (
) o maximize he domes ic wel a e in s age 1, and i m 1 decides whe he o
do FDI, licensing o FL in s age 2.
5.1 Ma ke ‑En y Decision o Fi m 1
The p oblem and solu ions in s age 3 he e a e o ally he same as hose unde he non-com-
mi ed policy. Hence, gi en he emission ee se by he domes ic go e nmen in s age 1, we
examine he ma ke -en y decision o i m 1 by compa ing i s p o i s unde FDI, licensing
and FL in s age 2.
5.1.1 FDI
I i m 1 unde akes FDI in s age 2, he p o i o i m 1 unde FDI is
𝜋
1=(A−c− )
2
+2
2
4
5.1.2 Licensing
I i m 1 licenses he echnology o i m 2 bu does no p oduce h ough FDI in s age 2,
i m 1 maximizes he exp ession (13) o de e mine he licensing ee. Since he equilib-
ium
L
equals
(
A−q2−c−
)
q2−
(
q2−a2
)
−
1
2
a
2
2
, he p o i o i m 1 educes o
𝜋
1=(A−c− )
2
+2 2−
2
4
. I is ob ious ha he op imal oyal y a e is 0 and he p o i o i m 1
unde licensing in s age 2 is
𝜋
1=(A−c− )
2
+2
2
4
, he same as ha o unde FDI. This esul is
e y di e en om he si ua ion o he non-commi ed policy. The eason is ha , unde he
Fig. 1 Fi m 1’s choice and he wel a e implica ions
2377
J.Cao, A.Mukhe jee
commi ed policy, i m 1 has no abili y o induce he hos -coun y go e nmen o educe
he emission ee by licensing.
5.1.3 FL
I i m 1 unde akes FL in s age 2, he maximiza ion p oblem o i m 1 is simila o he
si ua ion in subSec ion 4.3 wi h he excep ion ha he emission ee is gi en in s age 1
he e. Because
q2⋛
o
⋚
A−c−4
2
,
a2=
i he oyal y a e de e mined by i m 1 is
no g ea e han
A−c−4
2
; o he wise
a2=q2
. We ge he equilib ium oyal y a e unde FL as
=
A−c−3
2
,32 making
a2=q2
and he p o i o i m 1 unde FL is
𝜋
1=3(A−c− )
2
+10
2
12
, which
is g ea e han ha o unde FDI o licensing. Hence, i m 1 p e e s FL o bo h FDI and
licensing.
The eason o his is as ollows. Al hough licensing unde FL c ea es compe i ion and
he emission ee is no a ec ed by i m 1’s decision, FL sa es he o al ax paymen s by
educing i m 1’s ou pu and pollu an emission.33 In addi ion, i m 1 can use a posi i e
oyal y a e o so en compe i ion om i m 2.
5.2 Equilib ium
In s age 1, he go e nmen de e mines he emission ee o maximize (1) wi h
q1
and
q2
gi en by (19),
a1
gi en by (20),
a2=q2
,
=
A−c−3
2
and
𝜋2=0
. We ind he equilib ium
emission ee unde he commi ed policy is
C=
3(11d+5)(A−c)
121d+131
. The co esponding equi-
lib ium pollu ion aba emen s, ou pu s, pollu an emission, oyal y a e, ixed- ee, p o i s,
domes ic wel a e and wo ld wel a e a e as ollows:
Thus, he ollowing p oposi ion is immedia e om he abo e analysis.
a
C
1
=
3(11d+5)(A−c)
121d+131
aC
2
=
2(11d+5)(A−c)
121d+131
aC=
5(11d+5)(A−c)
121d+131
q
C
1
=
(33d+53)(A−c)
121d+131
qC
2
=
2(11d+5)(A−c)
121d+131
qC=
(55d+63)(A−c)
121d+131
q
C−aC=38(A−c)
121d+131
C=(11d+43)(A−c)
121d+131
LC=8(11d+5)
2
(A−c)
2
(121d+131)
2
𝜋
C
1=(5687d2+11858d+7103)(A−c)
2
2
(
121
d+
131
)
2𝜋C
2=0WC=(25d+39)(A−c)
2
2
(
121
d+
131
)
GW
C=2(2178d2+4963d+3053)(A−c)
2
(
121
d+
131
)
2
32 I i m 1 chooses
≤
A−c−4
2
, i a ains he maximum p o i
(
A−c− )
2
+3 2
4
(
<
3(A−c− )
2
+10 2
12
) a
=
A−c−4
2
.
33 The ax paymen unde FL (which is
[3(A−c)−11 ]
6
) is less han ha o unde FDI o licensing (which is
(A−c−3 )
2
) by
2
3
.
2378
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
P oposi ion 4: Fi m 1 always p e e s FL compa ed o bo h FDI and licensing in a pollu -
ing indus y when he hos -coun y go e nmen commi s o he emission ee be o e i m 1’s
ma ke -en y decision. The equilib ium licensing con ac unde FL consis s o a posi i e
ixed- ee and a oyal y.
We ha e
𝜕
C
𝜕
d
=2508(A−c)
(121d+131)
2>0, 𝜕 C
𝜕
d
=− 3762(A−c)
(121d+131)
2<0, 𝜕aC
𝜕
d
=4180(A−c)
(121d+131)
2>0, 𝜕q
C
𝜕
d
=− 418(A−c)
(121d+131)
2<
0,
𝜕(
q
C
−a
C)
𝜕
d
=− 4598(A−c)
(121d+131)
2<0, 𝜕𝜋
C
1
𝜕
d
=27588(d−3)(A−c)2
(121d+131)
3⋚
0
o
d
⋚3, 𝜕W
C
𝜕d=− 722(A−c)
2
(121
d
+131)
2<
0
and
𝜕
GW
C
𝜕d
=−
494(121d+359)(A−c)
2
(121d+131)
3<
0
, indica ing ha simila o FL unde he non-commi ed pol-
icy, he emission ee and pollu ion aba emen inc ease wi h he pollu ion in ensi y,
d
, he
oyal y a e, ou pu s, pollu an emission, domes ic wel a e and wo ld wel a e dec ease wi h
d
, while he p o i o i m 1 dec eases i s and hen inc eases wi h
d
.
5.3 Compa ison wi h heNon‑Commi ed Policy
Now compa e he equilib ium alues unde he commi ed hos -coun y policy wi h hose
o unde he non-commi ed hos -coun y policy. We deno e he equilib ium alues unde
he non-commi ed hos -coun y policy by supe sc ip N. Hence, hey a e equal o hose
unde licensing o
d≤d
and hose unde FL o
d>d
as shown in Sec ion4. Fo exam-
ple, he equilib ium emission ee unde he non-commi ed hos -coun y policy is
N= L
o
d≤d
and
N= FL
o
d>d
.
