STX
J
BEBR
5
1651
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2
FACULTY WORKING
PAPER NO. 90-1651
Flexibility
Versus Commitment in
Trade Policy Under Uncertainty:
Model of Endogenous Policy Leadership
Strategic
A
Lanny Arvan
The library
WORKING PAPER
SERIES
f
the
ON THE POLITICAL ECONOMY OF INSTITUTIONS
College of Commerce and Business Administration
Bureau of Economic and Business Research
University of Illinois Urbana-Champaign
NO. 39
BEBR
FACULTY WORKING PAPER NO. 90-1651
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
April 1990
Flexibility Versus Commitment in
Strategic Trade Policy Under Uncertainty:
A Model of Endogenous Policy Leadership
Lanny Arvan
Associate Professor, Department of Economics
University of Illinois
1206 South Sixth Street
Champaign, IL 61820 USA
I am grateful to Jim Brander and David Nickerson for providing me
with several important insights on the general subject with which
this paper is concerned. I also wish to acknowledge the helpful
suggestions of two anonymous referees. The usual disclaimer
applies
Digitized by the Internet Archive
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http://www.archive.org/details/flexibilityversu1651arva
ABSTRACT
I consider a noncooperative game between rival governments where the strategic
variable is an export subsidy. Governments can choose their policy level
either prior to observing the random, demand intercept or subsequent to this
observation. It is assumed that a policy choice made ex ante is completely
irreversible ex post. I show that the resulting equilibrium will frequently
involve asymmetric timing of policy choice. One government will move first
and, in effect, become the leader in the trade-policy game. The other
government will delay its commitment, thereby better tailoring its policy to
the actual economic environment. Equilibrium with asymmetric timing of
commitment exists when there is not too much noise in the system or, even in
the large noise case, when the number of firms differs across countries. When
there are two such equilibria, one of these equilibria may be focal, i.e., the
governments might agree on which should be the leader. In the large noise
case, the equilibrium with asymmetric timing of commitment is the unique
equilibrium of the overall game.
Introduction
I.
Within the
Export subsidies pose an enigma for economic theory.
traditional small country
paradigms
of
international
subsidies exists.
and large country
(competitive)
trade,
no
economic
Since these models
account
rationale
(monopoly)
export
for
for both extremes
in
market structure, one may wonder whether it is possible to rationalize
export subsidies on the basis of domestic Pareto improvement.
demonstrated in the seminal paper by Brander and Spencer
export subsidy can be explained by
a
"profit
Yet,
(1985)
,
as
an
shifting" motive which
emerges when the industry in question is oligopolistic.
Brander and Spencer consider a two stage game where, in stage one,
rival governments choose their trade policies and then,
in stage two,
producers in each country choose their strategic variables given the
joint trade policy choice of the rival governments made in the previous
stage.
In analogy
e.g., Dixit
the
(1980),
reaction
to the capacity investment
by an incumbent
firm,
an export subsidy by the domestic government shifts
function of
the
domestic
industry,
thereby moving the
resulting equilibrium along the foreign country's reaction function.
When
the
domestic
industry
is
characterized by
single
firm
operation, the effect of an export subsidy on domestic profits via the
direct effect on the domestic industry is negligible,
approximation,
because the' domestic industry was
profits prior to the subsidy.
However,
to a first order
already maximizing
such a subsidy significantly
An alternate, readily available explanation is that export subsidies are a form of
patronage to the targeted domestic industry and result even if some other sector of
the economy suffers.
Moreover,
The recent Japanese experience suggests otherwise.
even if export subsidies are nothing but patronage, it is still a mystery why export
subsidies rather than some other form of patronage result when so much of the benefit
from an export subsidy is captured by importing countries.
affects domestic profits via its affect on the actions taken by foreign
In the case of Cournot competition in the product market,
producers.
an
export subsidy increases the market share of the domestic producer while
lowering the
product
price.
*
Then,
a
small
export
subsidy
domestic profits while lowering overall industry profits,
raises
since the
Stackelberg leadership output exceeds the Cournot output; ergo, profit
shifting.
Though export subsidies might emerge in an equilibrium when rival
governments compete over their trade policies, it is not necessarily the
case
government
competition.
it is possible that export taxes are the outcome.
This is the
subsidies
that
Indeed,
will
from such
result
point of the paper by Eaton and Grossman (1986)
To understand why this
is
the case,
first
suppose the Cournot
assumption is maintained but allow any prespecified number of firms to
operate
in
concentrated,
domestic
either
country.
