Kobe University Repository : Kernel
Title
International Duopoly and Trade Policies Under Budget
Constraint(国際複占と予算制約下の貿易政策)
Author(s)
Okamoto, Hisayuki
Citation
国際協力論集,6(2):115-136
Issue date
1998-12
Resource Type
Departmental Bulletin Paper / 紀要論文
Resource Version
publisher
URL
http://www.lib.kobe-u.ac.jp/handle_kernel/00181278
Create Date: 2016-10-03
115
1
1
5
I
n
t
e
r
n
a
t
i
o
n
a
lD
u
o
p
o
l
ya
n
dT
r
a
d
eP
o
l
i
c
i
e
s
International
Duopoly
and
Trade
Policies
U
nderB
u
d
g
e
tC
o
n
s
t
r
a
i
n
t
Under
Budget
Constraint
H
Hisayuki
i
s
a
y
u
k
iO
OKAMOTO*
KAMOTO*
1
1.
.I
Introduction
n
t
r
o
d
u
c
t
i
o
n
R
Recently
e
c
e
n
t
l
ym
many
anyt
trade
r
a
d
et
theorists
h
e
o
r
i
s
t
sh
have
aveb
been
e
e
ns
studying
t
u
d
y
i
n
gt
the
h
ei
international
n
t
e
r
n
a
t
i
o
n
a
lt
trade
r
a
d
et
theh
e
ory
with
imperfect
competition
1). T
They
heyh
have
avec
constructed
o
n
s
t
r
u
c
t
e
dv
various
a
r
i
o
u
sm
models
odelso
offi
inn
o
ryw
i
t
hi
m
p
e
r
f
e
c
tc
o
m
p
e
t
i
t
i
o
n1).
ternational
oligopoly
and
analyzed
trade
polices.
One
off t
the
most
important
t
e
r
n
a
t
i
o
n
a
lo
l
i
g
o
p
o
l
ya
nda
n
a
l
y
z
e
dt
r
a
d
ep
o
l
i
c
e
s
.O
ne o
h
em
ost i
m
p
o
r
t
a
n
t
results
tso
offt
the
h
ea
analyses
n
a
l
y
s
e
si
isst
that
h
a
te
each
achc
country
o
u
n
t
r
yh
has
asa
anni
incentive
n
c
e
n
t
i
v
eo
offg
giving
i
v
i
n
ge
export
x
p
o
r
t
r
e
s
u1
subsidy
toot
the
domestic
firms
and
import
tariff
too f
foreign
firms
inn o
order
too
s
u
b
s
i
d
yt
h
ed
o
m
e
s
t
i
cf
i
r
m
sa
ndi
mportt
a
r
i
f
ft
o
r
e
i
g
nf
i
r
m
si
r
d
e
rt
improve
welfare
offt
the
country.
i
mprovew
e
l
f
a
r
eo
h
ec
o
u
n
t
r
y
.
When
markets
offt
two
countries
(home
and
foreign)
are
segmented,
trade
r
a
d
e
W
henm
arketso
woc
o
u
n
t
r
i
e
s(
homea
ndf
o
r
e
i
g
n
)a
r
es
egmented，t
polices
onnt
the
domestic
market
cannot
affects
the
quantities
offf
foreign
market
p
o
l
i
c
e
so
h
ed
o
m
e
s
t
i
cm
arketc
annota
f
f
e
c
t
st
h
eq
u
a
n
t
i
t
i
e
so
o
r
e
i
g
nm
arket
i
ssume，a
iffw
weea
assume,
assm
many
anyo
offt
the
h
el
literature
i
t
e
r
a
t
u
r
ed
doo2
2),
)，f
firms'
i
r
m
s
'm
marginal
arginal c
costs
o
s
t
sa
are
r
ec
cono
n
stant.
But
this
assumption
issn
not
soor
realistic,
and
nds
soot
the
h
ed
derived
e
r
i
v
e
dr
results
e
s
u
l
t
sm
might
ight
s
t
a
n
t
.B
utt
h
i
sa
ssumptioni
o
ts
e
a
l
i
s
t
i
c，a
bee u
unconvincing.
Ass a
a m
matter
off f
facts,
inn t
the
real
world
trade
restrictions,
h
er
e
a
lw
orld t
r
a
d
er
e
s
t
r
i
c
t
i
o
n
s，
b
n
c
o
n
v
i
n
c
i
n
g
.A
atter o
a
c
t
s，i
such
asst
tariffs
and/or
quotas,
imposed
byyo
one
country
affects
not
only
the
s
ucha
a
r
i
f
f
sa
nd/orq
uotas，i
mposedb
ne c
o
u
n
t
r
ya
f
f
e
c
t
sn
o
to
n
l
yt
h
e
m
arketo
h
ec
ountryb
u
ta
l
s
ot
h
em
arketso
h
er
e
s
to
h
ew
o
r
l
d
.F
ore
x
market
offt
the
country
but
also
the
markets
offt
the
rest
offt
the
world.
For
exa
mple，w
ample,
when
henT
Toyota
oyotah
had
adt
toor
reduce
e
d
u
c
eh
her
e
re
exports
x
p
o
r
t
sf
for
o
rt
the
h
eU
U.S.
.
S
.a
auto
utom
market
arketi
innt
the
h
e
cause
off“
"voluntary"
v
o
l
u
n
t
a
r
y
"e
export
x
p
o
r
tr
restrains
e
s
t
r
a
i
n
s(
(VER)
VER)，
,s
she
h
es
shifted
h
i
f
t
e
dt
the
h
ep
products
r
o
d
u
c
t
se
exceedx
c
e
e
d
c
a
u
s
eo
the
VER q
quantity
toot
the
other
markets,
such
uch a
ass J
Japan
apan a
and
nd E
ECC m
markets.
a
r
k
e
t
s
.
i
ing
n
gt
h
eVER
u
a
n
t
i
t
yt
h
eo
t
h
e
rm
arkets，s
T
h
i
sk
i
n
do
henomenonh
asn
o
tb
eenf
u
l
l
ye
x
p
l
a
i
n
e
db
r
a
d
et
h
e
o
r
i
s
te
x
c
e
p
t
This
kind
offp
phenomenon
has
not
been
fully
explained
byyt
trade
theorist
except
those
who
has
assumed
non-linear
cost
function
offa
ann0
oligopolist
3).
t
h
o
s
ew
hoh
asa
ssumedn
o
n
l
i
n
e
a
rc
o
s
tf
u
n
c
t
i
o
no
1
i
g
o
p
o
l
i
s
t3
)
.
*
*A
Adjunct
djunctL
Lecturer,
e
c
t
u
r
e
r，G
Graduate
raduateS
School
c
h
o
o
lo
off I
International
n
t
e
r
n
a
t
i
o
n
a
lC
Cooperation
o
o
p
e
r
a
t
i
o
nS
Studies,
t
u
d
i
e
s，K
Kobe
obeU
University.
n
i
v
e
r
s
i
t
y
P
Professor,
r
o
f
e
s
s
o
r，K
Kobe
University
obeU
n
i
v
e
r
s
i
t
yo
offC
Commerce.
ommerce.
1)
Studies
offB
Brander
(1981),
19
81
)
， B
Brander
r
a
n
d
e
ra
and
nd K
Krugman
rugman (
(1983),
19
8
3
)，B
Brander
r
a
n
d
e
ra
and
nd S
Spencer
p
e
n
c
町(1
(1984a,
9
8
4
a，1984b),
1
9
8
4
b
)，C
Cheng
heng (
(1988),
19
8
8
)，
1) S
t
u
d
i
e
so
r
a
n
d
e
r(
Dixit
(1984,
D
i
x
i
t(
19
8
4，1988),
1
9
8
8
)，E
Eaton
aton a
and
nd G
Grossman
rossman (
(1984),
19
8
4
)，K
Krishna
r
i
s
h
n
a(
(1989),
19
8
9
)，K
Krishna
r
i
s
h
n
aa
and
nd I
Itoh
t
o
h(
(1988),
19
8
8
)， K
Krugman
rugman (
(1984),
19
8
4
)，
U
Uekawa
ekawa (
(1993,
19
9
3，1995),
1
9
9
5
)，V
Venables
e
n
a
b
l
e
s(
(1985)
19
8
5
)a
and
ndm
many
any o
other
t
h
e
re
economists
c
o
n
o
m
i
s
t
sh
have
avem
made
adev
valuable
a
l
u
a
b
l
ec
contribution
o
n
t
r
i
b
u
t
i
o
nt
toot
this
h
i
st
theory.
h
e
o
r
y
.
2
2)) K
Krugman
rugman (
(1984)
19
8
4
)a
and
nd U
Uekawa
ekawa (
(1993)
19
9
3
)a
are
r
es
such
u
c
he
exceptions
x
c
e
p
t
i
o
n
so
offt
the
h
ea
above
bovel
literature
i
t
e
r
a
t
u
r
ei
innn
note
o
t
e1.
1
.
3)
Krugman
(1984)
and
Uekawa
(1993)
are
such
exceptions.
But
Krugman
(1984)
has
not
analyzed
the
foreign
market.
3
)K
rugman(
19
8
4
)a
ndU
ekawa(
19
9
3
)a
r
es
u
c
he
x
c
e
p
t
i
o
n
s
.B
utK
rugman(
19
8
4
)h
a
sn
o
ta
n
a
l
y
z
e
dt
h
ef
o
r
e
i
g
nm
a
r
k
e
t
.
Uekawa
(1993)
issa
am
model
offt
the
product
differentiation
and
sood
different
from
the
model
offt
this
paper.
Innv
view
offt
the
U
ekawa(
19
9
3
)i
odelo
h
ep
r
o
d
u
c
td
i
f
f
e
r
e
n
t
i
a
t
i
o
na
nds
i
f
f
e
r
e
n
tf
romt
h
em
odelo
h
i
sp
aper
.l
i
e
wo
h
e
model
which
will
beed
developed
innt
this
paper,
models
odelso
offO
Okamoto
kamotoa
and
ndY
Yoshida
oshida(
(1991,
19
9
1，1994)
1
9
9
4
)a
and
ndO
Okuguchi
k
u
g
u
c
h
i(
(1990)
19
9
0
)a
are
r
et
the
h
e
m
odelw
h
i
c
hw
i
l
lb
e
v
e
l
o
p
e
di
h
i
sp
a
p
e
r，m
most
similar
toot
the
present
paper.
But
their
purposes
offt
the
analyses
are
different
from
the
current
paper.
m
osts
i
m
i
l
a
rt
h
ep
r
e
s
e
n
tp
a
p
e
r
.B
utt
h
e
i
rp
u
r
p
o
s
e
so
h
ea
n
a
l
y
s
e
sa
r
ed
i
f
f
e
r
e
n
tf
romt
h
ec
u
r
r
e
n
tp
a
p
e
r
.
Journal
offl
International
Cooperation
Studies
Vol.6,
.
l
6
，N
No.2
o
.
2
J
o
u
r
n
a
lo
n
t
e
r
n
a
t
i
o
n
a
lC
o
o
p
e
r
a
t
i
o
nS
t
u
d
i
e
sV
o
国際協力論集
116
1
1
6
第 6巻 第 2号
I
Innt
this
h
i
sp
paper,
aper，w
wees
shall
h
a
l
ld
develop
e
v
e
l
o
pa
a t
trade
r
a
d
em
model
odel o
offi
international
n
t
e
r
n
a
t
i
o
n
a
ld
duopolists
u
o
p
o
l
i
s
t
s
。
who
supply
identical
product
inn e
each
others'
market,
inn w
which
hich d
demand
emand f
funcu
n
w
hos
u
p
p
l
yi
d
e
n
t
i
c
a
lp
roducti
ach o
t
h
e
r
s
'm
arket，i
t
tions
i
o
n
so
offt
the
h
em
markets
arketsa
are
r
en
non-linear,
o
n
l
i
n
e
a
r，a
and
ndw
whose
hosem
marginal
arginalc
costs
o
s
t
sa
are
r
ed
decreasing.
e
c
r
e
a
s
i
n
g
.
A
And
ndw
wees
h
a
l
la
n
a
l
y
z
et
h
et
wot
r
a
d
ep
o
l
i
c
yi
n
s
t
r
u
m
e
n
t
so
omec
o
u
n
t
r
y，p
shall
analyze
the
two
trade
policy
instruments
offh
home
country,
pror
o
duction
subsidy
and
import
tariff,
onne
each
achf
firm's
i
r
m
'
sp
production
r
o
d
u
c
t
i
o
no
offt
the
h
eg
good
ooda
and
nd
d
u
c
t
i
o
ns
u
b
s
i
d
ya
ndi
mportt
a
r
i
f
f，o
consumption
offt
the
good
inne
each
market,
assw
well
e
l
la
asst
the
h
ew
welfare
e
l
f
a
r
eo
offh
home
omec
couno
u
n
c
onsumptiono
h
eg
oodi
achm
arket，a
t
r
y
.T
hus，i
try.
Thus,
innt
this
h
i
sp
paper
aperw
wees
shall
h
a
l
ld
doot
the
h
es
similar
i
m
i
l
a
ra
analyses
n
a
l
y
s
e
sw
which
hichh
have
aveb
been
eend
done
one
innt
the
famous
papers
such
assC
Cheng
(1988),
Dixit
(1988),
and
Uekawa
(1993)
i
x
i
t(
19
8
8
)，a
nd U
ekawa (
19
9
3
)
i
h
ef
amousp
aperss
ucha
heng (
1
9
8
8
)，D
Though
the
analysis
toob
beep
presented
issv
very
similar
asst
those
offt
the
above
etc.
e
t
c
.T
hought
h
ea
n
a
l
y
s
i
st
r
e
s
e
n
t
e
di
e
r
ys
i
m
i
l
a
ra
h
o
s
eo
h
ea
bove
p
apers，t
papers,
there
h
e
r
ea
are
r
es
some
omei
important
mportantd
differences
i
f
f
e
r
e
n
c
e
sb
between
etweeno
our
ura
analysis
n
a
l
y
s
i
sa
and
ndt
theirs.
h
e
i
r
s
.
take
a
k
ei
into
n
t
oa
account
c
c
o
u
n
tt
the
h
ep
policy
o
l
i
c
ym
maker's
aker'sb
budget
udgetc
constraint,
o
n
s
t
r
a
i
n
t，a
and
nd-anaa
n
a
N
Namely,
amely，w
weet
lyze
the
effects
offt
two
trade
policies,
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
ya
and
ndi
import
mportt
tariff.
a
r
i
f
f
.
l
y
z
et
h
ee
f
f
e
c
t
so
wot
r
a
d
ep
o
l
i
c
i
e
s，p
A
lthoughn
e
i
t
h
e
ro
h
ea
bovem
entionedw
orksh
avee
x
p
l
a
i
n
e
dt
h
es
o
u
r
c
e
Although
neither
offt
the
above
mentioned
works
have
explained
the
source
o
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yo
x
p
o
r
ts
u
b
s
i
d
y，t
offp
production
subsidy
orre
export
subsidy,
they
h
e
yh
have
ave s
showed
howed t
that
h
a
tt
the
h
eo
optimal
p
t
i
m
a
l
production
subsidy
orre
export
subsidy
issp
positive.
But
this
result
could
beeq
quite
p
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yo
x
p
o
r
ts
u
b
s
i
d
yi
o
s
i
t
i
v
e
.B
utt
h
i
sr
e
s
u
l
tc
o
u
l
db
u
i
t
e
the
production
subsidy
orr e
export
subsidy
iss l
like
'a
ag
gift
i
f
tf
from
rom
obvious
when
o
b
v
i
o
u
sw
hen t
h
ep
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yo
x
p
o
r
ts
u
b
s
i
d
yi
i
k
e‘
H
e
a
v
e
n
'
.8
Heaven'.
So0 t
the
h
er
results
e
s
u
l
t
sw
which
hich d
doo n
not
o
ts
specify
p
e
c
i
f
yt
the
h
es
source
o
u
r
c
eo
off s
subsidy
u
b
s
i
d
ym
may
ay b
bee
I
ti
issn
needed
eededt
toos
specify
p
e
c
i
f
yt
the
h
ef
financial
i
n
a
n
c
i
a
lb
background
ackgroundo
offt
the
h
ec
cost
o
s
to
offs
subu
b
m
misleading.
i
s
l
e
a
d
i
n
g
.It
s
i
d
i
e
s，i
sidies,
iffy
you
ouw
want
antt
toot
treat
r
e
a
tw
welfare
e
l
f
a
r
ea
aspect
s
p
e
c
to
off t
the
h
ep
policies
o
l
i
c
i
e
sp
properly.
r
o
p
e
r
l
y
.T
Thus,
hus，w
wee
introduce
the
government
budget
constraint
toof
finance
the
production
subsidy
i
n
t
r
o
d
u
c
et
h
eg
overnmentb
udgetc
o
n
s
t
r
a
i
n
tt
i
n
a
n
c
et
h
ep
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
y
byyi
import
tariff.
f
.
b
mportt
a
r
i
f
I
Innt
this
h
i
sp
paper
aperw
wees
shall
h
a
l
le
establish
s
t
a
b
l
i
s
hf
following
o
l
l
o
w
i
n
gr
results:
e
s
u
l
t
s
:
(1)
Uniqueness
offt
the
Cournot
equilibrium
solution
containing
both
coun(
1
)U
niquenesso
h
eC
ournote
q
u
i
l
i
b
r
i
u
ms
o
l
u
t
i
o
nc
o
n
t
a
i
n
i
n
gb
oth c
o
u
n
-
tries'
markets
issi
investigated
and
a s
set
offs
sufficient
conditions
for
the
uniquet
r
i
e
s
'm
arketsi
n
v
e
s
t
i
g
a
t
e
da
nda
e
to
u
f
f
i
c
i
e
n
tc
o
n
d
i
t
i
o
n
sf
o
rt
h
eu
n
i
q
u
e
ness
n
e
s
so
h
es
o
l
u
t
i
o
ni
r
e
s
e
n
t
e
d
.
offt
the
solution
issp
presented.
Under
the
set
off c
conditions
for
the
umqueness
off t
the
solution,
the
(2)
(
2
)U
nder t
h
es
e
to
o
n
d
i
t
i
o
n
sf
o
rt
h
eu
n
i
q
u
e
n
e
s
so
h
es
o
l
u
t
i
o
n，t
h
e
h
omec
ountryp
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yi
n
c
r
e
a
s
e
st
h
es
u
p
p
l
yo
h
ei
m
p
e
r
f
e
c
t
l
yc
omhome
country
production
subsidy
increases
the
supply
offt
the
imperfectly
comp
e
t
i
t
i
v
eg
oodi
achm
arketa
ndd
e
c
r
e
a
s
e
st
h
ep
r
i
c
eo
h
eg
oodi
h
es
u
b
s
i
d
y
good
inne
each
market
and
decreases
the
price
offt
the
good
ifft
the
subsidy
petitive
IS
a g
gift
from
Heaven.
i
sa
i
f
tf
romH
e
a
v
e
n
.