As Fig.2(a) shows, he emission ee unde he commi ed policy is highe han ha o
unde he non-commi ed policy, i.e.
C> N
, i and only i
d<d1(≈ 24.032)
.34
Compa ed o he non-commi ed policy, he pollu ion aba emen is highe while pol-
lu an emission is lowe unde he commi ed policy, as shown in Fig. 2(b) and 2(c)
espec i ely.
Figu e2(d) shows ha al hough i m 1 makes he ma ke -en y decision a e he com-
mi ed emission ee, i s p o i is highe unde he commi ed policy compa ed o he non-
commi ed policy i and only i
d2(≈ 4.00676)<d<d3(≈ 42.8541)
.35
Figu e2(e) shows ha he o al ou pu unde he commi ed policy is lowe han ha o
unde he non-commi ed policy i
d<d4(≈ 0.41446)
o
d<d<d5(≈
6.68214
)
,36 indica -
ing ha he commi ed policy makes he consume s wo se o compa ed o he non-com-
mi ed policy i
d<d4
o
d<d<d5
.
The domes ic wel a e unde he commi ed policy is highe han ha o unde he
non-commi ed policy, as shown in Fig. 2( ). Howe e , as he commi ed policy low-
e s he p o i o i m 1 o
d<d2
, i makes he wo ld wel a e wo se o i and only i
d<d<d6(≈
2.47245
)
, as shown in Fig.2(g).37
34
d1
is he cu o alue o he pollu ion in ensi y o which he emission ee unde he commi ed policy is
he same o ha o unde he non-commi ed policy.
35
d2
and
d3
a e wo cu o alues o he pollu ion in ensi y o which he p o i o o eign i m unde he
commi ed policy is he same o ha o unde he non-commi ed policy.
36
d4
and
d5
a e wo cu o alues o he pollu ion in ensi y o which he o al ou pu unde he commi ed
policy is he same o ha o unde he non-commi ed policy.
37
d6
is he cu o alue o he pollu ion in ensi y o which he wo ld wel a e unde he commi ed policy is
he same o ha o unde he non-commi ed policy.
2379
J.Cao, A.Mukhe jee
Fig. 2 Compa ison be ween wo policies wi h A – c = 1
2380

Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
Based on he a o emen ioned compa isons, we ha e he ollowing wo esul s
immedia ely.
P oposi ion 5 Compa ed o he non-commi ed hos -coun y policy, he commi ed hos -
coun y policy inc eases he pollu ion aba emen and dec eases he pollu an emission.
Howe e , he p o i o i m 1 is highe unde he commi ed policy han he non-commi ed
policy i and only i
(
d<)d
2
(≈ 4.00676)<d<d
3
(≈ 42.8541
)
.
P oposi ion 6 Compa ed o he non-commi ed hos -coun y policy, al hough he commi -
ed hos -coun y policy inc eases he domes ic wel a e, i educes he consume su plus
i
d
<d
4
(≈ 0.41446)o d <d<d
5
(≈ 6.68214),and educes wo ld wel a e i d <d<d
6
(≈ 2.47245
)
.
The in ui ions o P oposi ions 5 and 6 a e as ollows. Fi m 1 p e e s licensing o
d<d
and FL o
d>d
unde he non-commi ed hos -coun y policy, while i p e e s FL unde
he commi ed hos -coun y policy. Fi s , conside
d<d
. He e, bo h i ms p oduce unde
he commi ed policy while only i m 2 p oduces unde he non-commi ed policy. Com-
pa ed o he non-commi ed policy, his ends o inc ease he ou pu and pollu an emission
o a gi en pollu ion aba emen and emission ee, which induces he go e nmen o se a
highe emission ee unde he commi ed policy. As a esul , i ms choose a highe pollu-
ion aba emen and a lowe pollu an emission occu s unde he commi ed policy com-
pa ed o he non-commi ed policy.
A he same ime, highe p oduc -ma ke compe i ion gi es i m 1 he incen i e o se a
highe oyal y a e unde he commi ed policy.38 Al hough he p oduc -ma ke compe i ion
unde he commi ed policy is highe , highe ma ginal cos due o a highe emission ee and
a highe oyal y a e makes he ou pu unde he commi ed policy lowe compa ed o he
non-commi ed policy o
d<d4
.
Al hough he consume su plus unde he commi ed policy may be lowe , he lowe
en i onmen al damage om he educed pollu an emission makes he domes ic wel a e
highe unde he commi ed policy compa ed o he non-commi ed policy.
Highe p oduc -ma ke compe i ion unde he commi ed policy helps o dec ease he
p o i o i m 1 unde he commi ed policy compa ed o he non-commi ed policy. How-
e e , his e ec is domina ed by he highe domes ic wel a e unde he commi ed policy o
make he wo ld wel a e unde he commi ed policy highe compa ed o he non-commi ed
policy.
Now conside
d>d
, whe e bo h i ms compe e in he p oduc -ma ke unde he non-
commi ed and commi ed policies. On he one hand, o a gi en oyal y a e, he non-com-
mi ed policy allows he hos -coun y go e nmen o cha ge a highe emission ee com-
pa ed o he commi ed policy by allowing o he go e nmen o mo e a e i m 1.39 On
he o he hand, i m 1 ies o induce he hos -coun y go e nmen o lowe he emission
38 We ind
C− L=
(
297d
3
+303d
2
+1355d+997
)
(A−c)
(121d+131)
(
27d2+54d+11
)
>
0
.
39 When bo h i ms compe e in he p oduc ma ke , he hos -coun y go e nmen se s a high emis-
sion ee, making
a2=q2
in equilib ium unde he non-commi ed and commi ed policies. Thus,
wi h
q1
and
q2
gi en by (19),
a1=
and
a2=q2
, o a gi en oyal y a e ha is less han
(4d+15)(A−c)
7
(
4
d+
5
)
, he
op imal emission ee unde he non-commi ed policy, i.e.,
(4d+1)(A−c+ )
16d+25
, is highe han ha o unde
he commi ed policy, i.e.
(4d−1)(A−c)+(4d+5)
4
(
4
d+
5
)
. A he same ime, we ge
(4d+15)(A−c)
7
(
4
d+
5
)
> FL > C om
(4d+15)(A−c)
7
(
4
d+
5
)
− FL =
(2d+11)(4d+1)(16d+25)(A−c)
7
(
4
d+
5
)(
144
d
2
+
380
d+
233
)
>
0
and
FL − C=(352d
3
+1162d
2
+2447d+2033)(A−c)
(
121
d+
131
)(
144
d
2
+
380
d+
233
)
>
0
.