As
domestic
the
industry
gets
the domestic reaction function shifts outward.
industry
is
sufficiently
competitive,
the
If
less
the
"cartelization"
motive will dominate the profit shifting motive and the optimal policy
for
the
Second,
domestic government
will
be
a
tax
rather
than
a
subsidy.
suppose the assumption concerning single firm operation in each
country is maintained but firms produce imperfect substitutes and are
Bertrand competitors choosing price rather than Cournot competitors
choosing quantity.
Again,
an export tax is optimal as such a tax will
encourage a higher foreign price.
In general,
the optimal policy will
depend on industry concentration as well as on whether domestic and
2
I am assuming that revenue and cost functions satisfy standard convexity conditions
and also that there is a unique equilibrium which is stable.
foreign firms compete in strategic substitutes or strategic complements.
(See Bulow,
Geanakoplos, and Klemperer (1985).)
An alternate critique of the Brander and Spencer approach has been
offered by Cooper and Riezman (1989)
the
arbitrary
restriction
to
These authors are concerned with
.
linear tax
a
or
Nonlinear
subsidy.
policies also have the effect of shifting reaction functions.
nonlinear policies
plethora
of
are
allowed in
equilibria
the
There
results.
stage
first
does
the
of
appear
not
But if
game,
a
be
a
to
compelling way to make an equilibrium selection in this case.
Cooper and Riezman suggest
a
They allow
way out of this dilemma.
for some actual uncertainty which is unresolved until after governments
have
committed to
their
policy
choices.
Then,
a
policy must
be
evaluated on the basis of how it performs for all realizations of the
underlying random variable rather than on just how it performs when this
random variable takes on its expected value.
Policies which perform
badly as the environment changes slightly are ruled out and the set of
equilibria is reduced.
One possible way to proceed at this juncture is to maintain the
two stage structure and, following Weitzman (1974), allow governments to
choose
arbitrary
nonlinear
incentive
schemes
in
the
first
stage.
Klemperer and Mayer (1989) take this type of an approach in an oligopoly
model where the firm commits itself ex ante to
a
supply function and ex
post chooses a point along this supply function.
In the trade context,
it seems unreasonable to assume that governments can directly choose an
aggregate supply function for their domestic producers,
there is more than one firm.
But,
in
a
at
least when
model where the government
chooses a unit subsidy which depends on aggregate output,
difficulties
and nonexistence
are created owing to intractability,
lack of realism,
of equilibrium.
Cooper and Riezman offer
^
As a consequence,
a
highly
admissible
stylized model where it is assumed that the only nonlinear,
policy is a fixed quantity regime.
Fixed quantity policies are completely inflexible in the face of
uncertainty and would never emerge in the equilibrium of
game.
a
two stage
Cooper and Riezman consider a three stage game, where governments
announce their policy type in the first stage,
either tax-subsidy or
fixed-quantity, and choose their policy level in the second stage, given
their first stage policy type choice.
stage game introduces a new wrinkle.
Consideration of this three
The stage one policy type choice
can affect the rival government's stage two policy level choice.
a
Then,
fixed-quantity policy may be attractive because, by adopting such
a
policy in stage one, the government immunizes its country from the rival
government's profit shifting in the ensuing subgame.
Since
a
tax-
subsidy policy allows firms to better approximate the ex post optimum,
a
tradeoff is created between being immune to the rival government's
profit shifting, on the one hand, or being vulnerable to profit shifting
but being flexible in the face of
(demand)
uncertainty,
on the other.
The optimal choice depends on the noisiness of the system.
Jones and Ostroy
(1985)
,
Following
Cooper and Riezman show that in the low noise
case the equilibrium yields an inflexible fixed-quantity regime while in
the high noise case a more flexible tax-subsidy regime emerges.
3
As pointed out by Myerson (1982), existence of equilibrium is problematic in such an
unrestricted environment. Fershtman and Judd (1987) offer these existence problems as
justification for looking at linear incentive schemes.
Spencer and Brander (1989) analyze this type of extensive form in an oligopoly model
and provide a variety of interesting applications for this structure.
While the tradeoff between commitment and flexibility in trade
policy is an important one,
modelled best via
it
is
not
obvious that this tradeoff is
Nor is
choice of policy type.
a
obvious that
it
governments are capable of temporally separating their choice of policy
type from their choice of policy level.
it might be
In other words,
more appropriate to collapse the first two stages of the Cooper and
Riezman model into
a
single stage.