Under
the
same
set
off c
conditions,
ann i
imposition
m
p
o
s
i
t
i
o
no
off d
domestic
o
m
e
s
t
i
ci
import
mport
(3)
(
3
)U
nder t
h
es
ame s
e
to
o
n
d
i
t
i
o
n
s，a
tariff
reduces
the
supply
offt
the
good
tood
domestic
market
but
ittd
depends
onnt
the
t
a
r
i
f
fr
e
d
u
c
e
st
h
es
u
p
p
l
yo
h
eg
oodt
omesticm
arketb
u
ti
ependso
h
e
cost
condition
whether
imposition
off t
tariff
increase
supply
off t
the
good
too
c
o
s
tc
o
n
d
i
t
i
o
nw
hether i
m
p
o
s
i
t
i
o
no
a
r
i
f
fi
n
c
r
e
a
s
es
u
p
p
l
yo
h
eg
ood t
I
International
n
t
e
r
n
a
t
i
o
n
a
lD
Dupoly
u
p
o
l
ya
and
n
dT
Trade
r
a
d
eP
Policies
o
l
i
c
i
e
sU
Under
n
d
e
rB
Budget
u
d
g
e
tC
Constraint
o
n
s
t
r
a
i
n
t
1
1
7
117
f
foreign
o
r
e
i
g
nm
market.
arket
.
(
(4)
4
)U
Under
ndert
the
h
es
same
ames
set
e
to
offc
conditions,
o
n
d
i
t
i
o
n
s，w
whether
hethert
the
h
ep
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
yi
mn
-
o
creases
the
supply
offe
each
market
depends
onn1> ¥
" tthe
he d
degree
e
g
r
e
eo
offm
marginal
arginal i
mn
c
r
e
a
s
e
st
h
es
u
p
p
l
yo
achm
arketd
ependso
crease
inn t
tariff
too f
finance
one
unit
off p
production
subsidy,
iff t
the
h
ed
domestic
o
m
e
s
t
i
c
c
r
e
a
s
ei
a
r
i
f
ft
i
n
a
n
c
eo
ne u
n
i
to
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
y，i
government's
budget
constraint
issc
considered.
But
under
the
same
set
offc
cong
overnment'sb
udgetc
o
n
s
t
r
a
i
n
ti
o
n
s
i
d
e
r
e
d
.B
utu
ndert
h
es
ames
e
to
o
n
ann i
increase
n
c
r
e
a
s
ei
inn p
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
yr
raises
a
i
s
e
st
the
h
es
supply
u
p
p
l
yo
off t
the
h
eh
home
ome
ditions,
d
i
t
i
o
n
s，a
each
market
and
reduces
that
offf
foreign
duopolist
when
the
govd
duopolist
u
o
p
o
l
i
s
ti
inne
achm
arketa
ndr
e
d
u
c
e
st
h
a
to
o
r
e
i
g
nd
u
o
p
o
l
i
s
tw
hent
h
eg
o
v
ernment
budget
constraint
issb
binding.
e
rnmentb
udgetc
o
n
s
t
r
a
i
n
ti
i
n
d
i
n
g
.
Under
the
same
set
offc
conditions
plus
one
minor
condition,
anni
ImpOSIm
p
o
s
i
(5)
(
5
)U
ndert
h
es
ames
e
to
o
n
d
i
t
i
o
n
sp
l
u
so
nem
inorc
o
n
d
i
t
i
o
n，a
t
i
o
no
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yw
hich i
i
n
a
n
c
e
db
mport t
a
r
i
f
fi
n
c
r
e
a
s
e
sn
a
tion
offp
production
subsidy
which
iss f
financed
byy i
import
tariff
increases
nat
i
o
n
a
lw
e
l
f
a
r
eo
omec
o
u
n
t
r
y
.8
tional
welfare
offh
home
country.
So0t
the
h
eo
optimal
p
t
i
m
a
lp
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
ya
and
ndi
import
mport
t
a
r
i
f
fa
r
ed
e
f
i
n
i
t
e
l
yp
o
s
i
t
i
v
e
.
tariff
are
definitely
positive.
T
her
emaindero
h
i
sp
aperi
r
g
a
n
i
z
e
da
o
l
l
o
w
s
.I
h
en
e
x
ts
e
c
t
i
o
n
The
remainder
offt
this
paper
iss o
organized
ass f
follows.
Inn t
the
next
section
w
h
a
l
lp
r
e
s
e
n
tt
h
em
odela
ndt
h
ea
ssumptionsf
o
r
m
a
l
l
ya
nds
howt
h
a
tu
nder
wees
shall
present
the
model
and
the
assumptions
formally
and
show
that
under
t
h
e
s
ea
ssumptionst
h
eC
ournote
q
u
i
l
i
b
r
i
u
ms
o
l
u
t
i
o
no
h
em
odeli
n
i
q
u
e
.I
these
assumptions
the
Cournot
equilibrium
solution
offt
the
model
issu
unique.
Inn
s
e
c
t
i
o
n3
section
3,，f
first,
i
r
s
t，w
wees
shall
h
a
l
le
examine
xaminet
the
h
ee
effects
f
f
e
c
t
so
offa
a d
domestic
o
m
e
s
t
i
cp
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
y
a
ndi
mportt
a
r
i
f
fo
onsumptiona
e
l
la
r
o
d
u
c
t
i
o
ni
achc
o
u
n
t
r
yi
h
e
and
import
tariff
onnc
consumption
assw
well
assp
production
inne
each
country
innt
the
c
a
s
eo
overnmentb
udgetc
o
n
s
t
r
a
i
nt
case
offn
noog
government
budget
constraint.
.T
Then,
hen，o
onnt
the
h
eb
base
aseo
offt
these
h
e
s
ea
analyses,
n
a
l
y
s
e
s，
w
h
a
l
le
examine
xaminet
the
h
ee
effects
f
f
e
c
t
so
offa
a d
domestic
o
m
e
s
t
i
cp
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
yi
innt
the
h
ep
presence
r
e
s
e
n
c
e
wees
shall
o
offg
overnmentb
udgetc
o
n
s
t
r
a
i
n
t
.I
e
c
t
i
o
n4
government
budget
constraint.
Inns
section
4,，w
wees
shall
h
a
l
lt
turn
u
r
no
our
ur a
attention
t
t
e
n
t
i
o
nt
too
the
analysis
offw
welfare
effects
off t
trade
policies
when
the
government
budget
t
h
ea
n
a
l
y
s
i
so
e
l
f
a
r
ee
f
f
e
c
t
so
r
a
d
ep
o
l
i
c
i
e
sw
hen t
h
eg
overnment b
udget
constraint
issi
imposed.
And
wees
shall
show
that
the
optimal
production
subsidy
c
o
n
s
t
r
a
i
n
ti
m
p
o
s
e
d
.A
ndw
h
a
l
ls
howt
h
a
tt
h
eo
p
t
i
m
a
lp
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
y
and
import
tariff
are
positive.
Innt
the
last
section,
wees
shall
h
a
l
lg
give
i
v
es
some
omec
concludo
n
c
l
u
d
a
ndi
mportt
a
r
i
f
fa
r
ep
o
s
i
t
i
v
e
.I
h
el
a
s
ts
e
c
t
i
o
n，w
i
ing
n
gr
e
m
a
r
k
s
.
remarks.
2
.T
he M
odel
2.
The
Model
2
.
1T
hef
rameworko
ft
h
em
odel
2.1
The
framework
of
the
model
There
are
two
countries,
home
ome c
country
o
u
n
t
r
y(
(country
c
o
u
n
t
r
yH
H)) a
and
nd f
foreign
o
r
e
i
g
nc
country
o
u
n
t
r
y
T
here a
r
et
wo c
o
u
n
t
r
i
e
s，h
(country
F),
inn w
which
hich t
two
wo g
good
ood X
X a
and
nd Z
Z a
are
r
ep
produced.
r
o
d
u
c
e
d
.G
Good
ood Z
Z,，t
taken
a
k
e
na
ass
(
c
o
u
n
t
r
yF
)，i
numeraire,
iss p
produced
roduced i
inn c
competitive
o
m
p
e
t
i
t
i
v
es
sector
e
c
t
o
ri
inn e
each
ach c
country.
o
u
n
t
r
y
.O
Onn t
the
h
eo
other
t
h
e
r
n
umeraire，i
hand,
a h
homogeneous
omogeneousg
good
oodX
X i
issp
produced
roducedb
byyo
one
nef
firm
i
r
mi
inne
each
achc
country.
o
u
n
t
r
y
.E
Each
ach
h
and，a
firm
supplies
offt
this
good
tooe
each
market
which
isss
segmented
and
soot
the
two'
f
i
r
ms
u
p
p
l
i
e
so
h
i
sg
oodt
achm
arketw
hichi
egmenteda
nds
h
et
wo'
国 際 協 力 論 集 第 6巻 第 2
号
118
1
1
8
f
firms
i
r
m
sa
are
r
ei
international
n
t
e
r
n
a
t
i
o
n
a
ld
duopolist
u
o
p
o
l
i
s
to
offg
good
oodX
X..
I
h
i
sp
aper w
h
a
l
la
n
a
l
y
z
et
wo t
r
a
d
ep
o
l
i
c
e
so
ome c
o
u
n
t
r
y
.T
he
Inn t
this
paper
wee s
shall
analyze
two
trade
polices
off h
home
country.
The
g
overnmento
omec
ountryi
mposesa
p
e
c
i
f
i
ci
mportt
a
r
i
f
fo
oodX
h
e
government
offh
home
country
imposes
a s
specific
import
tariff
onng
good
X a
attt
the
r
rate
a
t
eo
offt
t a
and
ndg
gives
i
v
e
sa
a s
specific
p
e
c
i
f
i
cp
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
yt
toot
the
h
ed
domestic
o
m
e
s
t
i
cp
producer
roducer o
off
good
X a
attt
the
rate
offs
s i
inno
order
rdert
toom
maximize
aximizen
national
a
t
i
o
n
a
lw
welfare
e
l
f
a
r
eo
off c
country
o
u
n
t
r
yH
H..
g
oodX
h
er
a
t
eo
We
We a
assume
ssumet
that
h
a
td
domestic
o
m
e
s
t
i
cg
government
overnments
set
e
tt
the
h
et
two
wor
rates
a
t
e
ss
sand
andt
t f
first
i
r
s
ts
subject
u
b
j
e
c
tt
too
her
budget
constraint,
then
h
e
ne
each
achd
duopolist
u
o
p
o
l
i
s
tt
takes
a
k
e
st
these
h
e
s
ev
values
a
l
u
e
si
into
n
t
oa
account
c
c
o
u
n
ta
and
nd
h
e
rb
udgetc
o
n
s
t
r
a
i
n
t，t
d
e
c
i
d
e
sh
owm
ucht
roducea
ndh
owm
ucht
u
p
p
l
yt
achc
o
u
n
t
r
y
'
sm
ardecides
how
much
toop
produce
and
how
much
toos
supply
tooe
each
country's
market
which
issC
Cournot
competitive.
For
simplicity
off a
analysis,
wee a
assume
ssume f
foro
r
k
e
tw
hichi
ournotc
o
m
p
e
t
i
t
i
v
e
.F
or s
i
m
p
l
i
c
i
t
yo
n
a
l
y
s
i
s，w
country
will
not
retaliate
for
these
policies
offc
country
H.
.
e
eign
i
g
nc
o
u
n
t
r
yw
i
l
ln
o
tr
e
t
a
l
i
a
t
ef
o
rt
h
e
s
ep
o
l
i
c
i
e
so
o
u
n
t
r
yH
L
Let
e
tp
pH(XH)
H(XH) a
and
ndp
pF(XF)
F(XF) r
represent
e
p
r
e
s
e
n
tt
the
h
ei
inverse
n
v
e
r
s
ed
demand
emandf
function
u
n
c
t
i
o
no
offi
identical
d
e
n
t
i
c
a
l
good
X i
inn d
domestic
market
and
foreign
market,
respectively,
e
s
p
e
c
t
i
v
e
l
y，w
where
hereX
XHH a
and
nd
g
ood X
o
m
e
s
t
i
cm
arket a
nd f
o
r
e
i
g
nm
arket，r
XFFa
are
the
amount
offd
demand
innr
respective
markets.
We a
assume
that
demand
X
r
et
h
ea
mounto
emandi
e
s
p
e
c
t
i
v
em
a
r
k
e
t
s
.We
ssumet
h
a
td
emand
curve
offe
each
market
issn
negatively
sloped,
that
h
a
ti
issp
pH'(XH)<O
H'(XH)<O a
and
ndp
pF'(XF)<O.
F'(XF)くO
.
c
u
r
v
eo
achm
arketi
e
g
a
t
i
v
e
l
ys
l
o
p
e
d，t
T
het
r
a
d
ep
o
l
i
c
yi
n
s
t
r
u
m
e
n
t
sc
o
n
s
i
s
to
o
m
e
s
t
i
ci
mportt
a
r
i
f
fa
nda
o
The
trade
policy
instruments
consist
offa
a d
domestic
import
tariff
and
a d
dom
e
s
t
i
cp
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yo
m
p
e
r
f
e
c
t
l
yc
o
m
p
e
t
i
t
i
v
eg
oodX
e
ta
o
m
e
s
t
i
c
mestic
production
subsidy
onni
imperfectly
competitive
good
X.. L
Let
a d
domestic
i
mportt
a
r
i
f
fr
a
t
eb
enotedb
import
tariff
rate
beed
denoted
byyt
t a
and
nda
a d
domestic
o
m
e
s
t
i
cp
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
yr
rate
a
t
eb
byy
s
s.. T
Then
hent
total
o
t
a
lp
profits
r
o
f
i
t
so
offd
domestic
omesticd
duopolist
uopolist
7lπ
H
Ha
and
nd f
foreign
o
r
e
i
g
nd
duopolist
uopolist
7lπ
F
Fare
a
r
e
represented
byy
r
e
p
r
e
s
e
n
t
e
db
0
O.D
.1
)π
7l H
H(XHH,
(XHH，X
XHF;
H
F
;X
XFF,
FF，X
XFH)
FH)=XHHpH(XH)
=XHHpH(XH)+X
XHFpF(XF)
HFpF(XF)-CH(QH)
CH(QH)+SQH.
+SQH
・
0
0.2)
.2)π
7lF(XFF,
F(XFF，X
XFH;
F
H
;X
XHH,
HH，X
XHF)=XFFpF(XF)+XFHpH(XH)-CF(QF)-tXFH.
HF)= XFFpF(XF)+
XFHpH(XH)-CF(QF)-t
X
F
H
.
w
where
hereX
XHk
H
k (
(XFK)
X
F
K
)d
denotes
e
n
o
t
e
st
the
h
ec
country
ountryH
H (
(county
c
o
u
n
t
yF
F)) d
duopolist's
u
o
p
o
l
i
st
'ss
supply
u
p
p
l
yo
offg
good
ood
X t
toot
the
market
off c
country
k,，t
thus
h
u
sX
XH
and
nd X
XF
can
an b
bee r
represented
e
p
r
e
s
e
n
t
e
da
ass X
XH=
H=
X
h
em
arket o
ountry k
Ha
Fc
X
HH+XFH a
nd X
F=XFF+XHF，w
h
i
l
e QH=XHH+XHF
QH三 XHH+XHF (QF=XFF+XFH)
(QF三 XFF+XFH) r
e
p
r
e
s
e
n
t
st
h
e
XHH+XFH
and
XF=XFF+XHF,
while
represents
the
amount
offp
production
offt
the
country
H (
(county
c
o
u
n
t
yF
F))d
duopolist.
u
o
p
o
l
i
s
t
.A
And
ndC
CH(CF)
H
(
C
F
)i
isst
the
h
e
a
mounto
r
o
d
u
c
t
i
o
no
h
ec
ountryH
cost
function
offt
the
country
H (
(country
c
o
u
n
t
r
yF
F)) d
duopolist.
u
o
p
o
l
i
s
t
.
c
o
s
tf
u
n
c
t
i
o
no
h
ec
ountryH
2
2.2
.
2B
Basic
a
s
i
ca
assumptions
ssumptionsa
and
nde
equilibrium
q
u
i
l
i
b
r
i
u
mc
conditions
o
n
d
i
t
i
o
n
s
Inn t
the
ensuring
analyses
wee a
assume
the
following
conditions
C.1
~C .4 t
too b
bee
I
h
ee
n
s
u
r
i
n
ga
n
a
l
y
s
e
sw
ssume t
h
ef
o
l
l
o
w
i
n
gc
o
n
d
i
t
i
o
n
sC
.
1~C.4
satisfied
byyt
the
inverse
demand
functions
and
the
cost
functions
offg
good
X..
s
a
t
i
s
f
i
e
db
h
ei
n
v
e
r
s
ed
emandf
u
n
c
t
i
o
n
sa
ndt
h
ec
o
s
tf
u
n
c
t
i
o
n
so
oodX
l
International
n
t
e
r
n
a
t
i
o
n
a
lD
Dupoly
u
p
o
l
ya
and
n
dT
Trade
r
a
d
eP
Policies
o
l
i
c
i
e
sU
Under
n
d
e
rB
Budget
u
d
g
e
tC
Constraint
o
n
s
t
r
a
i
n
t
C.
1
:PH+XHHPH'孟 0，
P
F+XFFPF'孟 0，
PF+XFFPF'~O,
o
C
C.2:
.
2
:C
CH'>O,
H'>O， C
CH"
H"系
~O
hHH三 PH'十 日HPH"<O，
h
HF三 P
F
'+
XHFPF"<0;
hHF=PF'+XHFPF"<O;
h
FH三 PH'十 XFHPH"<O，
hFH=PH'+XFHPH"<O,
h
FF三 P
F
'十 XFFPF"<0.
hFF=PF'+XFFPF"<O.
119
1
1
9
C
CF'>O,
F'>O， C
CF"
F
"孟
~O.
O
.
C.3:
pH'-2cH"<0,
pH'-2cF"<0;
pF'-2cF"<0,
pF'-2cH"<0.
C
.
3
:p
H'-2cH"<0， p
H'-2cF"<0; P
F
'一 2CF"<0， P
F
'一 2CH"<0.
C
C.4:
.
4
:h
hHH-hFH+PH'-2cH"<0,
HH-hFH+PH'-2cH"<0， ん
hHF-hFF+PF'-2cH"<0;
{F-h
FF+P
F
'-2CH"<0;
h
hFH-hHH+PH'
FH-hHH+PH'-2CF"<0,
2CF"<0， h
hFF-hHF+
FF-hHF+P
PF'
F
'-2CF"<0.
2CF"<0.
F
First,
i
r
s
t，C
C.1
.
1r
reqUlres
e
q
u
i
r
e
st
that
h
a
te
each
ach f
firm's
i
r
m
'
sm
marginal
arginal r
revenue
e
v
e
n
u
ei
inn e
each
ach m
market
arket i
iss
and
satisfies
the
Hahn
(1962)
19
6
2
)s
stability
t
a
b
i
l
i
t
yc
condition
o
n
d
i
t
i
o
nw
with
i
t
ht
the
h
en
negative
e
g
a
t
i
v
e
n
non-negative
o
n
n
e
g
a
t
i
v
ea
nds
a
t
i
s
f
i
e
st
h
eH
ahn(
offe
each
demand
function.
Second,
C.2
.
2r
requests
e
q
u
e
s
t
st
that
h
a
te
each
achf
firm's
i
r
m
'
sa
avv
s
slopedness
l
o
p
e
d
n
e
s
so
achd
emandf
u
n
c
t
i
o
n
.S
econd，C
erage
cost
and
marginal
cost
are
decreasing
and
(weakly)
convex
toot
the
orie
r
a
g
ec
o
s
ta
ndm
arginalc
o
s
ta
r
ed
e
c
r
e
a
s
i
n
ga
nd (
w
e
a
k
l
y
)c
onvext
h
eo
r
i
gin.
Third,
g
i
n
.T
hird，C
C.3
.