2381
J.Cao, A.Mukhe jee
ee by cha ging a highe oyal y a e unde he non-commi ed policy compa ed o he com-
mi ed policy. Since a highe pollu ion in ensi y ends o inc ease he emission ee, he oy-
al y a e is mo e e ec i e o educe he emission ee i he pollu ion in ensi y is no e y
high. Hence, i he pollu ion in ensi y is no e y high (i.e.
d<d1
), he emission ee is
highe unde he commi ed policy han he non-commi ed policy.
The emission ee unde he commi ed policy may be lowe o highe han ha o
unde he non-commi ed policy. Howe e , i he pollu ion in ensi y is no e y high (i.e.
d<d<d5(<d1)
), al hough he oyal y a e unde he non-commi ed policy is highe
han ha o unde he commi ed policy, he emission ee unde he non-commi ed policy
becomes much lowe han ha o unde he commi ed policy o make he ma ginal cos
lowe unde he o me han he la e . As a esul , he ou pu and consume su plus unde
he commi ed policy is lowe compa ed o he non-commi ed policy o
d<d<d5
.
A highe oyal y a e unde he non-commi ed policy compa ed o he commi ed pol-
icy no only helps o educe pollu ion aba emen by i m 1 by lowe ing he emission ee,
i also helps o educe he pollu ion aba emen by i m 2 by educing i s ou pu . Thus, he
pollu ion aba emen unde he commi ed policy is highe compa ed o he non-commi ed
policy. This makes he pollu an emission lowe unde he commi ed policy han he non-
commi ed policy, e en hough he ou pu unde he o me may be highe han ha o
unde he la e .
Fo a gi en oyal y a e, he hos -coun y go e nmen ends o se a lowe emission ee
unde he commi ed policy compa ed o he non-commi ed policy, hus making he p o i
o i m 1 highe unde he o me han he la e . Howe e , he highe oyal y a e unde he
non-commi ed policy compa ed o he commi ed policy may inc ease he p o i o i m 1 by
lowe ing he emission ee and educing he in ensi y o p oduc -ma ke compe i ion. I he
pollu ion in ensi y is low, he highe oyal y a e is e ec i e o educe he emission ee signi i-
can ly unde he non-commi ed policy, hus making he p o i o i m 1 highe unde he non-
commi ed policy compa ed o he commi ed policy. I he pollu ion in ensi y is high, he
highe oyal y a e makes he p o i o i m 1 highe unde he non-commi ed policy com-
pa ed o he commi ed policy by educing he p oduc -ma ke compe i ion unde he o me
han he la e . The e o e, he p o i o i m 1 is highe unde he commi ed policy compa ed
o he non-commi ed policy o mode a e pollu ion in ensi y (i.e.
d2<d<d3
).
The domes ic wel a e is highe unde he commi ed policy compa ed o he non-com-
mi ed policy since he commi ed policy helps o cu b i m 1’s powe o manipula e he
emission ee h ough he oyal y a e.
Al hough he commi ed policy helps o inc ease he domes ic wel a e compa ed o
he non-commi ed policy, he commi ed policy educes he p o i o i m 1 compa ed o
he non-commi ed policy o low and high pollu ion in ensi y. This lowe p o i o i m 1
unde he commi ed policy makes he wo ld wel a e lowe unde he commi ed policy
compa ed o he non-commi ed policy i he pollu ion in ensi y is no high, i.e.,
d<d6
.
6 S ackelbe g Compe i ion Unde FL
We ha e conside ed so a ha he i ms beha e like Cou no duopolis s unde all a ange-
men s. In his sec ion we wan o show he implica ions o S ackelbe g compe i ion unde
FL whe e, in s age 3, i m 1 chooses ou pu
q1
and pollu ion aba emen
a1
like he S ack-
elbe g leade and i m 2 chooses ou pu
q2
and pollu ion aba emen
a2
like he S ackelbe g
ollowe . We ind ha all ou main esul s hold unde S ackelbe g compe i ion.
2382
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
6.1 Non‑Commi ed Policy
6.1.1 FL
Unde FL, he maximiza ion p oblems o he i ms unde S ackelbe g compe i ion in s age
3 gi e he equilib ium ou pu s and he pollu ion aba emen s as:
In s age 2, he go e nmen de e mines he emission ee o maximize (1) subjec o (18),
(19’) and (20’). As shown in Appendix 8, he equilib ium emission ee se by he go e n-
men in s age 2 is as ollows.
As shown in Appendix 9, in s age 1, we can ha e he equilib ium oyal y a e unde FL
as
FL =
(6d+31)(A−c)
3
(
18
d+
23
)
. Acco dingly, unde FL, we ge he equilib ium emission ee, pollu ion
aba emen , ou pu s, pollu an emission, ixed- ee, p o i s, domes ic wel a e and wo ld wel-
a e, as ollows:
By compa ing he abo e-men ioned alues wi h hose unde FDI as shown in Appen-
dix 10, we ind ha Lemmas 3 and 4 hold wi h he excep ion ha he pollu ion aba emen
unde FL is highe compa ed o FDI only o
d
>
√
769−
13
36
. This happens since, compa ed o
Cou no compe i ion, he ou pu and pollu ion aba emen o i m 2 is lowe .
(19’)
q
1=
A−c−
2
q2=
A−c−2 −
4
(20’)
a
1= a
2=
{
, i q2≥
q2, i q2≤
(21’)
=
⎧
⎪
⎨
⎪
⎩
(33d+1)(A−c)−2(11d−1)
121d+61 , i 0 ≤ ≤(14−11d)(A−c
)
33(d+1)
A−c−2
5, i (14−11d)(A−c)
33(d+1)< ≤3(3−2d)(A−c)
18d+23
(6d+1)(A−c)
18d+23
, i 3(3−2d)(A−c)
18d+23
< ≤(6d+11)(A−c)
18d+23
FL =
(6d+1)(A−c)
18
d+
23 aFL
1=
(6d+1)(A−c)
18
d+
23 aFL
2=
(6d+1)(A−c)
3
(
18
d+
23
)
a
FL =
4(6d+1)(A−c)
3
(
18
d+
23
)
qFL
1=
(6d+11)(A−c)
18
d+
23 qFL
2=
(6d+1)(A−c)
3
(
18
d+
23
)
q
FL =
2(12d+17)(A−c)
3(18d+23)
qFL −aFL =
10(A−c)
18d+23
L
FL =7(6d+1)2(A−c)
2
18(18d+23)
2𝜋FL
1=5(36d2+84d+73)(A−c)2
3(18d+23)
2𝜋FL
2=
0
W
FL =2(144d2+453d+334)(A−c)
2
9
(
18
d+
23
)
2GWFL =(828d2+1083d+1763)(A−c)
2
9
(
18
d+
23
)
2
2383
J.Cao, A.Mukhe jee
6.1.2 Equilib ium Choice andWel a e Implica ions
E en i he i ms compe e like S ackelbe g duopolis s, i m 1 s ill p e e s FL compa ed o
FDI (see Appendix 10). We also ge
𝜋L
1⋛𝜋FL
1
o
d⋚
d
S
, whe e
d
S
≈1.26372
, indica -
ing ha he esul shown in P oposi ion 1 also holds.40
As shown in Appendix 11, by compa ing he consume su plus and wel a e unde
licensing wi h hose unde FL, we ge ha a esul simila o Lemma 5 holds in his sec ion
wi h a di e en cu o alue
≈0.387691
. Hence, he esul s like P oposi ions 2 and 3
also hold e en i he i ms beha e like S ackelbe g duopolis s unde FL.
