Otemo?i Economic
Export
15
Studies, 38（2005）
Subsidies and Retaliation under
Conditions
of Variable Marginal
Masayuki
Costs＊
Hayashibara
Abstract
Can domestic retaliation deter foreign export subsidies? We investigate this
issue using the model of a three-stage trade policy game
developed in particular by
Dixit（1988）and Collie（1991）. The foreign government
sets an export subsidy at
stage one, and at stage two the home
government
subsidy and a tariff.At stage three,one home
in the domestic
market in a Cournot
firm and one foreign firm compete
fashion. Related results regarding
subsidies and tariffssuggest that domestic
subsidies. However,
responds with a production
export
retaliation can deter foreign export
as Qiu （1995）emphases,
the co-existence of export subsidies
and countervailing tariffsis observed quite often. Therefore, to show
an eχample
of the co-eχistenceof an eχport subsidy and a countervailing tariff,we modify a
model
of three-stage trade policy game, allowing variable marginal costs of pro-
duction.
Then
we can show
that, though
the home
government
responds
increase in foreign export subsidies bv increasing its tariffsand
production
subsidies, the overall protection that is defined as the sum
and a production
subsidy may
to an
reducing its
of a tariff
be increasing or decreasing in the foreign export
subsidy. If the foreign eχport subsidy can reduce the overall protection, then, in
fact,the foreign government
Key Words:
should set a positive subsidy.
strategic Trade Policy,Export subsidy, Tariff,Retaliation,Decreasing
costs
TEL Classification Numbers
: F 12, F13
1
Can
domestic
Introduction
retaliation deter foreign export subsidies? We
investigate this
issue using the model 0f a three-stage trade policy game, developed in particular by
Dixit (1988)and
Collie(1991). In the setup of the model, the foreign government
an export subsidy at stage one, and at stage two the home
government
This is a revised version of chapter 10 in Hayashibara （2005）.
（1）
sets
responds with
16 Masayuki HAYASHIBARA
a production
compete
subsidy
and a tariff. At stage three. one home
in the domestic
Before presenting
results
regarding
market
our basic model,
export
oligopolistic, a foreign
retaliate, and
demand
governments
sets a production
subsidy
game.
Collie（1991）shows
gain
uses a tariff and
export
and
subsidy
subsidy
faced
non-linear
from
such
demand
the model
subsidy,
country
pursues
subsidy.
government
sets a
a foreign
trade policy
an optimal
foreign
response
the optimal
trade policy、
response
country
to a foreign
its production
eχport subsidy
（c）If the domestic
is a less than
product
the domestic
domestic
and
both
oligopoly
firms, then
（b）When
the optimum
the optimal
domestic
firms
not
that the home
of a three-stage
to increase its tariff and to reduce
such a response,
does
where
Besides, in a Cournot
that of domestic
but zero for linear demand,
onb' a tariff, the optimum
and faced with
the domestic
a response,
of domestic
equilibrium,
the foreign
case.
is Cournot
country
be shown
related
results in the case of a homogeneous
a foreign export
is generally
that
move
tariff and
consider
three main
a production
with
and
some
an industry
stage, it can
duopoly
is positive. （3）Next,
it will always
tariffs. （1）When
a simultaneous
in a Cournot
oligopoly, （a）When
to briefly summarize
is positive, if the domestic
of foreign firms is less than
export
Cournot
need
firms is less than
（2）In
firm and one foreign firm
fashion.
policy levels at the same
positive eχport subsidy
case, if the number
and
of foreign
too conveχ.
choose
government
subsidies
we
eχport subsidy
the number
is not
in a Cournot
subsidy,
is positive for
country
can use
fully countervailing
foreign eχpoi-tpolicy is usually
tariff,
an eχport
tax. Collie（1994b）shows
that, in the case of a differentiated
product
linear demand
Cournot
the domestic
optimal
trade
cannot
oligopoly,
to a foreign
production
foreign
when
be harmed
export
subsidy.
subsidy
When
is generally
the foreign
pursues
and
to increase
country
an
the optimum
domestic
its tariff and
faces such
policy it
response
to reduce
a response,
its
the optimal
policy is an eχport taχ.