One interpretation for this temporal
that
government
hierarchical
is
and
separation in decision is
individuals
different
hierarchy are making the moves at the different stages.
commit
to
a
appointees
general
pursue
the
policy
type
policy
in
level
in
the
Higher ups
stage
one
while
lower
level
choice
in
stage
two.^
This
interpretation has immediate plausibility.
Yet even this interpretation
does not produce the Cooper and Riezman extensive form unless it is also
assumed that the rival government can observe the internal, policy type
directive at the time this decision is made.
If,
the rival
instead,
government can only observe an actual policy level decision, their model
collapses into
a
two stage model.
An alternate, and perhaps more natural way to model the commitment
versus flexibility tradeoff is to posit a fixed policy type but allow
governments to determine the frequency with which policy levels are
adjusted.
policy.
adjusting
I
The more' frequent
This
is
policy
the
is
the
adjustment,
the more
approach taken in my model.
that
governments
learn
about
flexible the
The
motive
the
am indebted to James Brander for providing this interpretation to me.
for
economic
environment and can base their policy choice on what they have learned.
For simplicity, the three stage structure is maintained.
As in the Cooper and Riezman model,
the first two stages of my
model are reserved for government decisions.
government either chooses
a
about
governments.
the
Between the first and second stage some
economic
environment
known
becomes
to
the
If a government did not select a policy in stage one,
must do so in stage two.
it
that if a government
however,
It is assumed,
has selected a policy in stage one,
stage two,
each
tax-subsidy policy or opts to delay this
choice until the second stage.
information
In the first stage,
this choice cannot be altered in
regardless of what the government learns about the economic
environment.
'
In stage three,
domestic and foreign producers play
a
Cournot quantity game, as in the Cooper and Riezman model.
The primary consequence from adopting this alternative extensive
form is that the nature of the equilibrium changes
.
In equilibrium of
the Cooper and Riezman model, both governments adopt inflexible,
quantity policies in the low noise case.
In contrast,
exist
both
an
equilibrium of my model
where
relatively rigid decision to commit to
one.
Q
a
fixed-
there does not
governments make
the
tax-subsidy scheme in stage
This follows because it is strictly dominant for at least one of
An important question which is not considered in the paper is how governments
credibly commit to a rigid policy when such a policy is not optimal ex post.
In the
paper, it is merely assumed that governments have such a commitment capability.
More realistically, committing to a policy in stage one imposes an adjustment cost
in stage two that could have been foregone were the government to delay its policy
choice.
In the paper I restrict attention to the infinite adjustment cost case.
This type of equilibrium does exist if, with probability one,
governments learn
nothing about the economic environment between stages one and two.
the governments to delay its policy choice till stage two given that its
rival has chosen a policy in stage one.
In the low noise case there are typically two equilibria of my
In such an equilibrium one government acts like a Stackelberg
model.
leader by choosing its policy in stage one while the other government
acts like a Stackelberg follower by choosing its policy in stage two.
One of these equilibria may be focal in that it Pareto Dominates the
other equilibrium. I"
Note that this Stackelberg outcome occurs in spite
of the fact that neither government has a first mover advantage.
In
*
danand
this respect my model is similar to the model of Green and Sa
who consider endogenous Stackelberg leadership in oligopoly.
(1990)
However,
my
model
from those mentioned
differs
prediction for the high noise case.
players
adopt
more
sufficiently noisy.
unique
flexible
In
equilibrium of
equilibrium
governments.
entails
policies
contrast,
my
In these
it
is
above
in
other models,
when
its
all the
environment
the
is
possible for there to be
model
in
the
high
leadership
on
the
part
noise
of
case
one
of
and
the
a
this
two
This occurs when the follower government's tax-subsidy
policy is negatively correlated with the underlying uncertainty.
the leader government encourages both its
Then,
firms and the firms in the
other country to adjust to uncertainty by allowing greater variability
9
Weak dominance is obvious because in stage two each government could always choose
the policy it would have chosen in stage one.
Strict dominance for at least one
government occurs because for this government the second stage best response is not
constant in the underlying uncertainty.
This result contrasts with the finding of Dowrick (1986)
In his model either
both players prefer to be the leader or both prefer to be the follower.
Arvan (1985) demonstrates a similar result in a two-period duopoly model with
inventories
.
in the follower government's policy response.
This is achieved by the
leader government adopting an inflexible policy.
II
The Model
.
Following
Riezman
and
Cooper,
homogeneous good which is produced by
firms,
F,
fixed.