6.2 Commi ed Policy
6.2.1 FL
The equilib ium ou pu s and he pollu ion aba emen s unde FL in s age 3 a e gi en by
(19’) and (20’). Because
q2⋛
o
⋚
A−c−5
2
, we ge
a2=
, i he oyal y a e de e -
mined by i m 1 is no g ea e han
A−c−5
2
; o he wise
a2=q2
. The equilib ium oy-
al y a e unde FL is
=
3(A−c)−7
6
,41 making
a2=q2
and he p o i o i m 1 unde FL as
𝜋
1=3(A−c− )
2
+8 2
12
, which is g ea e han ha o unde FDI o licensing. Hence, i m 1 p e-
e s FL o bo h FDI and licensing.
6.2.2 Equilib ium
In s age 1, he go e nmen de e mines he emission ee o maximize (1) wi h
q1
and
q2
gi en by (19’),
a1
gi en by (20’),
a2=q2
,
=
3(A−c)−7
6
and
𝜋2=0
. We ge he equilib-
ium emission ee unde he commi ed policy as
C=
3(9d+5)(A−c)
81d+107
. The co esponding equi-
lib ium pollu ion aba emen s, ou pu s, pollu an emission, oyal y a e, ixed- ee, p o i s,
domes ic wel a e and wo ld wel a e a e as ollows:
a
C
1
=
3(9d+5)(A−c)
81d+107
aC
2
=
(9d+5)(A−c)
81d+107
aC=
4(9d+5)(A−c)
81d+107
q
C
1
=
(27d+46)(A−c)
81d+107
qC
2
=
(9d+5)(A−c)
81d+107
qC=
3(12d+17)(A−c)
81d+107
q
C−aC=31(A−c)
81d+107
C=9(d+4)(A−c)
81d+107
LC=7(9d+5)
2
(A−c)
2
2(81d+107)
2
𝜋
C
1=(1215d2+3024d+2266)(A−c)
2
(
81
d+
107
)
2𝜋C
2=0WC=(16d+33)(A−c)
2
2
(
81
d+
107
)
41 I i m 1 chooses
≤
A−c−5
2
, i a ains he maximum p o i
(
A−c− )
2
4
(
<
3(A−c− )
2
+8
2
12
) a
=
A−c−5
2
.
40
d
S
is a solu ion o he equa ion
972d4+2268d3+1287d2−2262d−6253 =0
, and is he cu o alue o
he pollu ion in ensi y o which he p o i o i m 1 unde licensing is he same o ha o unde FL.
2384
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
whe e
1=
16d(A−c)−(8d−3)
64d+33
and
0=
11(A−c)
32d+26
. The co esponding domes ic wel a e is:
I he emission ee is se a
≥ 0
, he domes ic wel a e is:
In his si ua ion, since
𝜕W
𝜕
=
(4d+1)(A−c+ )−(16d+25)
9
and
𝜕2
W
𝜕
2=−
16d+25
9
<
0
, he equilib-
ium emission ee is:
whe e
2=
(4d+1)(A−c+ )
16d+25
,
1=
7(A−c)
16d+18
and
2=
4(d+2)(A−c)
12d+17
. The condi ion
≤ 2
is o gua an-
ee
q2≥0
i he oyal y a e se in s age 1 is g ea e han
1
. The co esponding domes ic
wel a e is:
Compa ing
W1
wi h
W2
, we ha e:
Hence, he equilib ium emission ee se by he go e nmen in s age 2 will be:
Appendix4: P oo o  heEquilib ium Royal y Ra e insubSec ion4.3
We ge
=
{
1, i 1≤ 0i.e. ≤
0
0
, i
1
>
0
i.e. >
0
W
1=
{
2(14d+11)(A−c)
2
−4(15d+11)(A−c) +(55d+34)
2
128d+66 −L, i ≤
0
7(A−c)2−4(A−c) −4(4d+1) 2
32
−L, i > 0
W
=(5−d)(A−c)
2
−2(d+4)(A−c) −(d−5) 2+2(4d+1)(A−c+ ) −(16d+25) 2
18
−
L
=
{
0, i 2≤ 0i.e. ≤ 1
2
, i
2
>
0
i.e.
1
< ≤
2
W
2=
{
7(A−c)
2
−4(A−c) −4(4d+1) 2
32 −L, i ≤ 1
7(d+2)(A−c)2−2(9d+11)(A−c) +7(d+2) 2
32d+50
−L, i >
1
W
1−W2=
⎧
⎪
⎨
⎪
⎩
[(32d+26) −11(A−c)]2
32(64d+33)>0, i ≤ 0
0, i 0< ≤ 1
−[2(8d+9) −7(A−c)]2
512d+800
<0, i > 1
.
=
⎧
⎪
⎨
⎪
⎩
1, i 0 ≤ ≤ 0
0, i 0< ≤ 1
2, i 1< ≤ 2
.
2391

J.Cao, A.Mukhe jee
Since
𝜕𝜋
1
𝜕
>
0
o
≤ 0
52 and o
0< ≤ 1
, he equilib ium oyal y a e mus be
g ea e han
1
. Thus, he i s o de condi ion gi es he equilib ium oyal y a e unde FL
as
FL =
2(d+2)(8d+23)(A−c)
144d
2
+380d+233
Appendix5: P oo o Lemma 3
I is ob ious om he exp essions o
FL
and
LFL
ha he equilib ium oyal y a e and ixed-
ee unde FDI and licensing a e posi i e.