These results suggest
sidies. However,
countervailing
example
modify
country
by a foreign eχport subsidy,
that
tariffs is observed
of the co-eχistence
the model
costs of production.
to an increase
domestic
retaliation
as Qiu （1995）emphases,
Then
quite
trade
we can show
in the foreign
often.
policy
and
game,
that, though
subsidy,
the overall protection
production
subsidy
may
that is defined
or decreasing
（2）
foreign
of export
in
export
sub-
subsidies
and
to show
an
order
a countervailing
allowing
the home
eχport subsidy' bv increasing
production
be increasing
deter
Therefore,
of an eχport subsidy
of a three-stage
can
the co-existence
variable
government
tariff, we
marginal
responds
its tariff and reducing
as the sum
of a tariff and
in the foreign eχport subsidy.
its
a
If
EXPORT
SUBSIDIES
AND
RETALIATION
the foreign eχport subsidy
government
should
subsid}^ increases
export
foreign
subsidy
The remainder
is presented.
Section
costs are constant
dependent
on
is zero. as shown
national
and provides
welfare
our main
the other
MARGINAL
COSTS 17
hand, if the foreign eχport
the foreign
and
government
the demand
export
should
is linear, then
subsidy,
therefore,
set an
the overall
the optimal
by Collie（1991）｡
of this paper is organized
3 deals with
policy moves,
0n
a foreign
In particular, we derive
OF VARIABLE
the overall protection, then, in fact, the foreign
the overall protection, then
is not
export
can reduce
CONDITIONS
set a positive subsidy.
tax. If marginal
protection
UNDER
as follows : In section 2, a basic model
policy reaction
under
functions
an eχogenously
proposition.
Section
by two governments.
determined
4 provides
sequence
a summary
of
and
conclusion.
2.
We consider a two-country
compete
in the domestic
maximizes
Basic
model in which one home
market
in a Cournot
national welfare through
foreign government
model
maximizes
firm and one foreign firm
fashion.
a production
The
subsidy
and
home
government
a tariff,and the
national welfare （net profit）through
an eχport
subsidy.
Thegame
considered here has three stages, as follows:
Stage1 : The foreign government
Stage2 : The home
government
sets its eχport subsidy
sets its production subsidy and tar廿f
Stage3 : Firms choose outputs in a Cournot
Thesub-game
fashion.
perfect equilibrium is obtained by a process of backward
indue-
tion.
2.1 Demand
The home
for goods
country's household
utility function び(Q, z)is
strictly concave in terms of the total consumption
shown
differentiable and
of the homogenous
good
Q, as
by:
U(Q,z)＝aQ一半十z
where z denotes consumption
for utilitymaximization
＝u(Q)十z,
of the numeraire
0くa, b
good. From
the first-ordercondition
by a household, we obtain a linear inverse demand
p＝a−bQ，
（3）
function :
18 Masayuki HAYASHIBARA
wher印stands
for the product price and p＝du(Q)/dQ
holds. Defining the consumer
surplus as CS こUー(pQ十z)，substitution obtains CS ＝bQソ2＞0.
2｡2 Production
Considerthe third stage of the game.
the home
Taking the governments'
policiesas given,
firm and the foreign firm produce χ and y，respectively. Thus
holds. Let TC:c and TCy be the total costs of the home
Q＝x十y
firm and the foreign firm,
respectively. The gross profit of each firm is:
恥=px−TC,十sx,
and r*=ﾆPy−ア口一砂十ey,
where s and l denote a specific production subsidy to a home
imports levied by the home
government,
firm, and a tariffon
and 召denotes an eχportsubsidy to a foreign
firm provided by the foreign government.