+ N_
.
1
for
a country.
N.
of the firms
2.
(Hence,
Assume that the number and location of the firms is
)
c,
for firms in country
1
This
and by c 2 for firms
That is, cost functions across firms are identical within
Let p denote the product price.
which operates in country
n{ =
(1)
a
relatively small number of
Each firm is assumed to operate at constant marginal cost.
in country 2.
i
market
and N_ of the firms operate in country
marginal cost is given by
for
a
the
and consumed by a large group of consumers.
operate in country
F = N.
consider
(p -
i
and produces
q.
Then, the profit for a firm
units of output is given by
c.)q i ,
= 1,2.
As is now common in this literature,
reside in a third country.
it is assumed that consumers
This assumption is made so that governments
can pursue profit shifting and cartelization motives without having to
be concerned with the welfare
of
their consumers.
For
simplicity,
assume that the market demand curve is linear with random intercept.
The inverse demand curve is given by
(2)
p = a + 9 - bQ,
where Q is total output, a and b are parameters with a,b >
denote the ex post value of the demand intercept;
government
the
production subsidy equal to
country
in
s.
a =
where Q
a
per
unit
a
know the realization of
Then,
the typical
solves the following problem
i
maximize (a
q
(3)
Let a
and suppose that all firms engage in
the random demand intercept when playing this game.
firm in country
a
a + 9.
institutes
i
It is assumed that firms
Cournot output game.
9 is
nonzero variance.
random variable with zero mean and finite,
Suppose
and
0,
- bQ,
-
- c.
bq
+ s.)q,
denotes the aggregate output of all other firms.
This yields
the following output reaction function for a firm in country i
r
a
-
bQ
q, =
(4)
It
is
^
- c.
+ s.
^ .12
straightforward to derive the aggregate output,
reaction function from the above assuming the firms in country
achieved Cournot equilibrium.
Since each firm in country
i
country
i
have
produces the
same output in Cournot equilibrium, this equilibrium condition is given
by Q a =
(U^
- Dq^^ + Q.,
country other than
(5)
q i- =
Q.
v
i
12
Then, we have
i.
(N.
where Q. is the aggregate output of firms in the
+ l)b
~
(n.
+ i)b
ttt
"
bQ
" °i +
J
[a - bQ
.
J
- c.
i
S
i
]
^
+ s.i = n.q.
i^i
i
It is assumed that parameter values are restricted so as to always yield an
interior solution.
It is convenient to think of the number of firms in country i as
determining the slope of country i's output reaction function.
slope moves from - 1/2 to
-
moves from
as N.
1
convenient to think of the unit subsidy in country
to
1
i
Then,
*>,
This
it
is
as a shifter of the
reaction function intercept.
straightforward
also
is
It
to
derive
overall
the
The equilibrium country outputs,
equilibrium.
1
Qi =
(6)
for i f
= 1,2;
j
! l)b
(F
a
+
+ 1] (S
)
i " °i
(N
^
-
n
(
3l
-
Cl
)
- N
FT1
2
profit subsidies can be ignored.
n_,
n.
Ni
*—y"
=
[a +
(N.
- c
2
)
in accounting for aggregate
i.e.,
Then, the equilibrium country profits,
-
+ l)s.
(N.
+ l) Ci - N.(s. - c.)]
b
X [a
for i,j = 1,2; i *
Consider the
j,
where
Il
i
=
-
Ni s i -
(p*
following three
(N.
- c )Q
i
i
stage
+ l)c - N.(s.
i
i
subsidy,
d.
3^,.
Here,
commits to a policy,
di -
0,
while
Si,
d.
game which
c.)]
designed to
is
In stage one the
chooses an indicator variable,
denotes whether the government
- 1,
-
.
strategic competition between governments.
government in country
two,
o2
are given by
(F + 1)
capture
' C : )]
D
•
the revenue to finance the subsidies,
(8)
*V S
it is assumed that there are no distortions created in raising
Finally,
n i and
'
are given by
,
Then, the equilibrium price, p*, is given by
i * j.
P* -
(7)
[Ct
and Q-
Q,
Cournot
*
*
di
,
and a unit
in country i
or defers its policy choice until
stage
is the unit subsidy that is in effect in country
1
i
if the government has committed to a policy in stage one.
ignorant
are
realization
the
of
distribution is common knowledge.
of
stage
in
9
Governments
Governments
though
one
its
assumed to move
are
simultaneously in this stage.