We ge :
Appendix6: P oo o Lemma 4
We ha e:
W
FL −WF=(16128d5+93980d4+203740d3+199487d2+84594d+11175)(A−c)
2
2(9d+11)(144d
2
+380d+233)
2>
0
, and
𝜕𝜋
1
𝜕 =
⎧
⎪
⎨
⎪
⎩
(256d
2
+560d+77)(A−c)−2(320d
2
+520d+121)
(64d+33)2, i 0 ≤ ≤
0
2, i 0< ≤ 1
4(d+2)(8d+23)(A−c)−2(144d2+380d+233)
(16
d
+25)2, i 1< ≤ 2.
FL − F=−
2
(
36d
3
+143d
2
+140d+45
)
(A−c)
(9d+11)
(
144d2+380d+233
)
<
0
a
FL −aF=2(72d
3
+232d
2
+211d+21)(A−c)
(
9
d+
11
)(
144
d
2
+
380
d+
233
)
>
0
(
qFL −aFL
)
−
(
qF−aF
)
=3(18d
2
+23d+23)(A−c)
(9d+11)
(
144d2+380d+233
)
>
0
𝜋
FL
1−𝜋F
1=(324d
4
+1332d
3
+2143d
2
+1486d+411)(A−c)
2
(
9
d+
11
)
2
(
144
d
2
+
380
d+
233
)
>
0
q
FL −qF=
(
144d
3
+518d
2
+491d+111
)
(A−c)
(9d+11)
(
144d2+380d+233
)
>
0
GW
FL −GWF=(d+1)
(
238464d
5
+1414620d4+3233308d3+3480575d2+1721494d+314451
)
(A−c)
2
2
(
9d
+
11
)
2
(
144d2
+
380d
+
233
)
2>
0
52
𝜕𝜋1
𝜕
educes wi h o
≤ 0
bu
𝜕𝜋
1
𝜕
( = 0)=2(32d
2
+52d−5)(A−c)
(
16
d+
13
)(
64
d+
33
)
>
0
2392
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
Appendix7: P oo o Lemma 5
(i) Since consume su plus is
1
2
q
2
, he compa ison o o al ou pu s will help o compa e
he consume su plus. We ge
q
FL −qL=
(
432d4+2466d3+3647d2+696d−821
)
(A−c)
(
27d2+54d+11
)(
144d2+380d+233
)
⋛
0
o
d⋛
, whe e is he solu ion o he equa ion
432d4+2466d3+3647d2+696d−821 =0
.
(ii) W e h a e
W
FL −WL=Φ(A−c)
2
2(27d
2
+54d+11)
2
(144d
2
+380d+233)
2>
0
, and
GW
FL −GWF=Ψ(A−c)
2
2(27d
2
+54d+11)
2
(144d
2
+380d+233)
2>
0
, whe e
and
Ψ=(
2146176d
8+
19709244d
7+
75636288d
6+
153609759d
5+
170556655d
4
+
92075690d
3+
10554982d
2−
7498293d
−
988485
)
>
0
o
d
>
1
3
Appendix8: P oo o  heEquilib ium Emission Fee insubSec ion6.1.1
Because
q2⋛
o
⋚ 0=
A−c−2
5
, he go e nmen has wo choices. One is o se
≤ 0
making
a2=
in s age 3, and he o he is o se
≥ 0
making
a2=q2
in s age 3.
Suppose he go e nmen se s
≤ 0
. In his si ua ion, he domes ic wel a e is.
We ge om
𝜕
W
𝜕
=
(
33d
+
1
)
(A
−
c)
−
2(11d
−
1)
−
(121d
+
61)
16
and
𝜕2
W
𝜕
2=−
121d
+
61
16
<
0
ha he equi-
lib ium emission ee is:
whe e
1=
(33d+1)(A−c)−2(11d−1)
121d+61
and
0=
(14−11d)(A−c)
33(d+1)
in Sec ion 6. The co esponding
domes ic wel a e is:
I he emission ee is se a
≥ 0
, he domes ic wel a e is:
In his si ua ion, since
𝜕W
𝜕
=
(6d+1)(A−c)−(18d+23)
8
and
𝜕2
W
𝜕
2=−
18d+23
8
<
0
, he equilib ium
emission ee is:
Φ =(
1306368d
8
+12734172d
7
+52193592d
6
+115039071d
5
+
145585273d4
+
105466450d3
+
42080906d2
+
9326963d
+
1425861
)
>
0
W
=(11 −9d)(A−c)
2
+4(3d−5)(A−c) −4(d−3) 2+2(33d+1)(A−c) −4(11d−1) −(121d+61) 2
32
−
L
=
{
1, i 1≤ 0i.e. ≤
0
0
, i
1
>
0
i.e. >
0
W
1=
{
(53d+42)(A−c)
2
−4(25d+19)(A−c) +2(35d+23)
2
2(121d+61)−L, i ≤
0
(14−d)(A−c)2−2(3d+8)(A−c) −(9d−1) 2
50
−L, i > 0.
W
=(5−2d)(A−c)
2
−8(A−c) +4 2+2(6d+1)(A−c) −(18d+23) 2
16
−
L
2393
J.Cao, A.Mukhe jee
whe e
2=
(6d+1)(A−c)
18d+23
,
1=
3(3−2d)(A−c)
18d+23
and
2=
(6d+11)(A−c)
18d+23
in Sec ion 6. The condi ion
≤ 2
is o gua an ee
q2
≥
0
i he oyal y a e se in s age 1 is g ea e han
1
. The co e-
sponding domes ic wel a e is:
Compa ing
W1
wi h
W2
, we ha e:
Hence, he equilib ium emission ee se by he go e nmen in s age 2 will be:
Appendix9: P oo o  heEquilib ium Royal y Ra e insubSec ion6.1.1
In s age 1, he maximiza ion p oblem o i m 1 is he same as ha in subSec ion4.3 wi h
q1
and
q2
gi en by (19’),
a1
and
a2
gi en by (20’), and
gi en by (21’). We ge
Since
𝜕𝜋
1
𝜕
>
0
o
≤ 0
53 and o
0< ≤ 1
, he equilib ium oyal y a e mus be
g ea e han
1=
3(3−2d)(A−c)
18d+23
. Thus, he i s o de condi ion gi es he equilib ium oyal y
a e unde FL as
FL =
(6d+31)(A−c)
3
(
18
d+
23
)
, which is g ea e han
1
.
Appendix10: Compa ison Be ween FL andFDI insubSec ion6.1.1
I is ob ious om he exp essions o
FL
and
LFL
ha he equilib ium oyal y a e and ixed-
ee unde FL a e posi i e. We also ha e:
=
{
0, i 2≤ 0i.e. ≤ 1
2
, i
2
>
0
i.e.
1
< ≤
2
W
2={(14−d)(A−c)
2
−2(3d+8)(A−c) −(9d−1)
2
50 −L, i ≤ 1
(14d+29)(A−c)2−2(18d+23)(A−c) +(18d+23) 2
4
(
18d
+
23
)
−L, i > 1
.