Further, we specify the totalcost TCj of
firm ブas:
（1）TC,＝c,^x十
Crtズ''^
-
where Cxi＞0 and らi＞0.From
and TC,＝らiy十孚
the total cost functions, we can obtain the marginal
cost function for each firm as,
(2)MCχ＝Cxi十Cユ and MCy
Under
Cournot competition, assuming
(the reaction function)for
＝Cyi十らzy，
an interior solution, the firstorder condition
the profit maximization
(3)等＝ター訂C,十s一bx
by each firm will be :
= 0, and言刻）一MCy一Z十e一by＝O
The second order conditions. 2b十Ci'＞0 and 2b十ら2＞0，must hold. By solving the
equations in（3）for Cournot-Nash
x(s, y，e)＝
y(s,れ2)＝
where Do
Assume
(α−2ct
outputs, we obtain:
+2s十t
e)b十(a
−Cx＼十s)
仙
(a ＋c,i−
1−O −LjI十2e)b十(a−Cx＼−i一十〇Cr2
炳
＝3b- ＋2b(c,,十ら2)十Cx2ら,2.
that
（4）
EXPORT
SUBSIDIES AND RETALIATION
UNDER
CONDITIONS
OF VARIABLE
MARGINAL
COSTS 19
(4)卿(Cx2)＝-ﾂ宍万万万万ﾔ＜ら2，
then ￡o＞0 holds. The price of the product is shown
as :
p(s.いう
(a＋G1＋
-
炳
In this setup of the model, we can obtain the relation,
πニ(か十午)x"，and 7Z* =(b十午)ソ
Theabove results summarize
the output and price at the third stage in terms of
policy variables.
The comparative
static effects of a subsidy
ferentiatingバs, t,e),y(s,t,e)and球s,れe)
and
tariff are obtained by dif-
with policy variables. First,the effectsof
a production subsidy on output and price arc :
血
面
嗇＜0,
and首（か+Cv2悌
Second, the effects of a tariffcan be obtained as
昔＝嗇^，
ｿﾋﾞく0，and
dt
Third, the effects of a foreign eχportsubsidy can be obtained as
藷＝一犬＜0，昔＝ﾕことﾌﾞ旦＞0，and昔＝一丿九牛ヰ
An increase in s encourages
production
subsidy
effects of a tariff and
home
will increase
production
but discourages
the total supply
a foreign eχport subsidy
and
change
thus
foreign production.
reduce
the price.
can be interpreted
A
The
in a similar
way･
2.3 National
welfare and policy reaction function
The national welfare of the home
consumer
The home
country is assumed
surplus, the gross profitof the home
country welfare is summarized
to be the sum
firm and the net government
as:
（5）
of the
revenue.
20
Masayuki HAYASHIBARA
(5)SW(s,
t,e)＝CS十7Z−SX十ty.
Considering the third-stage competition and taking the foreign subsidy as given, the
home
government
chooses a production subsidy and a tariffso as to maχimize home
welfare. By partially differentiatingsw
stituting the comparative
∂SW(s,
t,e)
_
with respect to policy variables and sub-
staticresults,we obtain:
b(2b十Cx2八十bib十ら,2)3'−(2か十ら2)s一加
−
∂S D0
and
y一bs−(2b十C,2沁
dSW(s. i, e)＿b-x十(26十Cxi)(b十ら2
−
∂j 炳
Solving the reactionfunctions of the home
government in the policy game,
∂SW/∂s＝0 and ∂斗w/∂i=0,fors and t gives:
(6)s( の＝十ら＼￣゛顛＋2(“￣Cxi)らi畑
仙
and
(7)汀.)＝{(“ら十゛)咄十{Ctl￣ら十めb](b十ら2)，
仙
where
五)i=2が十(3c,2 ＋2ら,2)か＋2cx2ら,2
is positive
home
welfare
maχimization.
Assume
under
that, under
the second
order
condition
for
b十G2＞0，
(8)融白)ニ∠Uﾀｺﾞﾋﾞ駿白･
thenZ), ＞0 holds.