3d
demands
emandst
that
h
a
tt
the
h
ei
inverse
n
v
e
r
s
ed
demand
emand f
function
u
n
c
t
i
o
no
offe
each
ach m
market
arket i
iss
s
steep
t
e
e
pa
nd/ore
achm
a
n
u
f
a
c
t
u
r
e
r
'
sm
arginalc
o
s
tc
u
r
v
ei
l
a
t
.F
i
n
a
l
l
y，i
and/or
each
manufacturer's
marginal
cost
curve
issf
flat.
Finally,
innv
view
i
e
w
o
offc
condition
o
n
d
i
t
i
o
nC
.
3a
ndt
h
ed
e
f
i
n
i
t
i
o
n
so
C.3
and
the
definitions
offh
hij's
i
} '
sc
Cii,，j=H
j=H,，F
F)) ，
,C
C.4
.
4r
requires
e
q
u
i
r
e
st
that
h
a
tt
the
h
e
absolute
values
offP
PH"
H" a
and
ndP
PH"
H" a
are
r
en
not
o
tt
too
o
ol
large,
a
r
g
e，i
i.e.
.
e
.t
the
h
ed
degree
e
g
r
e
eo
offc
concavity
o
n
c
a
v
i
t
y
a
b
s
o
l
u
t
ev
a
l
u
e
so
o
o
n
v
e
x
i
t
yt
h
eo
ngmo
v
e
r
yi
n
v
e
r
s
ed
emandc
u
r
v
ei
o
tt
o
os
t
r
o
n
g
.
orrc
convexity
toot
the
origin
offe
every
inverse
demand
curve
issn
not
too
strong.
U
ndert
h
eC
ournota
ssumptiono
achf
i
r
m
'
sb
e
h
a
v
i
o
ri
achm
arket，t
Under
the
Cournot
assumption
onne
each
firm's
behavior
inne
each
market,
the
h
e
f
i
r
s
to
r
d
e
rc
o
n
d
i
t
i
o
n
sf
o
rp
r
o
f
i
tm
aximizationa
r
e
:
first
order
conditions
for
profit
maximization
are:
(
(2.1)
2.
1
)p
PH
H(
(XH)
XH)+XHHpH'(XH)
+XHHpH'(XH)-CH'(QH)
CH'(QH)+s=O,
+s=O，
(
(2.2)
2
.
2
)p
pF(XF)
F(XF)+XHFpF'(XF)
+XHFpF'(XF)-CH'(QH)
CH'(QH)+s=O,
+s=O，
(
(2.3)
2
.
3
)p
pF(XF)
F(XF)+
+X
XFFPF'
F
F
P
F
'(
(XF)
XF)一
-CF'(QF)
d(QF)=0
=0,，
(
(2.4)
2.
4
)p
PH
H(
(XH)
XH)+
+X
XFHpH'(XH)
FHpH'(XH)- C
CF'(QF)
F
'
(
Q
F
)-t=O.
t=O.
I
Innt
the
h
ef
following
o
l
l
o
w
i
n
gs
sections
e
c
t
i
o
n
sw
weei
investigate
n
v
e
s
t
i
g
a
t
et
the
h
en
nature
a
t
u
r
eo
offt
the
h
ea
above
bovee
equation
q
u
a
t
i
o
ns
sysy
s
tem
(2),
the
h
eC
Cournot
ournote
equilibrium
q
u
i
l
i
b
r
i
u
ma
and
ndt
the
h
ee
effects
f
f
e
c
t
so
offc
changes
hangesi
inns
sand
andt
t o
onnt
the
h
e
t
em(
2
)，t
equilibrium.
Before
proceeding
too t
these,
wee s
shall
h
a
l
le
explain
x
p
l
a
i
nt
the
h
eg
government
overnment
e
q
u
i
l
i
b
r
i
u
m
.B
e
f
o
r
ep
r
o
c
e
e
d
i
n
gt
h
e
s
e， w
budget
constraint.
.
b
udgetc
o
n
s
t
r
a
i
nt
2
2.3
.
3T
The
heg
government
overnmentb
budget
udgetc
constraint
o
n
s
t
r
a
i
n
t
We a
assume
that
the
government
offc
country
H c
collects
the
tariff
from
import
We
ssumet
h
a
tt
h
eg
overnmento
o
u
n
t
r
yH
o
l
l
e
c
t
st
h
et
a
r
i
f
ff
rom i
mport
offg
good
X i
inno
order
toof
finance
the
production
subsidy
toot
the
domestic
firm
and
o
oodX
r
d
e
rt
i
n
a
n
c
et
h
ep
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yt
h
ed
o
m
e
s
t
i
cf
i
r
ma
nd
120
1
2
0
国 際 協 力 論 集 第 6巻 第 2号
t
the
h
eb
budget
udgetc
constraint
o
n
s
t
r
a
i
n
ti
issa
always
lwayss
satisfied.
a
t
i
s
f
i
e
d
.T
Then
hent
the
h
ef
following
o
l
l
o
w
i
n
ge
equation
q
u
a
t
i
o
nh
holds:
o
l
d
s
:
(
3
) SQH= tXFH
If
I
fw
wees
stick
t
i
c
kt
too t
this
h
i
sb
budget
udget c
constraint,
o
n
s
t
r
a
i
n
t，w
wee c
can
an d
define
e
f
i
n
et
that
h
a
tt
the
h
er
rate
a
t
eo
off i
import
mport
tariff
t a
assa
a f
function
offt
the
rate
offp
production
subsidy
s..O
Offc
course,
o
u
r
s
e，i
iffw
weed
doo
t
a
r
i
f
ft
u
n
c
t
i
o
no
h
er
a
t
eo
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
ys
not
adhere
toot
this
constraint,
two
wor
rates
a
t
e
sa
are
r
es
simply
i
m
p
l
yi
independent
n
d
e
p
e
n
d
e
n
to
offe
each
acho
other.
t
h
e
r
.
n
o
ta
dheret
h
i
sc
o
n
s
t
r
a
i
n
t，t
8
So0l
let
e
tu
ussa
assume
ssumet
the
h
ef
following
o
l
l
o
w
i
n
ge
expression
x
p
r
e
s
s
i
o
nt
toot
treat
r
e
a
tt
the
h
eg
government
overnmentb
budget
udgetc
cono
n
-
s
t
r
a
i
n
tf
l
e
x
i
b
l
y
:
straint
flexibly:
(4)
t=¢(s)
¢'~O.
(
4
)t
=ゆ(
s
) ,， ゆ
'
注O
.
o
T
The
hem
meaning
eaningo
offt
this
h
i
se
equation
q
u
a
t
i
o
ni
isso
obvious.
b
v
i
o
u
s
.I
Innt
the
h
ec
case
a
s
eo
off ¢ '
'>0,
>0，t
the
h
eg
governo
v
e
r
n
m
ento
omec
o
u
n
t
r
ya
dheret
h
eb
udget c
o
n
s
t
r
a
i
n
ta
nd t
h
u
si
r
d
e
rt
ment
offh
home
country
adhere
toot
the
budget
constraint
and
thus
inn o
order
too
r
a
i
s
ef
u
n
d
so
o
s
i
t
i
v
ep
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
ys
raise
funds
offp
positive
production
subsidy
s (
(>0)
>0)s
she
h
eh
has
asn
necessary
e
c
e
s
s
a
r
yt
tooi
impose
mpose
import
tariff
t (
(>0).
>
0
)
.I
Inn t
the
h
ec
case
a
s
eo
off o
¢'
'=
= 0
0,， s
she
h
ed
does
o
e
sn
not
o
tk
keep
eep t
the
h
e
p
positive
o
s
i
t
i
v
ei
mport t
a
r
i
f
ft
b
udgetc
o
n
s
t
r
a
i
n
ta
ndt
h
e
r
e
fo
r
es
andt
budget
constraint
and
therefore
sand
tare
a
r
ei
independently
ndependent
l
yc
chosen
hosen4
4).
).
5
5)
)
3
. T
heA
n
a
l
y
s
i
s
3.
The
Analysis
3.1
The
uniqueness
of
the
solution
3
.
1T
heu
n
i
q
u
e
n
e
s
so
ft
h
es
o
l
u
t
i
o
n
Now
let
uss c
consider
changes
inn p
policy
instruments
sand
t o
onn t
the
Cournot
N
ow l
e
tu
o
n
s
i
d
e
rc
hanges i
o
l
i
c
yi
n
s
t
r
u
m
e
n
t
ss
and t
h
eC
ournot
equilibrium.
Totally
differentiating
the
equation
system
(2)
yields:
e
q
u
i
l
i
b
r
i
u
m
.T
o
t
a
l
l
yd
i
f
f
e
r
e
n
t
i
a
t
i
n
gt
h
ee
q
u
a
t
i
o
ns
ystem (
2
)y
i
e
l
d
s
:
hHH+
PH'
- C
CH"
h
HH+P
H'一
H"
(
(5)
5
)
。
。
0
-CH"
-CH
。
hHH
hHH
d
dXHH
XHH
-ds
-ds
0
d
dXHF
XHF
-ds
-ds
0
0
h
hFF
FF
h
FF+P
F'hFF+
PF'
- C
CF"
F"
一
-CF
-CF"
"
d
dXFF
XFF
。
h
hFH
FH
0
"
-CF
-CF "
hFH
hFH+pH'-CF"
十 PH'-CF"
dXFH
d
XFH
dtt
d
-CH"
-CH
"
hHF+
PF'
- C
CHF
h
HF+P
F'一
HF"
。
hHF
hHF
4
4)) N
Note
otet
that
h
a
te
expression
x
p
r
e
s
s
i
o
n(
(4)
4
)a
allows
l
l
o
w
st
the
h
ef
following
o
l
l
o
w
i
n
gc
case.
a
s
e
.N
Namely,
a
r
n
e
l
y，t
the
h
ec
case
a
s
et
that
h
a
tt
the
h
ed
domestic
o
r
n
e
s
t
i
cg
government
o
v
e
r
n
r
n
e
n
tw
wants
anlst
took
keep
e
e
p
b
udgetc
o
n
s
l
r
a
i
n
t，a
budget
constraint,
and
nds
soot
t a
and
nd s
s r
move
n
o
v
es
same
a
r
n
ed
direction
i
r
e
c
t
i
o
n(
(¢
φ'
'>0),
>0)，b
but
u
tt
that
h
a
ts
she
h
ec
cannot
annola
adhere
d
h
e
r
et
toot
the
h
eb
balanced
a
l
a
n
c
e
db
budget.
udget
.
5
S)) T
The
her
relation
e
l
a
l
i
o
nb
between
etweent
t a
and
nds
s i
issj
just
u
s
tl
like
i
k
ee
expression
x
p
r
e
s
s
i
o
n(
(4)
4
)w
when
henb
both
o
t
hr
rates
a
t
e
sa
are
r
ei
innt
the
h
en
neighborhood
e
i
g
h
b
o
r
h
o
o
do
offt
t=s=O.
=s=O. B
But
ut
w
hen t
when
t and~ s
s a
are
r
ep
positive
o
s
i
t
i
v
el
large
a
r
g
en
number,
u
r
n
b
e
r，i
ittr
may
n
a
yb
beed
doubtful
o
u
b
t
f
u
lt
that
h
a
tφis
¢' is p
positive.
o
s
i
t
i
v
e
.T
Thus,
hus，i
inn t
this
h
i
sp
paper
a
p
e
rw
weep
presupposes
r
e
s
u
p
p
o
s
e
s
t
t a
and
nd s
s a
are
r
en
not
o
ts
sooq
quite
u
i
t
el
large.
a
r
g
e
I
International
n
t
e
r
n
a
t
i
o
n
a
lD
Dupoly
u
p
o
l
ya
and
n
dT
Trade
r
a
d
eP
Policies
o
l
i
c
i
e
sU
Under
n
d
e
rB
Budget
u
d
g
e
tC
Constraint
o
n
s
t
r
a
i
n
t
1
2
1
121
T
The
he4
4x4
x4m
matrix
atrixo
offe
equation
quations
system
ystem (
(6),
6
)，w
which
hichwe
we s
shall
h
a
l
lr
refer
e
f
e
rt
tooa
assm
matrix
atrix
A
A h
hereafter,
e
r
e
a
f
t
e
r，i
iss t
the
h
e.
.Jacobian
J
a
c
o
b
i
a
nm
matrix
atrix o
off e
equation
quation s
system
ystem (
(2).
2
)
.L
Let
et u
uss c
consider
onsider
the
nature
offt
this
matrix.
From
C.1
all
the
diagonal
elements
off A
A a
are
t
h
en
atureo
h
i
sm
a
t
r
i
x
.F
romC
.
1~C.3,
~C.3 ， a
l
lt
h
ed
iagonal e
lements o
re
definitely
negative
and
from
C.4
.
4t
they
heya
are
ret
the
h
ed
dominant
ominante
elements
lementsi
inne
every
very c
colo
l
d
e
f
i
n
i
t
e
l
yn
e
g
a
t
i
v
ea
ndf
romC
u
mn6
)
.B
ecause，i
umn
6).
Because,
iffC
C.4
.
4h
holds,
olds，t
then
hen
つ
1I
h
hHH+PH'-CH"
HH+PH'-CH" 1
I一
- 1I
-CH"
-CH" 1
I-I
- 1h
hFH
I=一
= - (hHH-hFH+PH'-2cH"»0,
(hHH-hFH十 pH'-2cH >0，
F
H1
1I
h
hHF+PF'-CH"
HF+PF'一 CH" I-I-CH"
I-I-CH" 1I-I
1h
hFFI
FFI
=-(hHF-hFF+PF'-2cH"»0,
=-(hHF-hFF+PF'-2cHづ>0，
II
h
hFF+PF'-CF"
FF+PF'一 CF" II
一￨一
- I -CF"
CF" II
-I
- Ih
hHF
HFII
=-(hFF-hHF+PF'-2cF"»O,
=一 (hFF-hHF+P
F
'-2CF")>0，
II
h
hFH+PH'-CF"
FH+PH'一 CF" II
一
- II-CF"
CF" II
-I
- Ih
hHH
HHII
=-(hFH-hHH+PH'-2cF"»0.
=一 (
h
F
H-hHH+
PH'-2CFつ
>0.
T
hus，m
Thus,
matrix
atrixA
A h
has
asn
negative
e
g
a
t
i
v
ed
dominant
ominantd
diagonals.
i
a
g
o
n
a
l
s
.C
Consequently
onsequentlyi
ittc
can
ane
easily
a
s
i
l
yb
bee
s
eent
h
a
ta
l
lp
r
i
n
c
i
p
a
lm
inors o
rder t
wo a
re p
o
s
i
t
i
v
ea
nd t
hose o
rder
that
all
principal
minors
off o
order
two
are
positive
and
those
off o
order
seen
t
h
r
e
en
e
g
a
t
i
v
e
.S
i
n
c
ed
et(A)>O，we
three
negative.
Since
det(A»O,
we s
see
e
et
that
h
a
tA
A i
iss a
annN
N--P
P m
matrix,
atrix，s
soot
that
h
a
tt
the
h
e
s
o
l
u
t
i
o
nt
h
ee
quation s
ystem (
2
)m
ustb
nique7
)
.C
onsequently，w
solution
toot
the
equation
system
(2)
must
beeu
unique
7).
Consequently,
wee h
have
ave
e
s
t
a
b
l
i
s
h
e
dt
h
ef
o
l
l
o
w
i
n
gt
heorem:
established
the
following
theorem:
T
HEOREM1:
1
:T
The
he，
J
Jacobian
αc
o
b
i
αnm
matrix
atrixA
A o
offt
the
h
eC
Cournot
ournote
equilibrium
q
u
i
l
i
b
r
i
u
ms
solution
o
l
u
t
i
o
ns
sysy
s
THEOREM
t
em (
tem
(2)
2
)i
issα
an
nN-P
N- P m
matrix
atrixα
and
ndt
therefore
h
e
r
e
f
o
r
et
the
h
es
solution
o
l
u
t
i
o
nt
toot
the
h
es
system
ystemi
issu
unique.
n
i
q
u
e
.
N
otet
that
h
a
tt
this
h
i
st
theorem
heorema
assures
ssurest
the
h
eu
umqueness
niqueness o
offt
the
h
eC
Cournot
ournote
equilibrium
q
u
i
l
i
b
r
i
u
m
Note
s
o
l
u
t
i
o
ni
h
e
r
ee
x
i
s
t
sa
o
l
u
t
i
o
nt
quations
ystem (
2
)a
ll
solution
ifft
there
exists
a s
solution
tooe
equation
system
(2)
att a
all.
.T
The
he p
problem
roblem
a
bout t
h
ee
x
i
s
t
e
n
c
eo
o
l
u
t
i
o
ni
h
i
sC
ournot c
o
m
p
e
t
i
t
i
v
ei
n
t
r
a
i
n
d
u
s
t
r
y
about
the
existence
off a
a s
solution
inn t
this
Cournot
competitive
intra-industry
t
radem
odelh
asb
een s
o
l
v
e
db
ekawa a
nd O
hta (
1
9
9
3
)i
h
ec
ase o
n
trade
model
has
been
solved
byy U
Uekawa
and
Ohta
(1993)
inn t
the
case
off i
inc
reasingm
arginalc
o
s
t
.On
h
eo
therh
and，O
creasing
marginal
cost.
On t
the
other
hand,
Okuguchi
kuguchi (
(990)
19
9
0
)h
has
ass
shown
hownt
the
h
ee
exx
i
s
t
e
n
c
ea
nd t
h
es
t
a
b
i
l
i
t
yo
h
es
o
l
u
t
i
o
no
h
em
odel i
n
c
l
u
d
i
n
gd
ecreasing
and
the
stability
off t
the
solution
off t
the
model
including
decreasing
istence
m
arginalc
o
s
tc
a
s
e
.
marginal
cost
case.
L
etA
Let
Ajjd
denote
enotet
the
h
ec
cofactor
ofactoro
offt
the
h
e，
i
(
(i, j
j)-th
)
t
he
element
lementi
innA
A.
. T
Then
hent
the
h
es
solution
o
l
u
t
i
o
n
6
)A
nn
6)
An
nxn
xnm
matrix
a
t
r
i
xo
of
fA
A=
=α
(
(aij)
i
j
)i
is
ss
said
a
i
dt
to
oh
have
a
v
ed
dominant
o
m
i
n
a
n
td
diagonals
i
a
g
o
n
a
l
si
f
if t
there
h
e
r
ee
exist
x
i
s
tφ
dj>O
>0(j=
(j=l
1,，...
，
ー, η
n)
)s
such
u
c
ht
that
h
a
t
φ
α
dj￨
I aJi
1
III
>
> L
L:
:i
i**
j
jdi
d
iII
a
aji
j
iII f
for
o
ra
any
n
yj
j..
A
And
n
da
a m
matrix
a
t
r
i
xw
with
i
t
hd
dominant
o
m
i
n
a
n
td
diagonals
i
a
g
o
n
a
l
si
s
is n
nonsingular.
o
n
s
i
n
g
u
l
ar
.<
<See
S
e
eM
McKenzie
c
K
e
n
z
i
e(
0960,
19
6
0，p
p.49)
.
49
)f
for
o
rt
the
h
ep
proof.>
r
o
o
f
.
>
7)
An
nxn
matrix
is s
said
to
be
an
N- P
P m
matrix
if i
its
principal
minors
of
order
r h
have
the
sign
of
(r=
1..
...'