W
1−W2=
⎧
⎪
⎨
⎪
⎩
[33(d+1) +(11d−14)(A−c)]
2
50(121d+61)>0, i ≤ 0
0, i 0< ≤ 1
−[(18d+23) +3(2d+3)(A−c)]2
100(18d+23)<0, i > 1
.
=
⎧
⎪
⎨
⎪
⎩
1, i 0 ≤ ≤ 0
0, i 0< ≤ 1
2, i 1< ≤ 2
.
𝜕𝜋
1
𝜕 =
⎧
⎪
⎨
⎪
⎩
2(968d
2
+1837d+437)(A−c)−8(605d
2
+880d+239)
(121d+61)2, i 0 ≤ ≤
0
4(A−c)+2
25 , i 0< ≤ 1
(6d+31)(A−c)−3(18d+23)
4(18
d
+23), i 1< ≤ 2.
53
𝜕𝜋1
𝜕
educes wi h o
≤ 0
bu
𝜕𝜋
1
𝜕
( = 0)=2(484d
2
+561d+17)(A−c)
33
(d+
1
)(
121
d+
61
)
>
0
2394
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
a
FL −aF=
(
54d
2
+39d−25
)
(A−c)
3
(
9
d+
11
)(
18
d+
23
)
⋛
0
o
d
⋛
√
769−
13
36
W
FL −WF=(2268d
3
+6444d
2
+4839d+413)(A−c)
2
18(9d+11)(18d+23)
2>
0
, and
Appendix11: Compa ison Be ween Licensing andFL
insubSec ion6.1.2
(i) We ge
q
FL −qL=
(
162d
3
+621d
2
+372d−247
)
(A−c)
3(18d+23)
(
27d2+54d+11
)
⋛
0
o
d⋛
, whe e
is he solu ion o he equa ion
162d3+621d2+372d−247 =0
.
(ii) W e h a e
W
FL −WL=ΦS(A−c)
2
18(18d+23)
2
(27d
2
+54d+11)
2>
0
, and
GW
FL −GWF=Ψ
S
(A−c)
2
9(18
d
+23)2(27
d
2+54
d
+11)2>
0
, whe e
and
ΨS=(
131220d
6+
791694d
5+
1909737d
4+
2130948d
3+
760230d
2−
274026d
−
43771
)
>
0
o
d
>
1
3
.
Appendix12: The Ma ke ‑En y Decision o Fi m 1 inEquilib ium
insubSec ion7.2
Suppose he hos -coun y go e nmen se s a high emission ee in s age 1 o make i m 1
unde aking FL in s age 2. In his case, wi h
q
1=q2=
A−c−
3
,
a1=a2=
and
𝜋2=0
, we
ge 
𝜕W
𝜕
=
2[(8d+1)(A−c)−2(16d+11) ]
9
. Thus, unde he cons ain o 
≥(3
√
2−1)(A−c
)
17
, he equilib-
ium emission ee is:
FL − F=−
12(d+1)(A−c)
(
9
d+
11
)(
18
d+
23
)
<
0
(
qFL −aFL
)
−
(
qF−aF
)
=
18(d+1)(A−c)
(
9
d+
11
)(
18
d+
23
)
>
0
𝜋
FL
1−𝜋F
1=(2916d4+8100d3+12645d2+14754d+7393)(A−c)
2
6
(
9
d+
11
)
2
(
18
d+
23
)
2>
0
q
FL −qF=
(
54d2+93d+29
)
(A−c)
3
(
9
d+
11
)(
18
d+
23
)
>
0
GW
FL −GWF=
(
14580d
4
+53622d
3
+76185d
2
+50604d+13361
)
(A−c)
2
9(9d+11)
2
(18d+23)
2>
0
ΦS=(183708d6+1242216d5+3315735d4+4161780d3+2350926d2+539580d+118807)>0
2395
J.Cao, A.Mukhe jee
-
The co esponding domes ic wel a e is:
I a low emission ee is se in s age 1 so ha i m 1 unde akes FDI o licens-
ing, hen wi h
𝜋2=0
, we ha e
𝜕W
𝜕
=
(3d+1)(A−c)−(9d+11)
4
. Hence, unde he cons ain o
≤(3
√
2−1)(A−c
)
17
, he equilib ium emission ee is:
The co esponding domes ic wel a e is:
Compa ing
WH
wi h
WL
, we ha e
This indica es ha he hos -coun y go e nmen p e e s a high emission ee in s age 1 o
make i m 1 unde aking FL in s age 2.
Acknowledgemen s We hank wo anonymous e e ees o his jou nal o commen s and sugges ions. Jiyun
Cao acknowledges he inancial suppo om he Humani ies and Social Sciences Planning Fund om Chi-
nese Minis y o Educa ion (G an No. 21YJA790001) and he Fundamen al Resea ch Funds o he Cen-
al Uni e si ies om Nankai Uni e si y, Tianjin, China (P ojec Code: 63212010). The usual disclaime
applies.
Da a A ailabili y Da a sha ing no applicable o his a icle as no da ase s we e gene a ed o analysed du ing
he cu en s udy.
Open Access This a icle is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License,
which pe mi s use, sha ing, adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long
as you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Com-
mons licence, and indica e i changes we e made. The images o o he hi d pa y ma e ial in his a icle
a e included in he a icle’s C ea i e Commons licence, unless indica ed o he wise in a c edi line o he
=
⎧
⎪
⎨
⎪
⎩
(3
√
2−1)(A−c)
17 , i d<6
√
2+
5
8
(8d+1)(A−c)
2(16d+11), i d≥6√2+5
8
W
H=
⎧
⎪
⎨
⎪
⎩
2
��
56
√
2−81
�
d+13
√
2+7
�
(A−c)2
289 , i d<6√2+
5
8
(4d+5)(A−c)2
32d+22 , i d≥6
√
2+5
8
=
⎧
⎪
⎨
⎪
⎩
(3d+1)(A−c)
9d+11 , i d<12
√
2+1
21
(3√2−1)(A−c)
17 , i d≥12√2+
1
21
W
L=
⎧
⎪
⎨
⎪
⎩
(d+3)(A−c)2
18d+22 , i d<12
√
2+1
21
��720√2−1124�d+336√2+92�(A−c)2
4624 , i d≥12
√
2+
1
21
W
H−WL=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
��
2016
√
2−2916
�
d2+(2932
√
2−3601)d+572
√
2−559
�
(A−c)2
578(9d+11)>0, o d<12
√
2+1
21
��268√2−367�d+20√2+33�(A−c)2
1156 >0, o 12√2+1
21 ≤d<6√2+5
8
��4496−2880
√
2�d2+�5035−3324
√
2�d+2637−924
√
2�(A−c)2
1156
(
16
d+
11
)
>0, o d≥6
√
2+5
8
.