㈲
That is,the home
By
ds(e)
一心
differentiating
-
s(e) and
Ke)
with
respect
to e, we
can obtain :
言ﾚく0，and
government
responds to an increase in the foreign export subsidy
by increasing its tariffand by reducing its production subsidy. The logic behind this
result is shown
by Collie（1991）on pp. 315-317.
0nthe reaction functions for the home
s(e)=to(s(e),
Ke), e),
government,
relations,
and t(e)＝(b十ら2)y(s(e)，仄＼e),
e)，
hold, the firstof which implies ♪(s(e), t(e), e)＝訂Cr(s(e)，t(e)，e). Hereafter, we
(6)
EXPORT SUBSIDIESAND RETALIATION UNDER CONDITIONS OF VARIABLE MARGINAL COSTS 21
utilizex.)instead
of x(s(e), t(e),e), etc.
The national welfare of the foreign country can be defined as the net profitof the
foreign firm, that is:
(10)SW゛(s，れ2)＝py−TC,一ty.
The
reaction function
in a similar fashion.
of the foreign government
Partially
differentiating
in the policy game
SW＊with
respect
is characterized
to policy variable 召
gives
∂SW゛s，いう
b''y−(2b十Cx2≫
ゐ
￡,
Thus, the firstorder condition is∂SW*A∂e = 0. Reference to the comparative
static
results obtains:
（11）e(s,
t）
-t）
{(a十c.1−2
が
炳
where D2＝{2ぴ＋2(ca十ら2)ろ十Caらi}(2b十Cxi)ispositive for the second order condition for foreign welfare maχimization. Assume
that
(12)口.fc,)ニ￣⑤でｹ＜ら2
then五)2＞0 holds. On the reaction function for the foreign government,
e(s,t) ＝ が y(s,
助十Cj2
relation
t,威s, 0)
holds.
If both governments
choose
the same
stage of the policy game,
reaction functions （6）,
（7）and （11）simultaneously
by solving
for s, t, and e, the following
relations can be obtained:
(13)ダ＝bx'＞0，が＝(b十ら2)ゾ＞O and ^'＝ｿﾞ≒ニヅ＞0.
The
superscript S denotes
simultaneous
home
move
government
a simultaneous
move
policy game.
Thus, in the
policy equilibrium, even if the marginal costs are variable, the
sets its production subsidy and tariffand the foreign government
sets an eχportsubsidy.
（7）
22
Masayuki HAYASHIBARA
3.
The
case in which
the foreign
government
This case applies to the countervailing
Agreement
The
on Tariffs and
response
by the home
foreign government,
the home
government
when
functions
of the home
is optimal
s(e) and
of E
to an increase
t{:O in equations
in the foreign
reducing
its production
subsidy.
of any
World
given
Trade
(the General
Organization).
the eχport subsidy
anticipates
the optimal
t,e)/∂s = 0 and∂SW(s,
government
responds
domestic
(the
by the GATT
leader
set by the
response
by
it sets an eχport subsidj' at stage one.
function
In absence
the WTO
and the foreign government
In this case, first by solving∂SW(s,
the reaction
duties allowed
Trade)and
government
plays the Stackelberg
domestic
at the second
(6)and
(7). That
eχport subsidy
intervention,
t.e)/∂s = 0 for s and
stage are obtained
is, the home
by increasing
a foreign
as a
government
its tariff and
eχport subsidy
t，
may
by
reduce
welfare.' In fact, we can obtain
∂SWﾂ;Oパ)＝(/)一冊○背−y器
Dn
which is negative if(む十Cxz)y＜蝕holds. However,if the domestic country pursues an
optimal policy, then
(14)dS服(s(e).氏祚e)
面
＝φ○一MCA.)}言汗っ(う{旦謡土一寸
}十Z(○と万万上
＝緋.)＞0
holds, which implies that a foreign eχport subsidy always increases domestic welfare, even under variable marginal costs of production.^
Now consider the optimal policy for the foreign country.