,
xnm
a
t
r
i
xi
s
a
i
dt
ob
ea
nN
a
t
r
i
xi
f
t
sp
r
i
n
c
i
p
a
lm
i
n
o
r
so
fo
r
d
e
rr
a
v
et
h
es
i
g
no
f(_1)r
(
ー1
)r(
r=1
“
7
)A
nn
n
n )
)..A
And
n
di
f
if t
the
h
eJ
Jacobian
a
c
o
b
i
a
nm
matrix
a
t
r
i
xo
of
fe
equation
q
u
a
t
i
o
ns
system
y
s
t
e
mi
s
is a
an
nN
N- P
P m
matrix,
a
t
r
i
x，t
the
h
es
solution
o
l
u
t
i
o
no
of
ft
the
h
es
system
y
s
t
e
mi
s
is u
unique.
n
i
q
u
e
.<
<See
S
e
e
Nikaido
0968,
19
6
8，p
p.37j)
.
3
7J) f
for
o
rt
the
h
ep
proof.>
r
o
of
.
>
N
i
k
a
i
d
o(
122
1
2
2
国 際 協 力 論 集 第 6巻 第 2号
o
offe
equation
q
u
a
t
i
o
ns
system
ystem (
(5)
5
)c
can
anb
beew
written
r
i
t
t
e
na
assf
follows:
o
l
l
o
w
s
:
A
All
ll
A21
A2l
A31
A3l
A41
A4l
-ds
-ds
A
12
A12
A
22
A22
A
32
A32
A
42
A42
-ds
-ds
dXFF
dXFF
A
A13
13
A23
A
23
A
A33
33
A
A43
43
。
dXFH
dXFH
A14
A14
A24
A24
A34
A34
A44
A
44
dt
dt
dXHH
dXHH
(
6
)
(6)
I
dXHF
dXHF
=
=
[1/
[1/d
det(A)
e
t
(
A
)]
]
°
I
Innt
the
h
ef
following
o
l
l
o
w
i
n
gs
sections
e
c
t
i
o
n
sl
let
e
tu
ussc
consider
o
n
s
i
d
e
rt
the
h
en
nature
a
t
u
r
eo
offt
this
h
i
ss
solution.
o
l
u
t
i
o
n
.
3
3.2
.
2T
The
hee
effects
f
f
e
c
t
so
of
fa
a c
change
hange i
in
ns
s:
:i
independent
n
d
e
p
e
n
d
e
n
tc
case
a
s
e
Innt
this
sub-section,
wees
shall
h
a
l
li
investigate
n
v
e
s
t
i
g
a
t
et
the
h
ee
effects
f
f
e
c
t
so
offa
a c
change
hangei
inns
s o
onnp
producr
o
d
u
c
I
h
i
ss
u
b
s
e
c
t
i
o
n，w
tion
and
consumption
when
the
domestic
government
issf
free
from
budget
cont
i
o
na
ndc
onsumptionw
hent
h
ed
o
m
e
s
t
i
cg
overnmenti
r
e
ef
romb
udgetc
o
n
straint
and
chooses
s i
independently
n
d
e
p
e
n
d
e
n
t
l
yo
offt
t..
s
t
r
a
i
n
ta
ndc
hoosess
F
From
rom (
(6)
6
)w
weeo
obtain
b
t
a
i
nt
the
h
ef
following
o
l
l
o
w
i
n
ge
equations:
q
u
a
t
i
o
n
s
:
(7.1)
(
7.
1
)X
XHHs=
HHs三 δ
8 XHH/
XHH/ θ
8s
s=
=一
- (A
(Al
11
l十
+A
A2
21)/
1)/d
det(A»O,
et(A)>O，
(7.2)
(
7
.
2
)X
XHFs=
HFs三 δ
8 XHF/
XHF/ δ
8s
s=
=一
- (A
(A12
1
2+
+A
A2
22
2)/det(A»O,
)/det(A)>O，
(
(7.3)
7
.
3
)X
XFFs=
FFs三 δ
8 XFF/
XFF/ δ
8s
s=
=一
- (A
(A13
1
3+
+A
A2
23)/
3)/d
det(A)<O,
et(A)<O，
(7.4)
(
7.
4
) XFHs=
XFHs= a
8 XFH/
XFH/ δ
8s
s=
=一
- (A
(A14
14 十
+A
A4
44
4)/
)/d
det(A)<O.
et(A)<O.
(
Thes
i
g
n
so
q
u
a
t
i
o
n
sa
r
ee
xaminedi
ppendixA
(The
signs
offe
equations
are
examined
innA
Appendix
A.1.
.1
.a
and
ndA
Appendix
ppendixA
A.2.)
.2
.
)
From
wee f
find
that
ann i
increase
inn t
the
domestic
production
F
rom (7.1)~(7.4),
(7. 1) ~(7 .4)， w
i
n
dt
h
a
ta
n
c
r
e
a
s
ei
h
ed
o
m
e
s
t
i
cp
r
o
d
u
c
t
i
o
n
subsidy
promotes
the
domestic
firm's
supply
tooe
each
market
and
shrinks
the
s
u
b
s
i
d
yp
romotest
h
ed
o
m
e
s
t
i
cf
i
r
m
'
ss
u
p
p
l
yt
achm
arket a
nd s
h
r
i
n
k
st
h
e
f
o
r
e
i
g
nf
i
r
m
'
ss
u
p
p
l
yt
v
e
r
ym
arket
foreign
firm's
supply
tooe
every
market.
.T
Therefore,
h
e
r
e
f
o
r
e，w
wee c
can
an f
find
i
n
dt
that
h
a
tt
the
h
et
total
o
t
a
l
production
offt
the
domestic
duopolist
increases
and
that
offf
foreign
counterpart
p
r
o
d
u
c
t
i
o
no
h
ed
omesticd
u
o
p
o
l
i
s
ti
n
c
r
e
a
s
e
sa
ndt
hato
o
r
e
i
g
nc
o
u
n
t
e
r
p
a
r
t
decreases.
This
establishes
the
following
expressions:
d
e
c
r
e
a
s
e
s
.T
h
i
se
s
t
a
b
l
i
s
h
e
st
h
ef
o
l
l
o
w
i
n
ge
x
p
r
e
s
s
i
o
n
s
:
(
7
.
5
) QHs=XHHs+XHFs>O,
QHs三 日Hs+XHFs>O，
(7.5)
(7.6)
(
7
.
6
) QFs=
QFs三 X
XFFs+
FFs+X
XFHs<O.
FHs<O.
N
Now,
ow，l
let
e
tu
usst
turn
u
r
nt
toot
the
h
ee
effects
f
f
e
c
t
so
onnc
consumption
onsumptiono
offt
this
h
i
sg
good
oodi
inne
each
achc
couno
u
n
try.
We c
can
verify
the
following
expressions:
t
r
y
.We
anv
e
r
i
f
yt
h
ef
o
l
l
o
w
i
n
ge
x
p
r
e
s
s
i
o
n
s
:
I
International
n
t
e
r
n
a
t
i
o
n
a
lD
Dupoly
upolya
and
nd T
Trade
radeP
Policies
o
l
i
c
i
e
sU
Under
nderB
Budget
udgetC
Constraint
o
n
s
t
r
a
i
n
t
123
1
2
3
(7.7)
(
7
.
7
)X
XHs=XHHs+XFHs=-(All
Hs=XHHs+XFHs=一 (All+A21
+A21 十
+A14
A 14
+
+A4
A4
4
4)/det(A)
)/d
e
t(A)
つ
=一
- (
(1/2)
[pH'(pF'-2cF")
+PF'(PH'-2cF")]/
det(A»O,
=
1/2)(hHF+hFF+pF')
(hHF+hFF+p
F
'
)[
p
H
'(
p
F
'-2
C
F +
P
F
'(
P
H
'-2
C
F
"
)
]/d
e
t
(
A
)>0，
s三 XFFs+XHFs=一
(7.8)
(
7
.
8
) XF
XFs=XFFs+XHFs=
z
=
(A
(A12
12+
+A
A222
2+
+A
A 13
13
+
+A
A2
23)/
3
)/d
det(A)
e
t(A)
- 0/2)
0/2) (hHH+hFH+pH')
(hHH+hFH+PH')[
[pH'(PF'
p
H
'(
PF
'-2CF")
2CF")+PF'(pH'-2cF")]/
+PF'(pH'-2cF")]/d
det(A»O.
et(A)>O.
ー
(See
Appendix
A.3
for
the
derivation
offt
the
expressions.)
The
signs
off(
(7.7)(
S
e
eA
ppendixA
.3f
o
rt
h
ed
e
r
i
v
a
t
i
o
no
h
ee
x
p
r
e
s
s
i
o
n
s
.
)T
hes
i
g
n
so
7
.
7
)一
(
(7.8)
7
.
8
)s
stem
tem f
from
rom t
that
h
a
t (
(PF'
PF' - 2
2CF")<O
C
F
"
)くoa
and
nd (pH'
(
p
H
'- 2
2CF")<O
C
Fつくoh
hold
o
l
df
from
rom C
C.3.
.
3
.
Therefore
weec
can
claim
that
anni
increase
inns
s r
raises
both
countries'
total
conT
h
e
r
e
f
o
r
ew
anc
l
a
i
mt
h
a
ta
n
c
r
e
a
s
ei
a
i
s
e
sb
o
t
hc
o
u
n
t
r
i
e
s
't
o
t
a
lc
o
n
sumption
offg
good
X..T
Thus,
hus，s
since
i
n
c
et
the
h
ei
inverse
n
v
e
r
s
ed
demand
emand f
functions
u
n
c
t
i
o
n
sa
are
r
en
negatively
e
g
a
t
i
v
e
l
y
s
umptiono
oodX
h
ep
r
i
c
e
so
offg
good
oodX
Xi
innb
both
othm
markets
arketsd
decrease
e
c
r
e
a
s
ei
iffs
s r
rises.
i
s
e
s
.
s
sloped,
l
o
p
e
d，t
the
prices
avee
established
s
t
a
b
l
i
s
h
e
dt
the
h
ef
following
o
l
l
o
w
i
n
gt
theorem:
h
e
o
r
e
m
:
C
Consequently,
o
n
s
e
q
u
e
n
t
l
y，w
weeh
have
T
THEOREM
HEOREM2
2:: When
Whent
the
h
ep
production
roductions
subsidy
u
b
s
i
d
yi
issd
determined
e
t
e
r
m
i
n
e
di
independently
n
d
e
p
e
n
d
e
n
t
l
yb
byyt
the
h
e
d
domestic
o
m
e
s
t
i
cg
overnment，α
government,
an
九 m
increase
cre
αs
ei
inn t
the
h
ep
production
roduction s
subsidy
u
b
s
i
d
yr
raises
a
i
s
e
sd
domestic
omestic
p
roduction，d
production,
domestic
o
m
e
s
t
i
cc
consumption
onsumption α
and
ndf
foreign
o
r
e
i
g
nc
consumption,
onsumption，ω
while
h
i
l
ei
itt c
curtails
u
r
tαi
l
s
foreign
production.
And
ittr
reduces
the
prices
offg
good
X i
innb
both
markets.
αr
k
e
t
s
.
f
o
r
e
i
g
np
r
o
d
u
c
t
i
o
n
.A
ndi
e
d
u
c
e
st
h
ep
r
i
c
e
so
oodX
othm
3
.
3T
hee
f
f
e
c
t
so
hange i
nt
n
d
e
p
e
n
d
e
n
tc
a
s
e
3.3
The
effects
offa
a c
change
in
t:: i
independent
case
examine
xaminet
the
h
ee
effects
f
f
e
c
t
so
offa
a d
domestic
o
m
e
s
t
i
ci
import
mportt
tariff
a
r
i
f
fo
onnp
pror
o
I
h
i
ss
u
b
s
e
c
t
i
o
n，w
Innt
this
sub-section,
weee
d
u
c
t
i
o
na
ndc
onsumptiono
oodX
duction
and
consumption
offg
good
X i
inne
each
achc
country
o
u
n
t
r
yi
innt
the
h
ec
case
a
s
et
that
h
a
tt
the
h
ed
doo
m
mestic
e
s
t
i
cg
overnmenti
r
e
ef
romb
udgetc
o
n
s
t
r
a
i
n
ta
ndc
h
o
o
s
e
st
n
d
e
p
e
n
d
e
n
t
l
y
government
issf
free
from
budget
constraint
and
chooses
t i
independently
o
offs
s..
From
(6)
weeo
obtain
the
following
equations:
F
rom (
6
)w
b
t
a
i
nt
h
ef
o
l
l
o
w
i
n
ge
q
u
a
t
i
o
n
s
:
(8.1)
(
8.
1
)X
XHHt=
HHt=OXHH/
OXHH/δ
ot=A41/det(A»O,
t=A41/det(A)>0，
(8.2)
(
8
.
2
)X
XHFt=
H
F
t三 OXHF/
OXHF
/ Ot=A4
Ot= A 4
2
2/det(A)~O,
/det(A)孟0，
(
8
.
3
)X
F
F
t三 O
FF/Ot=A4
/d
et(A)孟
0，
(8.3)
XFFt=
0X
XFF/
0 t=A4 3
3/
det(A)
~o,
(8.4)
(
8
.
4
)X
XFHt=
F
H
t三 θ
OXFH/
XFH/Ot=A4
ot=A44
4/det(A)<O,
/det(A)<0，
(
(The
Thes
signs
i
g
n
so
offe
equations
q
u
a
t
i
o
n
sa
are
r
ee
examined
xaminedi
innA
Appendix
ppendixA
A.U
.
1
.
)
From
(8.1)-(8.4)
weef
find
that
anni
increase
inn t
the
import
tariff
promotes
F
rom (
8
.1
)-(8.
4
)w
i
n
dt
h
a
ta
n
c
r
e
a
s
ei
h
ei
mport t
a
r
i
f
fp
romotes
the
domestic
firm's
supply
too e
each
market
and
shrinks
the
foreign
firm's
t
h
ed
o
m
e
s
t
i
cf
i
r
m
'
ss
u
p
p
l
yt
ach m
arket a
nd s
h
r
i
n
k
st
h
ef
o
r
e
i
g
nf
i
r
m
'
s
124
1
2
4
国 際 協 力 論 集 第 6巻 第 2号
s
supply
u
p
p
l
yt
tooe
every
v
e
r
ym
market.
arke
t
.T
Therefore,
h
e
r
e
f
o
r
e，w
wee c
can
an f
find
i
n
dt
that
h
a
tt
the
h
et
total
o
t
a
lp
production
r
o
d
u
c
t
i
o
no
off
the
domestic
duopolist
increases
and
that
off f
foreign
counterpart
decreases.
t
h
ed
o
m
e
s
t
i
cd
u
o
p
o
l
i
s
ti
n
c
r
e
a
s
e
sa
nd t
h
a
to
o
r
e
i
g
nc
o
u
n
t
e
r
p
a
r
td
e
c
r
e
a
s
e
s
.
T
h
i
se
s
t
a
b
l
i
s
h
e
st
h
ef
o
l
l
o
w
i
n
ge
x
p
r
e
s
s
i
o
n
s
:
This
establishes
the
following
expressions:
(
(8.5)
8
.
5
)Q
QHt=XHHt+
泊 三X
HHt+
X
XHFt>O,
HFt>O，
(
8
.
6
)Q
F
t三 X
F
F
t十 XFHt<O.
(8.6)
QFt=XFFt+XFHt<O.
N
Note
otet
that
h
a
ti
inne
equations
q
u
a
t
i
o
n
s(
(8.2)
8
.
2
)a
and
nd (
(8.3)
8
.
3
)t
the
h
ee
equality
q
u
a
l
i
t
yh
holds
o
l
d
so
only
n
l
yi
iff C
CH"
H
"=
=CF"
CF"=
=0,
0，
t
that
h
a
ti
isse
every
v
e
r
yf
firm's
i
r
m
'
sm
marginal
arginalc
cost
o
s
ti
issc
constant.
onstant
.
N
Now
owl
let
e
tu
ussc
consider
o
n
s
i
d
e
rt
the
h
ee
effects
f
f
e
c
t
so
offa
a c
change
hange i
In
nt
the
h
ei
import
mport t
tariff
a
r
i
f
fo
onn c
cono
n
sumption
inne
each
country.
Considering
weec
can
verify
the
following
(8. 1) ~(8 .4)， w
anv
e
r
i
f
yt
h
ef
o
l
l
o
w
i
n
g
s
umptioni
achc
o
u
n
t
r
y
.C
o
n
s
i
d
e
r
i
n
g(8.1)~(8.4),
e
x
p
r
e
s
slOn
s
:
expressIons:
(
8
.
7
)X
Ht三 XHHt+XFHt=(A41十
A44
)/ d
e
t(A)
(8.7)
XHt=XHHt+XFHt=(A41
+A4
4)/det(A)
=
= (
(1/2)
1/2){
{(hFF+
(hFF+P
PF'
F
'一
- C
CF")
F
"
)[
[pH'
p
H
'(
(PF'
PF
'- 2
2CH")
C
H
"
)+
+P
PF'
F
'(
(PH'
PH
'-2
- 2CH")]
C
H
"
)
]
つ
+hHF[pH'(PF'-2cF")
+PF'(pH'-2cH")]}
/ d
det(A)<O,
+hHF[
p
H
'(
PF
'-2
C
F +
P
F
'
(
p
H
'
2
c
H
"
)
]
}/
et(A)<O，
(
(8.8)
8
.
8
)X
XFt=XFFt+XHFt=(A4
Ft三 XFFt+XHFt=(A42
2+
+A4
A43)
3)/det(A)
/ d
et(A)
= {hHH(PF'
- CF")
(CF"
- CH")
+ (
0/2)
CF"
=
{
h
H
H(
PF
'-C
F
"
)(
C
F
"-C
H
"
)+
1/2)C
F
"
つ
[pl/(pF'
-2CH")
+P
PF'(PH'
-2CH")]}
/ d
det(A).
[
p
l
/(
p
F
'2
C
H +
F
'(
PH
'-2
C
H
"
)
]
}/
et(A).
T
Thus,
hus，f
from·
r
o
m
.(
(8.7)
8
.
7
)w
wees
see
e
et
that
h
a
ta
anni
increase
n
c
r
e
a
s
ei
innt
the
h
ed
domestic
o
m
e
s
t
i
ci
import
mportt
tariff
a
r
i
f
fr
reduces
e
d
u
c
e
s
consumption
offg
good
X i
innt
the
home
country.
This
means
that
price
offg
good
X
c
onsumptiono
oodX
h
eh
omec
o
u
n
t
r
y
.T
h
i
sm
eanst
h
a
tp
r
i
c
eo
oodX
i
n
c
r
e
a
s
e
si
h
ed
o
m
e
s
t
i
cm
a
r
k
e
t
.B
utw
hetheri
n
c
r
e
a
s
e
sc
onsumptioni
h
e
increases
innt
the
domestic
market.
But
whether
itti
increases
consumption
innt
the
foreign
market
orrn
not
depends
onnc
changes
innc
cost
conditions
offt
the
duopolists.
f
o
r
e
i
g
nm
arketo
o
td
ependso
hangesi
o
s
tc
o
n
d
i
t
i
o
n
so
h
ed
u
o
p
o
l
i
s
t
s
.
From
(8.8),
wees
see
e
et
that
h
a
ti
iffC
CF"
F"
-C
CH"
H"孟
~o,
0，i
i.e.
.
e
.t
the
h
ed
degree
e
g
r
e
eo
offm
marginal
arginalc
cost
o
s
tr
reduce
d
u
c
F
rom (
8
.
8
)，w
the
domestic
firm
issn
not
sool
large
compared
with
the
foreign
firm,
the
h
e
t
tion
i
o
ni
innt
h
ed
omesticf
i
r
mi
o
ts
a
r
g
ec
omparedw
itht
h
ef
o
r
e
i
g
nf
i
r
m，t
total
supply
offg
good
X i
innt
the
foreign
market
decreases.