2396

Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
ma e ial. I ma e ial is no included in he a icle’s C ea i e Commons licence and you in ended use is no
pe mi ed by s a u o y egula ion o exceeds he pe mi ed use, you will need o ob ain pe mission di ec ly
om he copy igh holde . To iew a copy o his licence, isi h p://c ea i ecommons.o g/licenses/by/4.0/.
Re e ences
Al-Saadon Y, Das SP (1996) Hos -coun y policy, ans e p icing and owne ship dis ibu ion in in e na-
ional join en u es: A heo e ical analysis. In J Ind O gan 14:345–364
An elo M, Lou ei o ML (2009) Asymme ic in o ma ion, signaling and en i onmen al axes in oligopoly.
Ecol Econ 68:1430–1440
A ya A, Mi endo B (2006) Enhancing e ical e iciency h ough ho izon al licensing. J Regul Econ
29:333–342
Bane jee S, Podda S (2019) ‘To sell o no o sell’: Licensing e sus selling by an ou side inno a o . Econ
Model 76:293–304
Ba cena-Ruiz JC, Ga zon MB (2002) En i onmen al axes and s a egic delega ion. SpanEconRe
4:301–310
Basak D, Mukhe jee A (2022) Social e iciency o ma ke en y unde ax policy. The B.E. J Econ Anal Pol
22: 601–610.
Belde bos R (1998) FDI and licensing s a egies by Du ch mul ina ionals in Japan. Wo king Pape NIBOR
∕ RM ∕ 98 ∕ 02, Ne he lands Ins i u e o Business O ganiza ion and S a egy Resea ch, Maas ich
Uni e si y, The Ne he lands
B aina d SL (1993) A simple heo y o mul ina ional co po a ions and ade wi h a ade-o be ween p ox-
imi y and concen a ion. NBER, No. 4269.
B aina d SL (1997) An empi ical assessmen o he p oximi y-concen a ion ade-o be ween mul ina ional
sales and ade. Am Econ Re 87:520–544
Cai X, Lu Y, Wu M, Yu L (2016) Does en i onmen al egula ion d i e away inbound o eign di ec in es -
men ? E idence om a Quasi-Na u al Expe imen in China. J De Econ 123:73–85
Calzola i G, Denicolò V (2013) Compe i ion wi h exclusi e con ac s and ma ke -sha e discoun s. Am Econ
Re 103:2384–2411
Calzola i G, Denicolò V (2015) Exclusi e con ac s and ma ke dominance. Am Econ Re 105:3321–3351
Calzola i G, Denicolò V, Zanche in P (2020) The demand-boos heo y o exclusi e dealing. Rand J Econ
51:713–738
Cao J, Sinha UB (2020) In a-b and pa en licensing wi h in e -b and compe i ion. Ma h Soc Sci 104:71–77
Chang RY, Hwang H, Peng CH (2013) Technology licensing, R&D and wel a e. Econ Le 118:396–399
Chen Z, Sha e G (2019) Ma ke sha e con ac s, exclusi e dealing, and he in ege p oblem. Am Econ J:
Mic oeconomics 11:208–242
Chung S (2014) En i onmen al egula ion and o eign di ec in es men : E idence om Sou h Ko ea. J De
Econ 108:222–236
De San is RA, S ähle F (2009) Fo eign di ec in es men and en i onmen al axes. Ge man Econ Re
10:115–135
Dijks a B, Ma hew AJ, Mukhe jee A (2011) En i onmen al egula ion: An incen i e o o eign di ec
in es men . Re In Econ 19:568–578
Dunning J (1958) Ame ican in es men in B i ish manu ac u ing indus y. Allen and Unwin, London
E kal N (2005) Op imal licensing policy in di e en ia ed indus ies. Econ Reco d 81:51–64
Ee ola E (2006) In e na ional ade ag eemen s, en i onmen al policy, and eloca ion o p oduc ion. Resou c
Ene gy Econ 28:333–350
Fan i L, Buccella D (2017) P o i aising en y e ec s in ne wo k indus ies wi h co po a e social esponsi-
bili y. Econ Bus Le 6:59–68
Fa ell J, Gallini N (1988) Second-sou cing as commi men : Monopoly incen i es o a ac compe i ion.
Qua J Econ 103:673–694
Faulí-Olle R, Sandonis J (2002) Wel a e educing licensing. Games Econom Beha 41:192–205
Ghosh A, Saha S (2015) P ice compe i ion, echnology licensing and s a egic ade policy. Econ Model
46:91–99
G a z L, Reisinge M (2013) On he compe i ion enhancing e ec s o exclusi e dealing con ac s. In J
Ind O gan 31:429–437
Glass AJ, Saggi K (2002) Licensing e sus di ec in es men : implica ions o economic g ow h. J In
Econ 56:131–153
2397
J.Cao, A.Mukhe jee
Golombek R, G eake M, Hoel M (2010) Ca bon axes and inno a ion wi hou commi men . The B.E. J
Econ Anal Pol 10, A icle 32: 1–19
Ha o i K (2013) En i onmen al inno a ion and policy ha moniza ion in in e na ional oligopoly. En i on
De Econ 18:162–183
Ha o i K (2017) Op imal combina ion o inno a ion and en i onmen al policies unde echnology
licensing. Econ Model 64:601–609
Helm D, Hepbu n C, Mash R (2003) C edible ca bon policy. Ox Re Econ Policy 19:438–450
Ho s mann IJ, Ma kusen JR (1987) Licensing e sus di ec in es men : A model o in e naliza ion by
he mul ina ional en e p ise. Can J Econ 20:464–481
Ho s mann IJ, Ma kusen JR (1992) Endogenous ma ke s uc u es in in e na ional ade (na u a aci
sal um). J In Econ 32:109–129
Ishibashi I, Ma sushima N (2009) The exis ence o low-end i ms may help high-end i ms. Ma k Sci
28:136–147
Ishida J, Ma sumu a T, Ma sushima, N (2011) Ma ke compe i ion, R&D and i m p o i s in asymme ic
oligopoly. J Ind Econ 59: 484–505
Iida T, Mukhe jee A (2020) Make and buy in a pollu ing indus y. J Publ Econ Theo 22:1852–1874
Kabi aj T, Ma ji S (2003) P o ec ing consume s h ough p o ec ion: The ole o a i -induced echnol-
ogy ans e . Eu Econ Re 47:113–124
Kamien M (1992) Pa en licensing. in R.J. Aumann and S. Ha (eds), Handbook o game heo y wi h
economic applica ions 1: 331-354
Kim SL, Lee SH, Ma sumu a T (2018) Eco- echnology licensing by a o eign inno a o and p i a iza-
ion policy in a pollu ing mixed duopoly. Asia-Pac J Accoun Econ 25:433–448
Ki amu a H, Ma sushima N, Sa o M (2018) Exclusi e con ac s wi h complemen a y inpu s. In J Ind
O gan 56:145–167
Ki amu a H, Ma sushima N, Sa o M (2022) De ending home agains gian s: Exclusi e dealing as a su -
i al s a egy o local i ms. J Ind Econ, 71: 441–463
K ugman P (1983) The “new heo ies” o in e na ional ade and he mul ina ional en e p ise. in D.B.