The
home
govern-
ment' s countervailing tariffwill reduce foreign welfare and the reduction in the
production
subsidy may
subsidy will increase foreign welfare. The
be ambiguous.
By substitution,Sl'F*(s(e)，tie),
e) are obtained. Totalh'
differentiating this S 里忙)with
I See Dixit （1984）p.
2 See Collie （1991）pp.
overall effects of an eχport
respect to e, we can obtain
14.
315 −316, for a case of constant
（8）
marginal
costs.
EXPORT
SUBSIDIES
AND
RETALIATION
UNDER
CONDITIONS
OF
VARIABLE
MARGINAL
COSTS 9'^
お『.)＿{(c.汁Cv謳十CxZCy㈲O 十肺十G加
(15) de ￣￣ 2ぴ十(3Cx2＋2ら2)＆＋2Cx2ら2
For welfare maximization
dSW几)/面＝O
by the foreign government
in the firststage, solving
for e yields:
(16)が＝−{^l￣ら顛十{″ﾃｽﾞﾂﾞﾋﾟﾂﾞﾔ十C岫b十Cr2ら2}
forthe second order conditionfor foreign
Jここ
e maxでjJよこ十れごごthat
(17)ffl4fe2)＝几ﾄﾞﾌﾞ犬
then Z).,＞0 holds.
O hold, under
Moreover,
because
the assumption
export
subsidy
and
subsidy
can obtain
ψ.＼Å2)＞卿(cx2)forﾌﾟ＝0, 1,2, Dj＞
in (17). Further, an optimum
can be positive or negative,
optimal
we
but for constant
marginal
by the foreign government
tariff calculations
for the home
is zero.
government
が十(3a−4c,,十c
（18）ダ＝
foreign export
subsidy
costs and linear demand,
Using
／
the
(16), the optimal
are :
悌c,2＋3(a−Cx,)(か十
￡.
and
坤十(a一
（19）ド
Combining
cj}(b十
仙
the above results with the reaction functions for the home
government,
we can obtain the following relations:
(20)s'-'ニbx''＞0,
f=(b十ら2)げ＞0･and ノニ￣^十C丿b十G2ら2j／
＆十Cx2 ゛
From
the above argument, we can obtain the following proposition.
PROPOSITION
and
: Suppose
the home
Further,
government
at stage
sub-game
holds, then
the foreign government
sets both
three, firms
perfect equilibrium
the foreign
holds, then it is negative.
a production
choose
outputs
policy is obtained
eχport subsidy
To the foreign
sets an eχport subsidy
subsidy
in
（9）
a Cournot
as follows.
is positive,
subsidy,
and
whereas
the domestic
at stage one
a tariff at stage two.
fashion.
Then
the
If（cv9十C丿b十Cxlら2く0
if（Cv2十ら2悌十Cx2Cy2＞0
government
always
24
Masayuki HAYASHIBARA
responds with a positive production subsidy and tariff.
Inthis equilibrium, the foreign government
negative）at
stage one, and the home
sets an eχport subsidy （positive or
government
responds
production subsidy and tariffat stage two. This sub-game
the use of countervailing duties by the home
government
to it by setting its
can be used toeχamine
in response to the foreign
export subsidy.
What are the conditions for the positive eχport subsidy by the foreign government?
By adding the effects of a foreign eχport subsidy on a domestic production
subsidy and tariff,we can obtain the effects of an export subsidy on the overall
protection, that is:
d{s(e)十tie)}
＿(乱十ら加十Cv2ら2
−
面 D,
(21)
That
is, though
subsidy
the home
by increasing
protection
may
government
be increasing
reduces
the overall protection,
positive
subsidy.
On
and
then
zero for linear demand,
even
under
and
another
example,
a countervailing
tariff.