Onnt
the
other
hand,
iff
t
o
t
a
ls
u
p
p
l
yo
oodX
h
ef
o
r
e
i
g
nm
arketd
e
c
r
e
a
s
e
s
.O
h
eo
t
h
e
rh
and，i
CF"
-C
CH"
~0
0,，t
the
h
ed
degree
e
g
r
e
eo
off m
marginal
arginal c
cost
o
s
tr
reduction
e
d
u
c
t
i
o
ni
In
nt
the
h
ed
domestic
o
m
e
s
t
i
cf
firm
i
r
mi
iss
C
F
"H"ミ
large
enough,
itti
issp
possible
o
s
s
i
b
l
et
that
h
a
tt
the
h
et
total
o
t
a
ls
supply
u
p
p
l
yo
off t
this
h
i
sg
good
ood i
inn t
the
h
ef
foreign
o
r
e
i
g
n
l
a
r
g
ee
nough，i
market
increases.
m
arketi
n
c
r
e
a
s
e
s
.
avee
established
s
t
a
b
l
i
s
h
e
dt
the
h
ef
following:
o
l
l
o
w
i
n
g
:
Consequently,
weeh
have
C
onsequently，w
I
n
t
e
r
n
a
t
i
o
n
a
lD
u
p
o
l
ya
n
dT
r
a
d
eP
o
l
i
c
i
e
sU
n
d
e
rB
u
d
g
e
tC
o
n
s
t
r
a
i
n
t
Inte~national
Dupoly
and
Trade
Policies
Under
Budget
Constraint
1
2
5
125
T
THEOREM
HEOREM3
3:: When
Whent
the
h
ei
import
mportt
tariff
αr
i
f
fi
issd
determined
etermined i
independently
n
d
e
p
e
n
d
e
n
t
l
yb
byy t
the
h
ed
doo
mestic
government,
anni
increase
n
c
r
e
αs
ei
innt
the
h
ei
import
mportt
tariff
a
r
i
f
fr
raises
a
i
s
e
sd
domestic
omesticp
production
roduction
m
esticg
overnment，a
while
itt c
curtails
αi
l
sd
domestic
omestic c
consumption
onsumption α
and
ndf
foreign
o
r
e
i
g
np
production.
r
o
d
u
c
t
i
o
n
.A
And
nd i
itt i
inn
w
h
i
l
ei
u
r
t
creases
the
price
offg
good
X i
innd
domestic
omesticmα
market.
r
たe
t
. On
On t
the
h
eo
other
ther h
hand,
αnd
，w
whether
hether
‘
c
r
e
αs
e
st
h
ep
r
i
c
eo
oodX
i
itt i
increases
n
c
r
e
αses c
consumption
onsumption i
inn t
the
h
ef
foreign
oreign m
market
αrket o
orr n
not
ot d
depends
epends o
onn t
the
h
ec
cost
o
s
t
conditions.
But
iff C
CF"
- C
CH"
~0
0,，a
anni
increase
innt
the
import
tariff
decreases
forH"壬
n
c
r
e
αs
ei
h
ei
mportt
αr
i
f
fd
ecre
αs
e
sf
o
r
c
o
n
d
i
t
i
o
n
s
.B
uti
F
"一
e
L
g
nc
onsμmptwn.
eign
consumption.
3
3.4
.
4T
The
hee
effects
f
f
e
c
t
so
of
fa
a c
change
hangei
in
ns
s:
:b
binding
i
n
d
i
n
gb
budget
u
d
g
e
tc
constraint
o
n
s
t
r
a
i
n
tc
case
a
s
e
Innt
this
sub-section
wees
shall
investigate
the
effects
offc
changes
inns
s o
onnp
producI
h
i
ss
u
b
s
e
c
t
i
o
nw
h
a
l
li
n
v
e
s
t
i
g
a
t
et
h
ee
f
f
e
c
t
so
hangesi
r
o
d
u
c
tion
and
consumption
offg
good
X i
inne
each
country
innt
the
case
offb
binding
budget
t
i
o
na
ndc
onsumptiono
oodX
achc
o
u
n
t
r
yi
h
ec
a
s
eo
i
n
d
i
n
gb
udget
constraint.
From
(3),
and
weec
can
derive
the
following
(7. 1) ~(7 .4)， a
nd (8.1)~(8.4),
(8. 1) ~(8 .4)， w
and
e
r
i
v
et
h
ef
o
l
l
o
w
i
n
g
c
o
n
s
t
r
a
i
n
t
.F
rom(
3
)，(7.1)~(7.4),
results:
r
e
s
u
l
t
s
:
(
(9.1)
9
.
1
)d
dXHH/
XHH/d
ds=xHHs+
S=XHHs+X
XHHt(dt/
HHt(dt/d
ds)
s
)=XHHs+φ
=XHHs+ ¢ 'XHHt>O,
'
X
H
H
t
>
O，
(9.2)
dXHF/
XHF/d
ds=xHFs+xHFt(dt/
S=XHFs+XHFt(dt/d
ds)
s
)=XHFs+
=XHFs+φ
¢ 'XHFt>O,
'
X
H
F
t
>
O，
(
9
.
2
)d
o
(9.3)
dXFF/
XFF/d
ds=
s=X
XFFs+
F
F
s
+X
XFFt(dt/
FFt(
dt/d
ds)
s
)=
= X
XFFs+
F
F
s
+¢ 'XFFt<O,
'
X
F
F
t
く0
，
(
9
.
3
)d
(
(9.4)
9.
4
)d
dXFH/
XFH/d
ds=xFHs+xFht(dt/
S=XFHs十 XFht(dt/d
ds)
s
)=XFHs+
=X
F
H
s十 ゆ
¢ 'XFHt<O.
'
X
F
H
t
<
O
.
F
From
romt
the
h
ea
above
bovee
equations
q
u
a
t
i
o
n
sw
weef
find
i
n
dt
that
h
a
ta
a r
rise
i
s
ei
innt
the
h
ed
domestic
omesticp
production
r
o
d
u
c
t
i
o
ns
subu
b
byya
a c
corresponding
rise
innt
the
import
tariff
increases
the
domess
sidy
i
d
yf
financed
i
n
a
n
c
e
db
o
r
r
e
s
p
o
n
d
i
n
gr
i
s
ei
h
ei
mportt
a
r
i
f
fi
n
c
r
e
a
s
e
st
h
ed
omestic
t
i
cf
i
r
m
'
ss
u
p
p
l
yt
ach m
arket a
nd r
e
d
u
c
e
st
h
ef
o
r
e
i
g
nf
i
r
m
'
ss
u
p
p
l
yt
firm's
supply
too e
each
market
and
reduces
the
foreign
firm's
supply
too
every
market.
t
.T
Thus
hus i
itt p
promotes
romotes t
the
h
ep
production
r
o
d
u
c
t
i
o
no
off d
domestic
o
m
e
s
t
i
cd
duopolist
u
o
p
o
l
i
s
ta
and
nd
e
v
e
r
ym
arke
shrinks
that
offf
foreign
duopolist.
Therefore,
weeh
have
avet
the
h
ef
following
o
l
l
o
w
i
n
ge
equation:
q
u
a
t
i
o
n
:
s
h
r
i
n
k
st
h
a
to
o
r
e
i
g
nd
u
o
p
o
l
i
s
t
.T
h
e
r
e
f
o
r
e，w
(
(9.5)
9
.
5
) d
dQH/
QH/d
ds=dxHH/
s=dxHH/d
ds+dxHF/
s+dxHF/d
ds>O,
s>O，
(
(9.6)
9
.
6
) d
dQF/
QF/d
ds=dxFF/
s=dxFF/d
ds+dxFH/
s+dxFH/d
ds<O.
s
くO
.
L
Let
e
tu
ussc
consider
o
n
s
i
d
e
rt
the
h
ee
effects
f
f
e
c
t
so
offa
a c
change
hangei
inns
s w
with
i
t
ha
a a
accompanying
ccompanyingc
change
hangei
inn
onnc
consumption
inne
each
country.
We c
can
derive
the
following
expressions:
s
:
t
t o
onsumptioni
achc
o
u
n
t
r
y
.We
and
e
r
i
v
et
h
ef
o
l
l
o
w
i
n
ge
x
p
r
e
S
SlOn
(
9
.
7
) dXH/
ds=dxHH/ds+dxFH/dS=XHs十
φ'XHt，
126
1
2
6
国 際 協 力 論 集 第 6巻 第 2号
(
9
.
8
)dXF/ds=dxFF/ds+dxHF/dS=XFs+φ'XFt・
I
Innt
this
h
i
sc
case,
a
s
e，w
whether
hetherc
consumption
onsumptiono
offg
good
oodX
X i
increases
n
c
r
e
a
s
e
so
orrn
not
oti
inne
each
achm
market
arket
m
ainlyd
ependso
h
em
agnitudeo
mainly
depends
onnt
the
magnitude
offゆ
¢'
'
三
==. d
dt/
t/d
ds,
s，w
which
hichr
represents
e
p
r
e
s
e
n
t
st
the
h
em
marginal
arginal
rate
offt
tariff
toof
finance
a u
unit
offp
production
subsidy
rate
added.
¢'
depends
'd
epends
r
a
t
eo
a
r
i
f
ft
i
n
a
n
c
ea
n
i
to
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yr
a
t
ea
d
d
e
d
.o
onnt
the
relative
magnitude
offt
the
volume
offi
import
and
the
volume
offd
domestic
o
h
er
e
l
a
t
i
v
em
agnitudeo
h
ev
olumeo
mporta
ndt
h
ev
olumeo
o
m
e
s
t
i
c
p
r
o
d
u
c
t
i
o
n
.F
rome
q
u
a
t
i
o
n
s(
7
.7
production.
From
equations
(7.7),
)
， (
(7.8),
7
.
8
)，(
(8.7),
8
.
7
)，a
and
nd (
(8.8)
8
.
8
)w
weec
can
ane
estimate
s
t
i
m
a
t
et
that
h
a
t
s
s
u
r
e
sp
o
s
i
t
i
v
ev
a
l
u
e
so
XH/d
ndd
XF/d
s
.A
r
e
l
a
t
i
v
e
l
ys
m
a
l
lv
a
l
u
eo
f
φ
relatively
small
value
of
¢'，a
assures
positive
values
offd
dXH/
dssa
and
dXF/
ds.
Ass
a
attero
a
c
t，i
matter
offf
fact,
innt
the
h
ec
case
a
s
eo
offc
constant
o
n
s
t
a
n
tm
marginal
arginal c
costs
o
s
t
sc
case,
a
s
e，w
wee c
can
an d
derive
e
r
i
v
e
a m
the
following
equation:
t
h
ef
o
l
l
o
w
i
n
ge
q
u
a
t
i
o
n
:
φ')[
p
H
'
p
F
'(hHF+hFF+p
F
'
)]
/d
e
t
(
A
)
(
9
.9
) dXH/dS=XHs+ゆ'X
Ht=一(1i
fC
H
"=CF"=0.
(
9.
10
) dXF/dS=XF
S+ゆ'
X
F
t=-P
H
'
P
F
'(
h
H
H+h
F
H+p
H
'
)/d
e
t(A)>0
i
fC
H
"=C
F
"=0.
From
(9.9)
wees
see
that
consumption
innc
country
H i
increases
n
c
r
e
a
s
e
si
iff
¢φ'
'<1
<1i
innt
the
h
ec
case
a
s
e
F
rom(
9
.
9
)w
e
et
h
a
tc
onsumptioni
ountryH
offc
c]-J"
]
J
"=
=CF"
CF"=
=0.
0. O
Onnt
the
h
eo
other
t
h
e
rh
hand,
and，f
from
rom (
(9.10)
9.
10
)c
consumption
onsumption i
inn c
country
ountry F
F i
inn
o
c
r
e
a
s
e
sw
i
t
h
o
u
ta
ny a
d
d
i
t
i
o
n
a
lc
o
n
d
i
t
i
o
n
sw
hen t
h
em
arginal c
o
s
t
sa
r
ec
o
n
creases
without
any
additional
conditions
when
the
marginal
costs
are
cons
t
a
n
t
.T
h
i
si
ecause t
h
ee
f
f
e
c
t
so
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
yt
r
a
n
s
m
i
t
st
h
e
stant.
This
iss b
because
the
effects
off p
production
subsidy
transmits
too t
the
f
o
r
e
i
g
nm
arketb
u
tt
h
a
to
mportt
a
r
i
f
fd
oesn
otp
asst
hrought
h
em
arket
foreign
market
but
that
offi
import
tariff
does
not
pass
through
toot
the
market
8
o
ountryF
henC
offc
country
F w
when
CH"
正=
=CF"
CF"=
=0
08
)..
)
T
Thus
husw
weeh
have
avee
established
s
t
a
b
l
i
s
h
e
dt
the
h
ef
following
o
l
l
o
w
i
n
gt
theorem:
heorem:
T
THEOREM
HEOREM4
4::I
Innt
the
h
eC
case
αs
eo
offb
binding
i
n
d
i
n
gb
budget
udgetc
constraint,
o
n
s
t
r
αi
n
t，α
an
nm
increase
cre
αs
ei
innt
the
h
ep
prorod
u
c
t
i
o
ns
ubsidyp
romotest
h
es
upplyo
omesticd
u
o
p
o
l
i
s
tα
duction
subsidy
promotes
the
supply
offd
domestic
duopolist
and
ndc
curtails
u
r
t
a
i
l
st
that
h
αto
off
foreign
duopolist.
But
whether
the
consumption
inn e
each
αch m
market
αr
k
e
ti
increases
n
c
r
e
αs
e
so
orr
f
o
r
e
i
g
nd
u
o
p
o
l
i
s
t
.B
ut w
hether t
h
ec
onsumption i
n
otd
ependso
h
ev
not
depends
onnt
the
value
αl
u
eo
off¢O'
'==.
三 d
dt/
t/d
ds,
s，t
the
h
em
marginal
αr
g
i
n
a
lr
rate
αt
eo
offt
tariff
a
r
i
f
ft
toof
finance
i
n
αn
c
e
α
unit
n
i
to
offp
production
roductions
subsidy
u
b
s
i
d
yr
rate
αt
eα
added.
d
d
e
d
.
a u
8
8)) T
The
he r
reader
e
a
d
e
rc
can
an e
easily
a
s
i
l
yc
check
h
e
c
kt
this
h
i
sr
result
e
s
u
l
tf
from
rom (
(7.7).
7
.7
)
， (
(7.8),
7，
8
)， (
(8.7),
8，
7
)，a
and
nd (
(8.8)
8
.
8
)b
byy s
substituting
u
b
s
t
i
t
u
t
i
n
gt
the
h
ec
condition
o
n
d
i
t
i
o
nC
CH"
H"
=cp"=O.
=
C
f
'
'
'
=O
.
International
Dupoly
and
Trade
Policies
Under
Budget
Constraint
I
nternational D
upoly a
nd T
rade P
olicies U
nder B
udget C
onstraint
127
127
4
4.
.T
The
heO
Optimal
p
t
i
m
a
lT
Trade
rade P
Policy
o
l
i
c
y
Now,
let
e
tu
ussp
proceed
r
o
c
e
e
dt
tooo
optimal
p
t
i
m
a
lt
trade
r
a
d
ep
policy
o
l
i
c
yd
discussions.
i
s
c
u
s
s
i
o
n
s
.F
First
i
r
s
tw
wees
shall
h
a
l
la
assume
ssume
N
ow，l
t
h
a
tt
h
es
o
c
i
a
lu
t
i
l
i
t
yf
u
n
c
t
i
o
nt
a
k
e
st
h
es
e
m
i
l
i
n
e
a
rf
o
r
m
:
that
the
social
utility
function
takes
the
semi-linear
form:
U三 U(XH)十 Z，
w
hereZ
Z r
represents
e
p
r
e
s
e
n
t
st
the
h
ed
domestic
o
m
e
s
t
i
cd
demand
emand f
for
o
rc
competitively
o
m
p
e
t
i
t
i
v
e
l
yp
produced
roduced g
good
ood Z
Z,，
where
w
which
hichi
isst
the
h
en
numeraire
umerairei
innb
both
othc
country,
ountry，a
and
nds
soot
the
h
er
relative
e
l
a
t
i
v
ep
price
r
i
c
eo
offg
good
oodX
X i
iss
p
pH(XH)
H(XH) a
and
ndp
pF(XF)
F(XF) i
innc
country
ountryH
Hand
andF
F,，r
respectively.
e
s
p
e
c
t
i
v
e
l
y
.I
Inn t
this
h
i
sc
case
a
s
ew
welfare
e
l
f
a
r
ee
eff
9)
f
fects
e
c
t
so
r
a
d
ep
o
l
i
c
yc
anb
x
p
r
e
s
s
e
db
tandards
u
r
p
l
u
sm
easures9
offt
trade
policy
can
beee
expressed
byys
standard
surplus
measures
).. L
Lete
t
-W
W
d
denote
e
n
o
t
et
the
h
en
national
a
t
i
o
n
a
lw
welfare
e
l
f
a
r
eo
off t
the
h
eh
home
ome c
country,
o
u
n
t
r
y，w
which
hich c
consists
o
n
s
i
s
t
so
off t
the
h
ec
cono
n
s
u
m
e
r
s
's
u
r
p
l
u
s，t
sumers'
surplus,
the
h
er
rent
e
n
to
offt
the
h
ed
domestic
o
m
e
s
t
i
cd
duopolist,
u
o
p
o
l
i
s
t，a
and
ndt
the
h
ed
domestic
o
m
e
s
t
i
cg
governo
v
e
r
n
m
entb
udgets
u
r
p
l
u
s
.
ment
budget
surplus.
(10.1)
== [
[U(XH)
- XHpH(XH)]
[XHHpH(XH)
-CH(QH)
+SQH]
)一
(
1
0
.1
) W(s)
W(s)=
U(XH)-X
HPH(XH)]+
+[
ぬHpH(XH)+XHFpF(X
+ XHFpF(X
CH(QH)+
SQHJ
F
F)
十
tXFH-SQH]
+ [
[tXFH-SQH]
(XH)-X
HHpH(XH)+
HFpF(XF)CH(QH)+
t
X
F
H・
- XHHpH(XH)
+X
XHFpF(XF)
-CH(QH)
+tXFH.
ニ
μ
=U(XH)
lOO
D
i
f
f
e
r
e
n
t
i
a
t
i
n
g W(s)
W(s) w
i
t
hr
e
s
p
e
c
tt
i
e
l
ds
l
)
Differentiating
with
respect
toos
s y
yields
)::
0
00.2)
0
.
2
) W'(s)
W'(s)=
= (
(PH-XFHPH'
PH -XFHPH'一
- C
cH')dxHH/
H')dxHH/d
ds+
s+(t(t-X
XFHpH')dxFH/
FHpH')dxFH/d
ds+
s+(
(pF+XHFPF'
pF十 X
H
F
P
F
'- C
CH')
H')
dXHF
/ /d
dss十
+X
XHFPF'
dXFF
/ d
dss+
+X
XFH
¢'
,
d
XHF
H
F
P
F
'd
XFF
/
FHゆ
+
=
= (-XHHpH'
(- X
HHPH'-S
s-X
- XFHpH')dxHH/
F
H
p
H
'
)dXHH/d
ds+
s (t(
t-X
XFHpH')dxFH/
F
ザ H
')dxFH/d
ds-sdxHF/
s-sdxHF/d
ds
s
+
+ φ'.