Aud e sch and C. Kindlebe ge (Eds.), The mul ina ional co po a ion in he 1980s, Camb idge,
MIT P ess.
Lee S, Ma sumu a T, Sa o S (2018) An analysis o en y- hen-p i a iza ion model: wel a e and policy
implica ions. J Econ 123:71–88
Long VN, Soubey an A (2005) Selec i e penaliza ion o pollu e s: An In -con olu ion app oach. Econ
Theo 25:421–454
Ma sushima N (2006) Indus y p o i s and ee en y in inpu ma ke s. Econ Le 93:329–336
Mukhe jee A, Zhao A (2017) P o i aising en y. J Ind Econ 65: 214–219
Mukhe jee A, Pennings E (2006) Ta i s, licensing and ma ke s uc u e. Eu Econ Re 50:1699–1707
Mukhe jee A, Mukhe jee S (2008) Excess en y heo em: he implica ions o licensing. Manch Sch
76:675–689
Mukhe jee A, Tsai Y (2013) Technology licensing unde op imal ax policy. J Econ 108:231–247
Mukhe jee A (2000) Hos -coun y policy – commi men o no-commi men : A heo e ical analysis. Pol-
icy Re o m 4:75–89
Mukhe jee A (2005) Inno a ion, licensing and wel a e. Manch Sch 73:29–39
Mukhe jee A (2009) Technology licensing. In: Rajan RS, Reine KA (eds) P ince on encyclopaedia o
he wo ld economy. P ince on, P ince on Uni e si y P ess, pp 1072–1077
Mukhe jee A (2019) P o i aising en y in a e ical s uc u e. Econ Le 183:108543
Mukhe jee A, B oll U, Mukhe jee S (2009) The wel a e e ec s o en y: The ole o he inpu ma ke . J
Econ 98:189–201
Naylo RA (2002) Indus y p o i s and compe i ion unde bila e al oligopoly. Econ Le 77:169–175
Naylo RA (2002) The e ec s o en y in bila e al oligopoly. Uni e si y o Wa wick, Mimeo
Nea y JP, Leahy D (2000) S a egic ade and indus ial policy owa ds dynamic oligopolies. Econ J
110:484–508
Niu S (2019) Licensing e sus assignmen : Inno a ion ans e in an asymme ic duopoly. J Publ Econ
Theo 21:1286–1308
Pal D, Sa ka J (2001) A S ackelbe g oligopoly wi h noniden ical i ms. Bull Econ Res 53:127–134
Pal R (2012) Delega ion and emission ax in a di e en ia ed oligopoly. Manch Sch 80:650–670
Poyago-Theo oky J (2007) The o ganiza ion o R&D and en i onmen al policy. J Econ Beha O gan
62:63–75
Rugman A (1986) New heo ies o he mul ina ional en e p ise: An assessmen o in e na ionaliza ion he-
o y. Bull Econ Res 38:101–118
Rocke K (1990) The quali y o licensed echnology. In J Ind O gan 8:559–574
2398
Fo eign Di ec In es men andTechnology Licensing inaPollu ing…
Ros oke M (1984) A su ey o co po a e licensing. IDEA 24:59–92
Saggi K (1996) En y in o a o eign ma ke : Fo eign di ec in es men e sus licensing. Re In Econ
4:99–104
Saggi K (1999) Fo eign di ec in es men , licensing, and incen i es o inno a ion. Re In Econ 7:699–714
Saggi K (2002) T ade, o eign di ec in es men , and in e na ional echnology ans e : A su ey. Wo ld
Bank Res Obse 17:191–235
Shepa d A (1987) Licensing o enhance he demand o a new p oduc . Rand J Econ 18:360–368
Sibailly I (2013) On licensing and di usion o clean echnologies in oligopoly. Wo king pape s, hal-
00911453, HAL
Sikimic U, F a ini F, Chiesa V (2013) Managemen o echnology licensing as a o eign ma ke en y mode:
The case o leading I alian pha maceu ical and bio ech companies. J Bus Chem 10:3–21
Sinha UB (2010) S a egic licensing, expo s, FDI, and hos coun y wel a e. Ox Econ Pap 62:114–131
S aige R, Tabellini G (1987) Disc e iona y ade policy and excessi e p o ec ion. Am Econ Re 77:823–837
Tyagi RK (1999) On he e ec s o downs eam en y. Manage Sci 45:59–71
Ulph A (1996) En i onmen al policy and in e na ional ade when go e nmen s and p oduce s ac s a egi-
cally. J En i on Econ Manag 30:265–281
Ulsake SA (2020) Compe ing buye s, en ex ac ion and ine icien exclusion. In J Ind O gan 68:102556
Va ian HR (1992) Mic oeconomic analysis, 3 d edn. No on, New Yo k, USA
Vishwas ao S (1994) In ellec ual p ope y igh s and he mode o echnology ans e . J De Econ
44:381–402
Wang KCA, Wang YJ, Liang WJ (2016) How does in e na ional licensing a ec FDI? Acad Econ Pape s
44:361–386
Wang KCA, Wang YJ, Liang WJ (2016b) In ellec ual p ope y igh s, in e na ional licensing and o eign
di ec in es men . Asia-Pac J Accoun Econ 23:291–305
W igh DJ (1993) In e na ional echnology ans e wi h an in o ma ion asymme y and endogenous
esea ch and de elopmen . J In Econ 35:47–67
Xia H, Fan T, Chang X (2019) Emission educ ion echnology licensing and di usion unde command-and-
con ol egula ion. En i on Resou c Econ 72:477–500
Yang L, Maskus K (2009) In ellec ual p ope y igh s, echnology ans e and expo s in de eloping coun-
ies. J De Econ 90:231–236
Zhao X, Galina o GI, G aciano TA (2019) The wel a e e ec s o opening o o eign di ec in es men in pol-
lu ing sec o s. En i on Resou ce Econ 74:243–269
Publishe ’s No e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in published maps and
ins i u ional a ilia ions.
2399