Let us sketch
Figure
l defines Z),i
＝O which
vertical line at −26/3.
curve
D4 ＝0.Define
The
That
is, the optimal
set a
increases
the
tax. If marginal
and dt(e)/de ＝
foreign export
subsidy
Besides, Collie (1991)showed
is
that
costs, if the demand
is non-linear, the overall effect
the foreign country
to subsidize its eχports. Thus
with the co-existence
the above
set an export
subsidy
should
eχport subsidy
should
by Collie (1991).
marginal
of retaliation can be to encourage
we provided
if the foreign
eχport
the overall
export
government
is linear, then冶(の/面＝−1/2＜O
holds.
as shown
the constant
subsidy,
in e. If the foreign
the foreign government
1/2 ＞0, thus d{s{e)十てe)}/加＝O
its production
in fact, the foreign
hand,
the demand
to an increase in the foreign
by reducing
or decreasing
the other
overall protection, then
costs are constant
responds
its tar汀f and
argument
intersects
condition
of both a positive export
graphically.
with
The
dotted
curve
(p,＼(ca)in
the horizontal line at −か/2, and
Z),i＞0 holds in the upper
a vertical real line y″ニ0 in Figure
right-hand
subsidy
with
the
region
of
l as :
臨 −ヅ￣らﾔ＜o
(α−らi)
Under
皿＞0,
intersection
region
the foreign supply
in the right-hand
of curve
is positive, y″＞0, if Cx／＜Cx2 holds, which
region
of line ソニ0
).x＝ﾆ0.Neχt, define a declining
∩∩
and
the upper
real curve ド＝0
as:
and
defines an
right
hand
EXPORT
SUBSIDIES
AND
RETALIATION
UNDER
CONDITIONS
OF VARIABLE
MARGINAL
COSTS 25
＿ {(2α−3ら十ら.i)か十(3>a ＋Ac,x十らl)Cx2畑
(PズCx2)−− 3(a−c,-i)(&十Cx2)
Then
the domestic
holds, which
output
is positive, が＞0
defines the upper
right-hand
under
D,i＞0, if and
only if 戦(Ci-2)＜ら2
region fromχ'''＝0. Further,
we can obtain:
{(Cv,一心,1)＆十(α−らi)cxo}柚
<P.l(Cx2)一戦(Cx)＝ 3
(a一c.vi)(b十Crf)
From
these relationships,
intersect
holds.
Thus
right-hand
we can obtain
side of liney≒=O
in this region.
positive.
export
the following
at point Q in Figure
Thus,
subsidy
On
the region
and
First, Cx2＝Cx2'，戦(cx)and
the intersection
for positive outputs
the right-hand
the other hand,
can be shown
is clear.
1. Second, if 0x丿＜Cx->,thatis,／＞0,then
below
curve
as the intersection
side of curve
／＝0,a
eχport subsidy
and
Cx2
eF±O
x≒)or()、(cx2)
D4司or
1 The
qn(c^d)
set of feasible outputs with a positive export subsidy
(11)
can be
that for a positive
as non-empty.
り
Figure
on the
x''＝0. 工,,＞0 also holds
foreign
of the set for positive outputs
印,i(Cx2)
＼'.￨(Cx2)くら(Cx'z)
26
Masayuki HAYASHIBARA
4. Summary
In this paper, we have
firm and
um
To
that in the Cournot
one foreign firm compete
policy implies
export
shown
subsidy
the following
in a home
subsidy
subsidy
reduces
positive
subsidy. 0n
market,
the domestic
government
the other
always
then
hand,
the foreign
if the foreign
overall protection, then the foreign government
and
the demand
is zero for linear demand,
the sub-game
where
as shown
one home
perfect equilibri-
responds
intuition indicates
the overall protection,
costs are constant
model
the foreign
if (Cx2十ら2)＆十Ct2ら2＞0 holds, then it is negative.
and tariff.Economic
subsidy
duopoly
result. If (Cx2十ら2)わ十CxZら2くO holds, then
is positive, whereas
the foreign
production
and conclusion
should
is linear, then
with
a positive
that if the foreign export
government
eχport subsidy
should
set a
increases
the
set an eχport tax. If margina!
the optimal
foreign export
subsidy
by Collie (1991).
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