十
日F
P
F
'd
XFF
/d
s X
FH¢
+ XHFPF'
dXFF/
ds
XFH
T
The
heo
optimal
p
t
i
m
a
lr
rate
a
t
eo
offp
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
yS
sop
op a
and
ndt
the
h
ec
corresponding
o
r
r
e
s
p
o
n
d
i
n
go
optimal
p
t
i
m
a
li
imm
昨
9
9)) A
Assuming
ssumingt
that
h
a
t(
(1)
1
)l
labor
a
b
o
ri
isst
the
h
eo
only
n
l
yp
production
r
o
d
u
c
t
i
o
nf
factor.
a
c
t
o
r
.(
(2)
2
)l
labor
a
b
o
ri
issf
fully
u
l
l
ye
employed.
m
p
l
o
y
e
d
.(
(3)
3
)i
international
n
t
e
r
n
a
t
i
o
n
a
lp
payments
aymentsa
are
r
e
a
lwaysb
a
l
a
n
c
e
db
u
m
e
r
a
i
r
eg
oodZ
nd(
4
)o
n
eu
n
i
to
u
m
e
r
a
i
r
eg
oodi
r
o
d
u
c
e
db
n
eu
n
i
to
a
b
o
r
.w
a
n
always
balanced
byyn
numeraire
good
Z..a
and
(4)
one
unit
offn
numeraire
good
issp
produced
byyo
one
unit
offl
labor.
weec
can
e
x
p
r
e
s
st
h
es
o口 a
express
the
social
lu
utility
t
i
l
i
t
yl
level
e
v
e
lo
offc
country
o
u
n
t
r
yH
H a
assf
follows:
o
l
l
o
w
s
:
U=u(XH)U=u(XH)-XHPH+
XHPH+π
JrH+txFH+LH
H+txFH+LH
w
where
hereL
LH
Hr
represents
e
p
r
e
s
e
n
t
st
the
h
ee
endowment
ndowmento
offl
labor
a
b
o
ri
innc
country
o
u
n
t
r
yH
H.
.T
The
hef
first
i
r
s
tt
two
wot
terms
e
r
m
so
offt
the
h
eR
RHS
HSe
express
x
p
r
e
s
sc
consumers'
o
n
s
u
m
e
r
s
's
suru
r
plus
offc
country
H.. T
Thus,
hus，i
iffw
weea
assume
ssumet
the
h
ec
constancy
o
n
s
t
a
n
c
yo
offl
labor
a
b
o
re
endowment.
ndowment. a
a c
change
hange i
inn t
the
h
es
social
o
c
i
a
lu
utility
t
i
l
i
t
yl
level
e
v
e
li
inn
p
l
u
so
o
u
n
t
r
yH
country
H i
issf
fully
described
byy t
the
social
welfare
function
W.
c
o
u
n
t
r
yH
u
l
l
yd
e
s
c
r
i
b
e
db
h
es
o
c
i
a
lw
e
l
f
a
r
ef
u
n
c
t
i
o
n W.
N
Note
otea
also
l
s
ot
that
h
a
tt
this
h
i
sm
model
odelc
can
a
nb
beer
regarded
e
g
a
r
d
e
da
assa
a f
fully
u
l
l
yg
general
e
n
e
r
a
le
equilibrium
q
u
i
l
i
b
r
i
u
mm
model
odelw
with
i
t
hi
imperfectly
m
p
e
r
f
e
c
t
l
yc
competitive
o
m
p
e
t
i
t
i
v
eg
good.
o
o
d
.
o
n
c
ew
ssumet
h
e
r
ei
n
l
yo
n
ef
a
c
t
o
ro
r
o
d
u
c
t
i
o
ni
h
i
sm
odel
once
weea
assume
there
isso
only
one
factor
offp
production
innt
this
model.
1
0
)T
hel
a
s
te
q
u
a
l
i
t
yi
e
r
i
v
e
df
rom u
s
i
n
gt
h
ee
q
u
i
l
i
b
r
i
u
mc
o
n
d
i
t
i
o
n
s(
last
equality
issd
derived
from
using
the
equilibrium
conditions
(2.1)-(2.4).
2
.1
)-(2.
4
)
10)
The
国 際 協 力 論 集 第 6巻 第 2号
128
1
2
8
O
Pa
port
tariff
tOP
are
defined
byy
p
o
r
tt
a
r
i
f
ft
r
ed
e
f
i
n
e
db
(
11
) W'(soP)=0
P= φ(
and tO
s
O
P
).
I
Inno
order
rdert
tooe
establish
s
t
a
b
l
i
s
hw
whether
hethert
the
h
eo
optimal
p
t
i
m
a
lr
rate
a
t
eo
offp
production
r
o
d
u
c
t
i
o
ns
subsidy
u
b
s
i
d
yi
issp
positive
o
s
i
t
i
v
e
orrn
not
weem
must
investigate
the
sign
offW'(O).
W'(O). If
I
fW'(O»O
W'(O)>Ot
then
h
e
nt
the
h
eo
optimal
p
t
i
m
a
lr
rate
a
t
e
o
o
tw
usti
n
v
e
s
t
i
g
a
t
et
h
es
i
g
no
offp
production
subsidy
should
beep
positive.
I
fW'(O)<O
W'(O)<O t
then
h
e
ni
itt s
should
h
o
u
l
db
bee n
negae
g
a
o
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
ys
h
o
u
l
db
o
s
i
t
i
v
e
. If
I
fW'(O)
W'(O)=
=00t
then
h
e
nf
free
r
e
et
trade
r
a
d
ei
isst
the
h
eb
best
e
s
tp
policy.
o
l
i
c
y
.L
Let
e
tu
usse
examine
xaminet
the
h
es
sign
i
g
no
off
t
tive.
i
v
e
.If
W'(O).
W'(O).
S
Substituting
u
b
s
t
i
t
u
t
i
n
gs=t=O
s=t=O i
into
n
t
o(
(10.2)
10
.
2
)y
yields:
i
e
l
d
s
:
o'
'/pH'J
/
P
H
'
J
(12)
(
1
2
) W'(O)
W'(O)=
= -XHHPH'dxHH/
XHHPH'dxHH/d
dS-XFHpH'[dxHH/
S-XFHpH'[dxHH/d
ds+dxFH/
s+dxFH/dsds- ¢
+XHFPF'dxFF/
+XHFPF'dxFF/d
ds.
s
.
I
Innt
the
h
ea
above
bovee
equation,
q
u
a
t
i
o
n，t
the
h
ed
derivatives
e
r
i
v
a
t
i
v
e
sa
are
r
ee
evaluated
v
a
l
u
a
t
e
da
att s
s=t=O.
=t=O. T
The
he f
first
i
r
s
ta
and
nd
the
third
terms
offt
the
RHS
offe
equation
(12)
12
)a
are
r
ep
positive.
o
s
i
t
i
v
e
.T
Therefore,
h
e
r
e
f
o
r
e，i
ifft
the
h
es
sece
c
t
h
et
h
i
r
dt
ermso
h
eR
HSo
q
u
a
t
i
o
n(
o
ndt
ermo
h
eR
HSo
ond
term
offt
the
RHS
off (
(12)
12
)i
issn
not
o
tn
negative,
e
g
a
t
i
v
e，W'(O)
W'(O) i
issp
positive.
o
s
i
t
i
v
e
.T
The
hek
key
eyp
probr
o
b
lem
isst
the
sign
off [
[ ]
].
. If
I
f[
[ ]
] o
off (
(12)
1
2
)i
issp
positive,
o
s
i
t
i
v
e，t
then
h
e
nt
the
h
es
second
econdt
term
ermo
off
l
emi
h
es
i
g
no
the
RHS
off(
(12)
issa
also
positive.
Byyu
using
conditions
offC
C.l-C.4,
，
4
.w
weec
can
anp
prove
r
o
v
e
t
h
eR
HSo
1
2
)i
l
s
op
o
s
i
t
i
v
e
.B
s
i
n
gc
o
n
d
i
t
i
o
n
so
.1-C
t
h
a
ti
u
r
e
l
yp
o
s
i
t
i
v
e
.
that
itti
isss
surely
positive.
LEMMA
LEMMA 5
5:: Under
Under Conditions
Conditions G
G.I-C.4,
.I-C
，
4
.ザ
if h
hFH-2cF"
FH-2cF"豆
~O
oh
holds,
olds，t
then
hen
>0.
dXHH/ds+dxFH/ds
- ¢'/pH'
d
XHH/ds+dxFH/ds O'/pH' >0.
P
Proof:
r
o
o
f
:U
Using
sing (
(9.1)-(9.7)
9.
1)-(9.7) w
weec
can
and
derive
e
r
i
v
et
the
h
ef
following
o
l
l
o
w
i
n
ge
equation:
q
u
a
t
i
o
n
:
(
1
3
.1
) dXHH/ds+dxFH/ds-φ'/pH'=XHHS+ XFHs+ゆ'(XHHt+xFHt-1/pH').
F
From
rom(
(7.7)
7
.
7
)X
XHHs+
HHs+
XFHs=
XFHs=
XX
issp
positive.
o
s
i
t
i
v
e
.X
XHHt+
HHt+ X
XFHt-l/
F
H
t一 1/
P
PH'
H' c
can
anb
beer
represented
e
p
r
e
s
e
n
t
e
da
ass
H
si
Hs
follows:
f
o
l
l
o
w
s
:
11)
1
1
)N
Note
ote t
that
h
a
td
det(A)
e
t
(
A
)=
=hFHA
hFHA4
4 11+
+ (-cF")A
(
ーC
F
"
)
A4
43
3+
+(
(hFH+
h
F
H
+
P
PH'-cF")A
H
'
c
F
"
)
A4
44
4.・
I
International
n
t
e
r
n
a
t
i
o
n
a
lD
Dupoly
upolya
and
ndT
Trade
radeP
Policies
o
l
i
c
i
e
sU
Under
nderB
Budget
udgetC
Constraint
o
n
s
t
r
a
i
n
t
129
1
2
9
(
13
.
2
) XHH
t
+ XFHt-1/pH'=[l/pH'det(A)][pH'A41+pH'A44-det(A)].
If
I
fw
weee
expand
xpandt
the
h
ed
det(A)
et(A) b
byyt
the
h
el
last
a
s
tr
row,
ow，a
and
ndr
rearrange
earranget
the
h
ea
above
bovee
expression
x
p
r
e
s
s
i
o
n
l
l:
weeo
obtain
the
following
expressionll):
w
b
t
a
i
nt
h
ef
o
l
l
o
w
i
n
ge
x
p
r
e
s
s
i
o
nl
(
(13.3)
1
3
.
3
)P
pH'A4
H
'A411十
+pH'A4
pH'A44
4 -det(A)
det(A)=
= (
(PH'-hFH)A4
PH'-hFH)A411+CF"A4
+cF"A43
3 - (
(hFH-CF")A4
hFH-CF")A44
4
=
=-(hFH-2CF")(A4
一 (hFH-2cF")(A41
1+
+A4
A44
4)
)
+
十(
pH'
-2cF")A4
CF"(
A44
A4
3).
(PH'
-2CF")A
4 11-CF"
(A4
4 -A
43).
←
From
(8.7)
A4
4 11+
+A
A4
4 4
4 <0
<0,，a
and
from
Appendix
A.1
and
Appendix
A.4
A 4
4 11>0
>0
F
rom (
8
.
7
)A
nd f
rom A
ppendix A
.
1a
nd A
ppendix A
.4A
a
ndA
and
A4
4 4
4- A
A4
4 3
3<
<0.
0.We
We c
can
anc
conclude
o
n
c
l
u
d
et
that
h
a
tt
the
h
eL
LHS
HS o
off (
03.3)
13
.
3
)i
iss n
negative
e
g
a
t
i
v
ei
iff t
the
h
e
following
inequalities
holds:
f
o
l
l
o
w
i
n
gi
n
e
q
u
a
l
i
t
i
e
sh
o
l
d
s
:
(
14
)h
FH-2cF"=PH'+XFHPH"-2CF"豆o
.
Then
T
hen f
from
rom (
03.2)
13
.
2
)w
wee c
can
an e
easily
a
s
i
l
yc
check
heck t
that
h
a
tt
the
h
eL
LHS
HS o
off (
(13.2)
1
3
.
2
)i
iss p
positive.
o
s
i
t
i
v
e
.
Therefore,
the
LHS
off (
(13.1)
issp
positive
iff (
(4)
isss
satisfied.
(Q.E.DJ
T
h
e
r
e
f
o
r
e，t
h
eL
HSo
1
3
.1
)i
o
s
i
t
i
v
ei
14
)i
a
t
i
s
f
i
e
d
.(
Q
.E
.DJ
S
i
n
c
eP
H
'-2
C
F
"くof
rom C
.
3，i
H" i
o
tg
r
e
a
t
e
rt
han s
ome s
u
f
f
i
c
i
e
n
t
l
y
Since
pH'-2cF"<0
from
C.3,
iffP
PH"
iss n
not
greater
than
some
sufficiently
small
positive
number
(i.e.
PH"
~- [
[pH'
-2CF"J
/ X
XFH),
the
above
condition
isss
sats
m
a
l
lp
o
s
i
t
i
v
en
umberC
i.
e
.P
H"豆一
p
H
'2
C
F
"
]/
F
H
)，t
h
ea
bovec
o
n
d
i
t
i
o
ni
a
t
isfied.
Thus,
the
h
ec
condition
o
n
d
i
t
i
o
n(
(14)
1
4
)d
demands
emandst
that
h
a
tt
the
h
ei
inverse
n
v
e
r
s
ed
demand
emand f
function
u
n
c
t
i
o
no
off
i
s
f
i
e
d
.T
hus，t
c
ountryH
h
o
u
l
dn
otb
o
oc
oncavet
h
eo
ngm.
country
H s
should
not
beet
too
concave
toot
the
origin.
N
oww
avee
s
t
a
b
l
i
s
h
e
dt
h
ee
f
f
e
c
t
so
n
c
r
e
a
s
ei
h
ep
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
y
Now
weeh
have
established
the
effects
offa
anni
increase
innt
the
production
subsidy
f
rom0
from
0,，w
which
hichi
issf
financed
i
n
a
n
c
e
db
byyt
the
h
ec
corresponding
orrespondingi
increase
n
c
r
e
a
s
ei
innt
the
h
ei
import
mportt
tariff
a
r
i
f
fo
onn
t
h
en
a
t
i
o
n
a
lw
e
l
f
a
r
eo
h
ed
omesticc
o
u
n
t
r
y
. It
the
national
welfare
offt
the
domestic
country.
I
ti
improves
mprovesn
national
a
t
i
o
n
a
lw
welfare.
e
l
f
a
r
e
.
THEOREM
6:: I
Inn t
the
h
eC
case
αs
eo
offb
binding
i
n
d
i
n
gb
budget
udgetc
constraint,
onstr
αi
n
t，i
iffo
one
neα
additional
d
d
i
t
i
o
n
αlc
cono
n
T
HEOREM6
dition
(J4)
isss
satisfied,
an
increase
innt
the
J4
)i
αt
i
s
f
i
e
d
，α
nm
creαs
ei
h
ep
production
roductions
subsidy
ubsidyf
from
rom0
0 t
too s
some
ome
d
i
t
i
o
n(
positive
number,
，w
which
hichi
issf
financed
i
n
αncedb
byyt
the
h
ec
corresponding
orrespondingi
increase
n
c
r
eαs
ei
innt
the
h
ei
import
mport
p
o
s
i
t
i
v
en
umber
tariff
rate,
improves
mproves t
the
h
en
national
a
t
i
o
n
a
lw
welfare
e抑 r
eo
off t
the
h
ed
domestic
omestic c
country.
ount
乃人 T
Thus
hus t
the
h
e
t
a
r
i
f
fr
a
t
e，i
optimal
production
subsidy
rate
and
the
associated i
import
mportt
tariff
a
r
i
f
fr
rate
a
t
eα
are
r
ed
defiej
ふ
o
ptimalp
roductions
ubsidyr
αt
eα
ndt
h
eαssoc~αted
nitely
positive,
which
are
defined
inne
equation
(JJ
1)
.
n
i
t
e
l
yp
o
s
i
t
i
v
e，w
hichα
r
ed
e
f
i
n
e
di
qu
αt
i
o
n(
J
)
.
国 際 協 力 論 集 第 6巻 第 2号
130
1
3
0
5
5.
.C
Concluding
o
n
c
l
u
d
i
n
gR
Remarks
emarks
Inn t
this
paper
wee h
have
examined
the
characteristics
off t
the
international
I
h
i
sp
aper w
ave e
xamined t
h
ec
h
a
r
a
c
t
e
r
i
s
t
i
c
so
h
ei
n
t
e
r
n
a
t
i
o
n
a
l
duopolist
model
with
intra-industry
trade
offi
identical
product.
t
.T
The
he m
model
odel w
wee
d
u
o
p
o
l
i
s
tm
odelw
i
t
hi
n
t
r
a
i
n
d
u
s
t
r
yt
r
a
d
eo
d
e
n
t
i
c
a
lp
roduc
constructed
isst
the
most
general
and
realistic
one
innw
which
each
firm
has
h
have
avec
o
n
s
t
r
u
c
t
e
di
h
em
ostg
e
n
e
r
a
la
ndr
e
a
l
i
s
t
i
co
nei
hiche
achf
i
r
mh
as
decreasing
marginal
cost
curve
and
each
market
has
non-linear
inverse
ded
e
c
r
e
a
s
i
n
gm
arginal c
o
s
tc
u
r
v
ea
nd e
ach m
arket h
as n
o
n
l
i
n
e
a
ri
n
v
e
r
s
ed
e
mand
curve,
and
ndt
the
h
ep
policy
o
l
i
c
ym
maker
akers
should
h
o
u
l
db
bees
subject
u
b
j
e
c
tt
toob
budget
udgetc
constraint.
o
n
s
t
r
a
i
n
t
.We
We
m
andc
u
r
v
e，a
h
avei
n
v
e
s
t
i
g
a
t
et
h
a
ta
hangei
r
o
d
u
c
t
i
o
ns
u
b
s
i
d
ya
nda
mportt
a
r
i
f
fo
have
investigate
that
a c
change
inna
a p
production
subsidy
and
anni
import
tariff
onn
production
and
consumption
inn e
each
country
especially
inn t
the
case
that
the
p
r
o
d
u
c
t
i
o
na
nd c
onsumption i
ach c
o
u
n
t
r
ye
s
p
e
c
i
a
l
l
yi
h
ec
a
s
et
h
a
tt
h
e
two
policy
instruments
are
combined
with
budget
constraint.
.B
Byyt
these
h
e
s
ea
analyses
n
a
l
y
s
e
s
t
wop
o
l
i
c
yi
n
s
t
r
u
m
e
n
t
sa
r
ec
ombinedw
i
t
hb
udgetc
o
n
s
t
r
a
i
nt
weeh
have
extended
the
Krugman
(1984)
19
8
4
)a
analyses
n
a
l
y
s
e
sw
which
hichh
have
avee
examined
xaminedo
only
n
l
yt
the
h
e
w
avee
x
t
e
n
d
e
dt
h
eK
rugman (
effects
offa
anni
import
tariff
onne
each
firm's
supply
tooh
home
market
alone.
Assw
wee
e
f
f
e
c
t
so
mportt
a
r
i
f
fo
achf
irm'ss
upplyt
omem
arketa
l
o
n
e
.A
the
h
en
non-linearity
o
n
l
i
n
e
a
r
i
t
yo
offc
cost
o
s
tf
function
u
n
c
t
i
o
nm
means
eanst
that
h
a
td
domestic
o
m
e
s
t
i
c
have
mentioned
above,
h
avem
entioneda
bove，t
a
ndf
o
r
e
i
g
nm
arketsc
annotb
e
p
a
r
a
t
e
d，a
and
foreign
markets
cannot
bees
separated,
and
nds
soow
weem
must
uste
examine
xamineb
both
othm
marark
e
t
st
n
v
e
s
t
i
g
a
t
et
h
et
r
a
d
ep
o
l
i
c
ye
f
f
e
c
t
sf
u
l
l
ya
ndp
r
o
p
e
r
l
y
.
kets
tooi
investigate
the
trade
policy
effects
fully
and
properly.
We
l
s
oh
avee
xaminedt
h
ew
e
l
f
a
r
ee
f
f
e
c
t
so
r
a
d
ep
o
l
i
c
i
e
sw
hicha
r
ec
omWe a
also
have
examined
the
welfare
effects
offt
trade
policies
which
are
comb
i
n
e
dw
i
t
hb
udgetc
o
n
s
t
r
a
i
n
t
. We
aves
hownt
h
a
ta
m
a
l
lp
o
s
i
t
i
v
ep
r
o
d
u
c
t
i
o
n
bined
with
budget
constraint.
We h
have
shown
that
a s
small
positive
production
s
u
b
s
i
d
yw
hichi
i
n
a
n
c
e
db
o
r
r
e
s
p
o
n
d
i
n
gp
o
s
i
t
i
v
ei
mportt
a
r
i
f
fi
mprovest
h
e
subsidy
which
issf
financed
byyc
corresponding
positive
import
tariff
improves
the
n
a
t
i
o
n
a
lw
e
l
f
a
r
eo
h
ed
o
m
e
s
t
i
cc
ountryi
h
ei
n
v
e
r
s
ed
emandf
u
n
c
t
i
o
no
o
national
welfare
offt
the
domestic
country
ifft
the
inverse
demand
function
offd
dom
e
s
t
i
cm
arketi
o
tt
o
oc
oncavet
h
eo
r
i
g
i
n
.T
h
i
sr
e
s
u
l
ti
u
i
t
en
ewo
n
e
.O
mestic
market
issn
not
too
concave
toot
the
origin.
This
result
issq
quite
new
one.
Off
c
o
u
r
s
et
h
i
sr
e
s
u
l
ti
oreg
e
n
e
r
a
lt
hant
h
a
to
heng (
1
9
8
8
)a
ndD
i
x
i
t(
1
9
8
8
)
course
this
result
issm
more
general
than
that
offC
Cheng
(1988)
and
Dixit
(1988)
w
hichh
avea
ssumedt
h
ec
o
n
s
t
a
n
tm
arginalc
o
s
tc
u
r
v
e
s
.A
ndt
h
i
si
l
s
om
ore
which
have
assumed
the
constant
marginal
cost
curves.
And
this
issa
also
more
general
than
that
offO
Okamoto
and
Yoshida
(1991,
which
have
assumed
g
e
n
e
r
a
lt
hant
h
a
to
kamotoa
ndY
oshida (
19
9
1，1994)
1
9
9
4
)w
hich h
ave a
ssumed
t
h
a
tt
h
em
arginalc
o
s
tc
u
r
v
e
sa
r
en
o
n
c
o
n
s
t
a
n
tb
u
tt
h
ei
n
v
e
r
s
ed
emand f
u
n
c
that
the
marginal
cost
curves
are
non-constant
but
the
inverse
demand
funct
i
o
n
sa
r
el
i
n
e
ar
tions
are
linear.
.
R
References
e
f
e
r
e
n
c
e
s
J.E.Brander,
I
n
t
r
a
i
n
d
u
s
t
r
yT
Trade
rade i
inn I
Identical
d
e
n
t
i
c
a
lC
Commodities,"
ommodities，
" J
Journal
ourn
αl 0
of1
J
.
E
.
B
r
a
n
d
e
r，“"Intra-industry
I
n
t
e
r
n
International
αt
i
o
n
αlE
Economics,
conomics，V
VoLll
ol
.
11(
(1981)
19
81
)p
ppJ-14.
p.
11
4
.
J.E.Brander
and
P.Krugman,
“"A
A'
'Reciprocal-Dumping'
R
e
c
i
p
r
o
c
a
l
D
u
m
p
i
n
g
'M
Model
odelo
off I
International
n
t
e
r
n
a
t
i
o
n
a
l
J
.
E
.
B
r
a
n
d
e
ra
ndP
.Krugman，
Trade,"
Journal
of
International
Economics,
VoLl5
(1983)
pp.313-321.
"J
ourn
αl0
1I
n
t
e
r
n
αt
i
o
n
αlE
conomics，V
ol
.
15(
19
8
3
)p
p
.
3
1
3
3
21
.
T
rade，
J
J.A.Brander
.A
.Brandera
and
ndB
B.Spencer,
.
S
p
e
n
c
e
r，
“"Tariff
T
a
r
i
f
fP
Protection
r
o
t
e
c
t
i
o
na
and
ndI
Imperfect
m
p
e
r
f
e
c
tC
Competition,"
o
m
p
e
t
i
t
i
o
n，
"i
m:
n
:
d
.，M
Monopolistic
o
n
o
p
o
l
i
s
t
i
cC
Competition
o
m
p
e
t
i
t
i
o
nα
and
nd I
International
n
t
e
r
n
αt
i
o
n
αlT
Trade,
r
αd
e，
H
H.. K
Kierzkowski,
ierzkowski，e
ed.,
I
International
n
t
e
r
n
a
t
i
o
n
a
lD
Dupoly
upoly a
and
ndT
Trade
radeP
Policies
o
l
i
c
i
e
sU
Under
nderB
Budget
udgetC
Constraint
o
n
s
t
r
a
i
n
t
131
1
3
1
Oxford
University
Press,
pp.194-206.
O
xfordU
n
i
v
e
r
s
i
t
yP
r
e
s
s，1994a,
1
9
9
4
a，p
p
.
1
9
4
2
0
6
.
J
.A
J.A.Brander
.Brandera
and
ndB
B..S
Spencer,
pencer，
“"Trade
TradeW
Welfare:
e
l
f
a
r
e
:T
Tariffs
a
r
i
f
f
sa
and
ndC
Cartels,"
a
r
t
e
l
s，
"J
Journal
ournal0
oj1
I
n
t
e
r
n
International
αt
i
o
n
a
lE
Economics,
conomics，V
Vo1.16
o1
.
16(
(1984b)
19
8
4
b
)p
pp.227-242.
p
.
2
2
7
2
4
2
.
L
.K
L.KCheng,
.Cheng，
“"Assisting
A
s
s
i
s
t
i
n
gD
Domestic
omesticI
Industries
n
d
u
s
t
r
i
e
su
under
nderI
International
n
t
e
r
n
a
t
i
o
n
a
lO
Oligopoly:
l
i
g
o
p
o
l
y
:T
The
he
off t
the
Nature
offC
Competition
too O
Optimal
Policies,"
"A
American
meric
αn
R
Relevance
e
l
e
v
a
n
c
eo
h
eN
ature o
o
m
p
e
t
i
t
i
o
nt
ptimal P
o
l
i
c
i
e
s，
E
conomicR
e
v
i
e
l
Economic
Review,
ρ，V
Vo1.78
o.
17
8(
(1988)
19
8
8
)p
pp.746-758.
p
.
7
4
6
7
5
8
.
A.Dixit,
A
.D
i
x
i
t，
“"International
I
n
t
e
r
n
a
t
i
o
n
a
lT
Trade
rade P
Policies
o
l
i
c
i
e
sf
for
o
rO
Oligopolistic
l
i
g
o
p
o
l
i
s
t
i
cl
Industries,"
n
d
u
s
t
r
i
e
s，
"E
Economic
conomic
J
ourn
Journal,
αl
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8
4
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A
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.
D
i
x
i
t，
“"Anti-Dumping
Anti-Dumpinga
and
ndC
Countervailing
o
u
n
t
e
r
v
a
i
l
i
n
gD
Duties
u
t
i
e
su
under
nderO
Oligopoly,"
l
i
g
o
p
o
l
y，
"E
European
urope
αn
E
conomicR
e
v
i
eω，V
o.
13
2(
1
9
8
8
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p
.
5
5
6
8
.
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J.Eaton
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u
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t
r
i
a
lP
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o
l
i
c
yu
under
nder
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.
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a
t
o
na
nd G
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"Q
Quarterly
u
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r
l
yJ
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4
0
6
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O
l
i
g
o
p
o
l
y，
F.H.Hahn,
Stability
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the
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Review
of1
The S
t
a
b
i
l
i
t
yo
h
eC
ournot O
l
i
g
o
p
o
l
yS
o
l
u
t
i
o
n，
" R
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F
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conomicS
t
u
d
i
e
sV
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2(
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1
9
6
2
)p
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p
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9
3
31
.
K
KKrishna,
.Krishna，“"Trade
Trade R
Restrictions
e
s
t
r
i
c
t
i
o
n
s a
ass F
Facilitating
a
c
i
l
i
t
a
t
i
n
g P
Practices,"
r
a
c
t
i
c
e
s，
" J
Journal
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of1
I
n
t
e
r
n
International
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conomics，V
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6(
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8
9
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p
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5
1
2
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0
.
K
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.Krishna a
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.
It
ω
o
九
h
1， "Content Protection and Oligopolistic Interactions,"
R
Review
e
即m
印e
u
ω
.
u0
oj
1E
Economic
conomicS
Studies,
t
u
d
i
e
s，V
Vo1.55
o
.
15
5(
(1988)
1
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8
8
)p
pp.107-125.
p.
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1
2
5
.
P
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P.R.Krugman,
.Krugman，“"Import
lmport P
Protection
r
o
t
e
c
t
i
o
n a
ass E
Export
xport P
Promotion
romotion : I
International
n
t
e
r
n
a
t
i
o
n
a
l
C
o
m
p
e
t
i
t
i
o
ni
h
eP
r
e
s
e
n
c
eo
l
i
g
o
p
o
l
i
e
sa
ndE
conomieso
c
a
l
e，
Competition
innt
the
Presence
offO
Oligopolies
and
Economies
offS
Scale,"
"i
innH
H..
K
ierskowski， e
Kierskowski,
ed.,
d
.， M
Monopolistic
o
n
o
p
o
l
i
s
t
i
c C
Competition
o
m
p
e
t
i
t
i
o
n α
and
nd I
International
n
t
e
r
n
αt
i
o
n
αl T
Trade,
r
αd
e，
O
Oxford
xfordU
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n
i
v
e
r
s
i
t
yP
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r
e
s
s，1984,
1
9
8
4，p
pp.180-193.
p.
18
0
1
9
3
.
“"Matrices
M
a
t
r
i
c
e
sw
with
i
t
hD
Dominant
ominantD
Diagonals
i
a
g
o
n
a
l
sa
and
ndE
Economic
conomicT
Theory,"
heory，
"i
In
n
L
L.W.McKenzie,
.W.McKenzie，
K
KJ.
.J
.A
Arrow,
rrow，S
S..K
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a
r
l
i
n，a
and
ndP
P..S
Suppes,
uppes，e
eds.,
d
s
.，M
Mathematical
αthem
αt
i
c
a
lM
Methods
ethods i
inn t
the
h
e
S
o
c
i
αlS
c
i
e
n
c
e
s，S
Stanford
t
a
n
f
o
r
dU
University
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i
v
e
r
s
i
t
yP
Press,
r
e
s
s，1960,
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6
0，p
pp.47-62.
p
.
4
76
2
.
Social
Sciences,
巴
onvexS
Structures
t
r
u
c
t
u
r
e
sα
and
ndE
Economic
conomicT
Theory,
heory， A
Academic
cademicP
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r
e
s
s，1968.
1
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6
8
.
H
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N
i
k
a
i
d
o，C
Convex
H.Okamoto
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C.. Y
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A T
Three-Country
hree-Country M
Model
odel o
off T
Trade
rade U
Under
nder
H
.Okamoto a
nd C
oshida，“"A
I
m
p
e
r
f
e
c
tC
o
m
p
e
t
i
t
i
o
n
:D
e
c
r
e
a
s
i
n
gM
arginalC
o
s
t
sC
ase，
Imperfect
Competition:
Decreasing
Marginal
Costs
Case,"
" Working
WorkingP
Paper
I
α
:
p
e
r
#
# 118,
1
1
8，K
Kobe
obeU
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n
i
v
e
r
s
i
t
yo
offC
Commerce,
ommerce，1991.
1
9
91
.
H
H.Okamoto,
.Okamoto，“"International
I
n
t
e
r
n
a
t
i
o
n
a
l D
Duopoly
uopoly a
and
nd T
Trade
rade P
Policies
o
l
i
c
i
e
s U
Under
nder B
Budget
udget
Constraint:
Non-Linear
Cost
and
Demand
Functions,"
" Working
Working P
Paper
I
α
:
p
e
r
C
o
n
s
t
r
a
i
n
t
:N
on-Linear C
ost a
nd D
emand F
u
n
c
t
i
o
n
s，
#
# 140,
1
4
0，K
Kobe
obeU
University
n
i
v
e
r
s
i
t
yo
offC
Commerce,
ommerce，1994.
1
9
9
4
.
132
1
3
2
国際協力論集
第 6巻 第 2号
H
H.Okamoto
.Okamoto a
and
nd C
C.Yoshida,
.Yoshida，
“"Cournot
Cournot C
Competition,
o
m
p
e
t
i
t
i
o
n，I
Intra-Industry
n
t
r
a
I
n
d
u
s
t
r
yT
Trade
rade a
and
nd
N
on-Constancy o
arginal C
o
s
t
s
:A
Non-Constancy
off M
Marginal
Costs:
A T
Three-Country
hree-Country C
Case,"
ase，
"J
Journal
ourn
αl0
of1
Economics,
Vo1.60
o.
16
0(
(1994)
19
9
4
)p
pp.155-176.
p.
15
5
1
7
6
.
E
conomics，V
K
.Okuguchi，
“"Transport
Transport C
Cost
ost i
inn C
Cournot
ournot D
Duopoly
uopoly w
with
i
t
hS
Several
e
v
e
r
a
lM
Markets,"
arkets，
"
K.Okuguchi,
S
Studies
t
u
d
i
e
si
innR
Regional
egion
αlS
Science,
c
i
e
n
c
e，V
Vo1.20
o.
12
0(
(1990)
1
9
9
0
)p
pp.95-105.
p
.
9
5
1
0
5
.
Y
.Uekawa，
“"The
The R
Relevance
e
l
e
v
a
n
c
eo
off t
the
h
eN
Nature
ature o
offC
Competition
ompetition t
too O
Optimal
ptimal P
Polices
o
l
i
c
e
s
Y.Uekawa,
under
International
Oligopoly
and
Nonlinear
Cost
Functions
-AA G
General
u
nder I
n
t
e
r
n
a
t
i
o
n
a
lO
l
i
g
o
p
o
l
ya
nd N
o
n
l
i
n
e
a
rC
ost F
u
n
c
t
i
o
n
se
n
e
r
a
l
Bertrand
vs.
Cournot-,"
" D
Discussion
i
s
c
u
s
s
i
o
np
Paper
α
per #
#5
5,，
Equilibrium
Analysis:
E
q
u
i
l
i
b
r
i
u
mA
n
a
l
y
s
i
s
: B
ertrand v
s
. C
ournot-，
，
C
Chukyo
hukyoU
University,
n
i
v
e
r
s
i
t
y，1991.
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Y
Y.Uekawa,
.Uekawa，
“"Tariff
T
a
r
i
f
fP
Protection
r
o
t
e
c
t
i
o
nw
with
i
t
hI
Imperfect
m
p
e
r
f
e
c
tC
Competition
o
m
p
e
t
i
t
i
o
na
and
ndE
Existence
x
i
s
t
e
n
c
eo
offt
the
h
e
General
Equilibrium
Solution
with
Intra-Industry
Trade,"
"i
innM
M..B
Boldrin,
o
l
d
r
i
n，R
R..
G
eneralE
q
u
i
l
i
b
r
i
u
mS
o
l
u
t
i
o
nw
i
t
hI
n
t
r
a
I
n
d
u
s
t
r
yT
rade，
Becker,
R.W.
B
ecker，R
.W.J
Jones,
ones，a
and
ndW
W..T
Thompson,
hompson，e
eds.,
d
s
.，G
Genaral
e九α
r
αlE
Equilibrium,
q
u
i
l
i
b
r
i
u
m，G
Growth,
rowth
，
α
and
ndT
Trade,
r
αde，A
Academic
c
αdemicP
Press,
ress，1993,
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9
9
3，p
pp.541-554.
p
.
5
4
1
5
5
4
.
Y.Uekawa
and
H.Ohta,
“"Imperfect
I
m
p
e
r
f
e
c
tC
Competition
o
m
p
e
t
i
t
i
o
na
and
nd E
Existence
x
i
s
t
e
n
c
eo
offt
the
h
eG
General
e
n
e
r
a
l
Y
.Uekawaa
ndH
.Ohta，
Equilibrium
Solution
Under
Intra-Industry
Trade,"
innH
Herberg,
H.. a
and
N..
E
q
u
i
l
i
b
r
i
u
mS
o
l
u
t
i
o
nU
nderI
n
t
r
a
I
n
d
u
s
t
r
yT
rade，
"i
erberg，H
nd N
Van
Long,
eds.,
Trade
and
Economic
Policies,
University
off
V
an L
ong，e
d
s
.， T
r
αde Welfare,
Weσ
αr
e， α
nd E
conomic P
o
l
i
c
i
e
s，U
n
i
v
e
r
s
i
t
yo
M
ichigan，1993,
1
9
9
3，p
p
.
2
5
52
6
6
.
Michigan,
pp.255-266.
白
A.J.VenabIes,
A
.J
.
V
e
n
a
b
I
e
s，
“"Trade
Tradea
and
ndT
Trade
radeP
Policy
o
l
i
c
yw
with
i
t
hI
Imperfect
m
p
e
r
f
e
c
tC
Competition:
o
m
p
e
t
i
t
i
o
n
:T
The
heC
Case
ase
off I
Identical
Products
and
Free
Entry,"
Journal
of1 I
International
o
d
e
n
t
i
c
a
l P
roducts a
nd F
ree E
ntry，
" J
ourn
αl 0
n
t
e
r
n
αt
i
o
n
α
J
E
conomics，V
Economics,
Vo1.l9
o1
.
l9(
(1985)
19
8
5
)p
pp.1-19.
p.
11
9
.
A
ppendix
Appendix
I
Innt
this
h
i
sA
Appendix
ppendixw
wees
shall
h
a
l
ls
show
how (
(1)
1
)t
the
h
ee
expressions
x
p
r
e
s
s
i
o
n
sa
and
ndt
the
h
es
SIgn
i
g
no
offA
Au's,
'
us，(
(2)
2
)
t
the
h
ep
proof
roofo
offe
equation
q
u
a
t
i
o
n(
(7.4),
7.
4
)
， (
(3)
3
)t
the
h
ep
proof
roofo
offe
equations
q
u
a
t
i
o
n
s(
(7.7)
7
.
7
)a
and
nd(
(7.8),
7
.
8
)，(
(4)
4
)t
the
h
e
offe
equations
(8.7)
and
(8.8),
and
nd (
(5)
5
)t
the
h
ep
proof
roofo
offA
A4
444- A
A4
433く
<0.
O
.
d
derivation
e
r
i
v
a
t
i
o
no
q
u
a
t
i
o
n
s(
8
.
7
)a
nd (
8
.
8
)，a
A
A.l
.lT
The
hes
signs
i
g
n
so
offA
Ai/s
i
/
S
Innt
this
sub-section
wees
shall
show
the
expressions
and
signs
offt
the
cofactor
off
I
h
i
ss
u
b
s
e
c
t
i
o
nw
h
a
l
ls
howt
h
ee
x
p
r
e
s
s
i
o
n
sa
nds
i
g
n
so
h
ec
o
f
a
c
t
o
ro
matrix
A.. S
Since
i
n
c
em
matrix
atrixA
A i
issa
annN
N -P
- P m
matrix,
atrix，w
wee c
can
an i
immediately
m
m
e
d
i
a
t
e
l
yo
obtain
b
t
a
i
nt
the
h
e
m
atrixA
results:
f
following
o
l
l
o
w
i
n
gr
e
s
u
l
t
s
:
det(A»O,
A'i<Oo(
(jj =
=1,
1
，
…
...
，, 4
4).
)
.
d
et(A)>O， んく
I
International
n
t
e
r
n
a
t
i
o
n
a
lD
Dupoly
upolya
and
ndT
Trade
radeP
Policies
o
l
i
c
i
e
sU
Under
nderB
Budget
udgetC
Constraint
o
n
s
t
r
a
i
n
t
133
1
3
3
U
Using
singt
the
h
et
technique
e
c
h
n
i
q
u
eo
offd
dominant
ominantd
diagonal
i
a
g
o
n
a
lm
matrix,
atrix，w
weec
can
and
determine
eterminet
the
h
es
signs
i
g
n
s
o
v
e
r
yo
t
h
e
rc
o
f
a
c
t
o
r
so
o
l
l
o
w
s
:
offe
every
other
cofactors
offA
A a
assf
follows:
I
A21=￨CH1FF+pj-CF"
A2 I = cH"hFF+PF'-CF"
cF"hHHhFF壬0，
II++cF"hHHhFF~O,
ー
CF"
-CF"
￨ 一
CF"flFH+pd-cF"￨
-CF"
hFH+PH'-CF"
II
A41
=ー CH"CF"hHF-hHH h
HF十P
F
'一 CF"
A41 =-CH"CF"hHF-hHH
hHF+PF'-CF"
+cF"hF品
H
II+CF"hFHhHF
〆
，
一 〆"一
C〆
F
-CF"
A
正
" 1
附 +PF CF
All2
2 =CH
=CH"
hFF+PF'-CF"
-CF"
￨ 一
CF"
1>0，
hFF+PF'-CF"
h
FF+PF'-CF" I
hFF
h
FF
II
1>0,
h
HF
hHF
加 f
~O,
hFH+PH'-CF"
h
FH+PH'一 CF" ￨
I
A4
A4 2
2=
= -CF"
-CF" h
hHF(hHH+PH'-CH")
HF(hHH+PH'-CH")-CH"
-CH" h
hHH(hFF+PF'-CF")
HH(hFF十PF'-CF")孟
~O,
0，
A
Al13
3=
= -CH"
-CH" h
hFF(hFH+PH'
FF(hFH+PH'-CF")
CF")-CF"
CF"h
hFH(hHF+PF'-CH")
FH(hHF+PF'-CH")孟
~O,
0，
A
23
hF
h
HH+PH'一 C H " h H hHH
H￨-CH
" C F 1 F H > O，
F II
F
A2
3=
= -hF
hHH+PH'-CH"
I-CH"CF"hFH>O,
h
hFH+PH-CF"
FH十 PH一 CF" I
h
hFH
FH
A4
=cH"hHHhFF+CF" II
h
J
IH+PH'一 CH"
A4 3
3 =cH"hHHhFF+CF"
hHH+PH'-CH"
-CH
-CH"
I
C H " ￨孟
0，
-CH"
~O,
h
hHF+PF'-CH"
HF十 PF'-CH"
A
14=-CH"CF"hFF-hFH
= -CH"CF"hFF-hFHI
I
h
HF十PF'-CF"
A14
hHF+PF'-CF"
1>0,
hHF
h
HF
1>0，
hFF+
PF'
- C
CF"
h
FF+P
F'ー
F" I
h
FF
hFF
A
A24
24=
= 一
-CF"
CF"h
hFF(hHH+PH'
FF(hHH+PH'-CH")
CH")-CH"
-CH" h
hFH(hFF+PF'-CF")
FH(hFF+P
F
'-CF")詮
~O,
0，
A
A.2
.2 T
The
he p
proof
r
o
o
fo
offe
equation
q
u
a
t
i
o
n(
(7.4)
7
.
4
)
B
Byyu
using
s
i
n
gt
the
h
ee
elementary
lementaryp
properties
r
o
p
e
r
t
i
e
so
offd
determinant,
eterminant，w
weec
can
and
derive
e
r
i
v
et
the
h
ef
following
o
l
l
o
w
i
n
g
e
quatlOn
:
equation:
。
A
14+A44=
A14+A44=
PH'一 CH" -CH"
- CH"
hHF+P
F
'一 CH"
hF
F
CF"
C
F
PH'-CH"
p
H一 CH
hHF
-CH"
-CH"
hFF+pF'一 CF"
CF"
。
o
-CH"
-CH
PF'
-CH"
P
F
'-CH"
F
'+ CF"
-P
hHF
hF
F
'-CF"
F+P
つ
=
(hFF+
PF'
-CF")
[(pH'
-CH")
(PF'
-CH")
- (
(CH")2]
=(
hFF+P
F
'CF")[
(
p
H
'一
CH (
PF
'一
CH")一
CH")
2
J
十
+hHF[(PH'
hHF[(pH'
-CH")
-CH")
(PF'
(pF-CF")
'-CF")
-CH"
-CH CF"]
F"]
つ
つ
]
=(
(hFF+
PF'
-CF")
(1/2)
[pH'(PF'
-2CH")
+P
pF'(pH'
-2CH")]
=
九FF+P
F'一
CF (
1/2)[
p
H
'(
PF'
-2cH")+
F'(pH'
-2cH
+
C
1
+P
PF'
(pH'
- 22CH")].
つ+
F
'
(
p
H
'CH")J.
hHFCl/2)
[pH'
(PF'
- 2
2CF")
十h
HF /2)[
p
H
'(
PF
'CF
T
Thus
husw
weeo
obtain
b
t
a
i
ne
equation
q
u
a
t
i
o
n(
(7.4).
7.
4
)
.(
(Q.E.DJ
Q
.E
.DJ
国 際 協 力 論 集 第 6巻 第 2号
134
1
3
4
A
A.3
.3T
The
hep
proof
r
o
o
fo
of
fe
equations
q
u
a
t
i
o
n
s(
(7.7)
7
.7
)a
and
nd (
(7.8)
7
.
8
)
F
i
r
s
t，w
e
r
i
v
et
h
ee
x
p
r
e
s
s
i
o
nf
o
r(A
(A1111+
1)+
(A114
h
ed
e
f
i
First,
weed
derive
the
expression
for
+A
A2
2 1)
+ (A
4+
+A
A 24)
24) 三
== α
a..B
Byyt
the
defioffc
cofactor,
weeo
obtain
b
t
a
i
nt
the
h
ef
following
o
l
l
o
w
i
n
ge
equation:
q
u
a
t
i
o
n
:
n
i
t
i
o
no
o
f
a
c
t
o
r，w
nition
α IhHF+PF'
hHF
-hHH
h
FF h
FF+PF'-CF" hFF
hFF+PF'-CF"
-CF"
CF"
o
o
十
-CF"
hFH+PH'-CF"
CF" h
FH+PH'一 C
F
"
。
IhHH十 PH'
一 (hHF+
p
F
'
)
。
o
hFF十 PF'-CF"
hFF
hFH
hHF+P
F
'
-hHF
-CF"
CF
hHH
hHF
hHF+PF'
hHF
。
-hHH-PH'
。
Fh
nFF
TPF-C
F -C
F
FF h
hFF+
FF十 P
PF'
F'
--C
CF"
F"
hFF
0
hF
+
￨h
-CF
"
o
-CF" hFH+PH'-CF"
0
o
C
F"
h
hFH
FH
hHF十 P
F
'
。
o
hFF
，
hHF
，
,
h
hHF+PF
HF+PF
PH
CF"
hFF+PF'-CF" C
F"
一
-CF"
h
hFF
FF
O
0
PH'-CF"
P
H'-CF
hHF十 PH'
-hHF+PH'
,，
- hFF-PF'
FF-P
F
'-PH
- PH'
h
FF+PF -h
hFF+PF
h
hHF
HF
-CF"
CF"
PH'
P
H
F
"II
h
HF+P
F
' P
H'+
F
' II
=
H'[
(hHF+p
F
'
)(hFF+
(hFF+p
F
'
)-h
H
F
h
F
F
]+
=P
PH'
[(hHF+
pF')
pF')
- hHFhFFJ
+C
CF"
hHF+
PF'
PH:
+P
PF',
I
h
hFF
FF
-PF
PF'-PH
PH' I
=
H'pF'(
hHF十九
FF+p
F
'
)F
"(
PH'+
F
'
)(
hHF+h
FF+p
F
'
)
=P
PH'PF'
(hHF+
hFF+
pF')
- C
CF"
(PH'
+p
pF')
(hHF+
hFF+
pF')
=
hHF十 h
= (
(hHF+
hFF+
FF+p
pF')
F
'
)[
[pH'pF'
p
H
'
p
F
'-C
CF"
F"(
(pH'
p
H
'+P
pF')
F')]
J
= (
(hHF+
hFF+
pF')
0/2)
/2)[
[pH'
p
H
'(
(PF'
PF
'-2
- 2CF")
C
F
"
)+
+P
PF'
F
'(
(pH'
p
H
'- 2
2CF")
C
F
"
)
]
J..
=
hHF+h
FF+p
F
'
)0
I
h
ea
bovee
x
p
r
e
s
s
i
o
n，t
Innt
the
above
expression,
the
h
ef
first
i
r
s
te
equality
q
u
a
l
i
t
yi
issd
derived
e
r
i
v
e
df
from
romc
calculating
a
l
c
u
l
a
t
i
n
g (A
(A1111+
+
A
A2
21
1)
)十
+ (A
(A114
4+
+A
A 24)
24) b
byyu
using
s
i
n
gd
definition
e
f
i
n
i
t
i
o
no
offc
cofactor.
o
f
a
c
t
o
r
.T
The
hee
ensuing
n
s
u
i
n
ge
equalities
q
u
a
l
i
t
i
e
sa
are
r
e
derived
from
elementary
properties
offd
determinant.
d
e
r
i
v
e
df
rome
lementaryp
r
o
p
e
r
t
i
e
so
e
t
e
r
m
i
n
a
n
t
.
N
ext，w
Next,
weed
derive
e
r
i
v
et
the
h
ee
expression
x
p
r
e
s
s
i
o
nf
for
o
r (A
(A112
2 +
+A
A 22)
22) +
+ (A
(A113
3 +
+A
A 23)
23) 三
== β
[3.
.U
Using
sing
the
same
technique
innt
the
above,
weeh
have
avet
the
h
ef
following:
o
l
l
o
w
i
n
g
:
t
h
es
amet
e
c
h
n
i
q
u
ei
h
ea
bove，w
β =I
hHH十 PH'
。
-hHF
hHH
一C
F"
hFF+P
F
'-C
F
"
hFH
-I
hHH+pH'
。
hFH
-CF"
hFH+PH'-C
F
"
一(hHF+PF')
。
hFF
hHH
-CF"
hFH+P
正一 C
F
"
J
International
n
t
e
r
n
a
t
i
o
n
a
JD
Dupoly
upolya
and
ndT
Trade
radeP
Policies
o
l
i
c
i
e
sU
Under
nderB
Budget
udgetC
Constraint
o
n
s
t
r
a
i
n
t
hHH+
PH'
o
P
F
'
hHH
P
F
'一 CF"
hFH
hHH十 PH'
o
-CF
hF
H+PH'-CF"
一 CF"
135
1
3
5
P
F
'
-PH'
PF'-CF"
hFH
-CF"
-Cp
PH'-CF
つ
=
= (
(hHH+
hHH+p
pH')
H')[
[CpF'
(
PF
'- C
CF")
P (
CpH'
pH'
--C
CF")
F")一
- (
(CF")2]
CF")2]+
+h
hFH
FH[
[pH'
p
H
'(pF'
(
p
F
'- C
CF")
F")- p
PF'
p
'C
CF"]
F"]
つ
十
=
(hHH+ h
FH+p
H')(
1/2)[
p
H
'(pF'
(
p
F
'2CF +P
F'(
PH'-2cF")].
= (hHH+
hFH+
pH')
(1/2)
[pH'
-2CF")
PF'CpH'-2cF")].
A
A.4
.4T
The
hep
proof
r
o
o
fo
of
fe
equations
q
u
a
t
i
o
n
s(
(8.7)
8
.
7
)a
and
nd (
(8.8)
8
.8
)
F
i
r
s
t，w
First,
weed
derive
e
r
i
v
et
the
h
ee
expression
x
p
r
e
s
s
i
o
nf
for
o
rA
A4
4 11十
+A
A4
44.
4 B
Byyt
the
h
ed
definition
e
f
i
n
i
t
i
o
no
offc
cofactor,
o
f
a
c
t
o
r，w
wee
・
C
CH
H"
0
h
hFF
FP
O
0
hFF+
PF'
- C
CF"
F"
h
PF+P
F'一
"
-CF
CF"
HH十P
H'--C
F"
hHH+
PH'
CF"
+ Ih
。
。
ー
CH"
"
-CH
-CH"
-CH "
0
h
HF+pF'-CH"
hHF+pF'-CH"
h
hFF
FF
。
-CH
-CH "
"
"
P
PF'-CH
F-CH"
0
" h
h
hHF+pF'-CH
HF+pF'一 CH"
hHF
HF
"
C
CF
F"
h
FH
hFH
hFF+
PF'
--C
CF"
F'
F"
h
FF十 P
h
hFF
FP
0
"
一
-CH
ー CH"
。
一
-CH
CH"
"
十
PFF
P
hHH
h
hHF
HF
h
HF十 PF'-CH"
hHF+PF'-CH"
，
,
H
H
A41+A44=A41+A44=
一
h
。
o
b
t
a
i
nt
h
ef
o
l
l
o
w
i
n
ge
q
u
a
t
i
o
n
:
obtain
the
following
equation:
P
PFF-CH
-CH "
一
ー CH"
-CH
"
"
h
FF十 PP'-Cp"
hFF+PF'-CF
0
,
h
hHF
HF
-P
〆-CF"
-PF'-CF
" h
hFF+
FF十 P
PF'
F'
--C
CF"
F"
C
F"
"
CF
=
= (hFF+
(
h
F
F十 P
PF'CF"F+)
F'CF"F+)[
[(pH'
(
p
H
'- C
CH")
H")(
CpF'
PF
'-CH")
-CH") - (
(CH'')2]
CH''
)
2
]
+hHF[CpH'
+hHF[(
PH
'-CH")
-CH") (pF'
(
p
F
'-CF")
CF")-CH"
-CH" C
CF"J.
F"].
N
Next,
ext，w
weed
derive
e
r
i
v
et
the
h
ee
expression
x
p
r
e
s
s
i
o
nf
for
o
rA
A4
4 2
2 十
+A
A4
43.
3. U
Using
s
i
n
gt
the
h
es
same
amet
technique
e
c
h
n
i
q
u
ei
inn
o
o
hHF
-CH"
CH
hHH+pd-CH"-CF"
hHH+pH'-CH"
-CF"
-CH"
-CH"
0
-PF'-CH"
-PF'-CH "
PI
P
-ャ
。
-CH"
-CH "
hFF
。
h
hHH
HH
0
-CF "
" -CF"
P
F'-CF"
PF'-CF
。
o
PF
h
hHF+PF'-CH"
HF+PF'-CH"
o
-CH "
h
HH十PH'-CH"
" -CH
"
hHH+PH'-CH
F
hFF十 PF'-CF"
C
- l
。
o
H
A42+A43= I
hHH+PH'-CH"
。
o
'
nH
avet
the
h
ef
following:
o
l
l
o
w
i
n
g
:
t
the
h
ea
above,
bove，w
weeh
have
-CH "
" -CH"
PH'-CH
PH'-CH "
-CH'
-CH "
"
-PF'-CH
-PF'-CH "
-CF "
-CF
"
"
P
PF'-CF
F'-CF"
。
h
hHH
HH
0
CF"
-CF
"
国際協力論集
136
1
3
6
=
I
hHH(
PF'-CF")(CF"-CH")
第 6巻 第 2号
づ(pF'一 CFつ-CH"CF"].
+CF"[
(
P
F
'一 CH
A.5 T
The
hep
proof
r
o
o
fo
of
fA
A444
4-A4
A 43
3<0
くO
A.5
Let
ussd
define
det(D)
=A
A44-A43
44 - A 43.・ T
Then
henf
from
romt
the
h
ed
definition
e
f
i
n
i
t
i
o
no
offc
cofactors,
o
f
a
c
t
o
r
s，w
weec
can
an
L
e
tu
e
f
i
n
ed
et(D)三
derive
the
following
expression:
d
e
r
i
v
et
h
ef
o
l
l
o
w
i
n
ge
x
p
r
e
s
s
i
o
n
:
det(D)=A44-A
= I
hHH+PH'-CH"
h
HH+PH'-CH"
d
e
t
(
D
)三 A44-A4
433=
-CH"
-CH"
o
o
hHH
h
HH
-CH"
-CH"
h
hHF+PF'-CH"
HF十 PF'-CH"
h
hFF
FF
h
hHF
HF
h
hFF+PF'-2cF"
FF+PF'-2cF"
F
From
roma
above
bovee
equation,
q
u
a
t
i
o
n，i
itti
isso
obvious
b
v
i
o
u
st
that
h
a
ta
all
l
lt
the
h
ed
diagonal
i
a
g
o
n
a
le
elements
l
e
m
e
n
t
so
of
fm
matrix
atrixD
D
a
are
r
en
negative.
e
g
a
t
i
v
e
.F
Furthermore
urthermore t
they
h
e
ya
are
r
et
the
h
ed
dominant
ominant e
elements
l
e
m
e
n
t
si
In
ne
every
v
e
r
yr
row.
ow.
B
ecausef
o
l
l
o
w
i
n
gi
n
e
q
u
a
l
i
t
i
e
sh
o
l
d
:
Because
following
inequalities
hold:
II
hHH+PH'-CH"
- II-CH"
-CH" I
- II
hHH
=-(pH'-2cH"»0,
h
HH+PH'-CH" II
一
I一
h
HHI1
=一 (pH'-2cHつ
>
0，
II
h
hHF+PF'-CH"
HF+PF'一 CH" II
一￨一
- I -CH"
CH"￨
I一
- II
h
hHF
HFI1
==一
- (pF'-2cH"»0,
(
PF
'- 2CH")>
0，
II
hFF+
PF'
2CF"
- II
hFF
=
- (
(PF'
--2
2CF")
>0.
h
FF+P
F'--2
cF" II
一
h
FFI1
=一
pF'
cFつ
>
0
.
T
Thus
husm
matrix
atrixD
D h
has
asn
negatively
e
g
a
t
i
v
e
l
yd
dominant
ominantd
diagonals
i
a
g
o
n
a
l
sa
and
nds
sooi
itti
issa
a N
N -P
- P m
matrix.
a
t
r
i
x
.
T
herefored
e
t
(
D
)三
Therefore
det(D)
=A
A44
44 - A
A 43
43 m
must
ustb
been
negative.
e
g
a
t
i
v
e
.(
(Q.E.D.)
Q
.E
.D
.
)