Between stage one and stage two governments get to observe
the government of country
chooses
it
a
observation
analytic convenience,
move in all cases.
ai
,
where
ai =
m^
That is,
-
Then,
(m il ,m
(d i ,s il
)
a
3
i?'
the play
of
on
t ^ie
Das i s
stage
in
and
and m i2 e {0,1}
X9t,,
e {0,1}
= s
i2
m.- (m. 1 ,ia..,0)
assumed to move simultaneously in this stage.
.
its
of
For
one.
a
stage two
strategy for the government in country
m L1
i2 ),
two,
assumed that governments make
is
it
stage
knowledge
and its
of
has not committed to a policy in stage one,
i
subsidy in
unit
If
8.
2
X
3
<R
i
is
-»SR.
Governments are also
After play in both stage
one and stage two has been completed, the unit subsidy that is in effect
in country i, s if is given by
stage
In
three,
s.^
= d s
+
i il
choose
firms
(1
-
d i )s i2
output.
.
stage
This
has
been
described extensively above.
Indeed,
of the third stage subgame
In this subgame the equilibrium output of
.
readily yields the equilibrium
(6)
*
each firm in country
country
i
i
is Q. /N.
.
It is assumed that the
government of
is interested in maximizing the expected aggregate profits of
the firms located in country
i.
Then,
along with the distribution
(8)
over 9 induces a map from joint strategies into joint expected profits.
III.
The
Stage
Two
Subgame
Suppose the government in country
has set
i
—
d.
=
in stage one.
an.
From
(8)
and the first order condition, t
as.
two, tax-subsidy reaction function
= 0,
one obtains the stage
12
r
1
_
Si "
(9)
for i,
j
=
1,2;
i
*
+ 1 - N.] [a -
[N.
2N.CNJ J-J-
From
j.
it
(9)
is
(N.
+ l)c.
- N.( Sj
- C.)]
easy to obtain the following
proposition.
Proposition
sign t
1:
Bs
= - sign -r—
Moreover,
.
T
.
5-* <
when
ds.
when
Finally,
—
< N. + 1.
N.
i
J
^
=
when
>
when N i > N. +
Ni
= N.
government to pursue
a
+
= N. + 1,
1,
s.^
and
1.
0,
i.e.,
it
optimal
is
for
the
laissez-faire policy regardless of the demand
shock or the policy in country
j.
Since the slope of the tax-subsidy reaction function plays such an
important role in the later analysis, it is appropriate to provide some
insight into the determinants of this slope.
by an examination of figure
Some intuition is provided
1.
In the figure there are two output reaction functions for country
2,
Q2 s 2
I
country
anc* $2
1,
Q1
.
'
s2
w ^- tn s 2
<
s2
'
anc*
an out P ut
The subsidy level in country
is such that s = s^Sj).
1
for
1
that determines Q,,
s,,
This can be seen by noting that l's isoprofit
curve through the Cournot country outputs,
output reaction function.
1
reaction function for
^
which is tangent to Q_
point A,
is tangent to 2's
now consider the (undrawn)
|
2
.
isoprofit curve
If the tangency point happens to be at
Recall that these unit subsidies shift the output reaction function but are not
counted in the profit calculation. Hence,
l's isoprofit curve need not be horizontal
where it crosses l's reaction function, as must be the case when s. = 0.
13
B,
then l's tax-subsidy reaction function is perfectly inelastic.
the tangency point
is
to
the
right
of
B
r
along Q 2
subsidy reaction function is upward sloping.
to shift
1
ls 2
That is,
,
If
then l's taxit is necessary
reaction function upwards to obtain the tangency
l's output
point as the equilibrium of the third stage subgame.
Similarly,
the
tax-subsidy reaction function is downward sloping when the tangency
r
point is to the left of B along Q_
1
|
2
.
Recall that the number of firms in country
country l's output
reaction function.
As
N.,
1
affects the slope of
increases,
country l's
output reaction function through A gets flatter and the point B moves to
the left along Q 2
ls 2 .^ 4
But,
the number of firms in country
affect the shape of the isoprofit curves.^
unchanged as H 1 increases.
Consequently,
1
does not
The tangency points remain
for small values of N 1 the
tangency is to the left of B while for large values of N 1 the tangency
is to the right of B.
This explains why the slope of the tax-subsidy
reaction function depends on the relative number of firms in the two
countries.
14 As
N^
increases, the subsidy needed to sustain point A as the Nash equilibrium of
the third stage subgame also changes.
This is a consequence of the constant marginal cost assumption.
If firm costs were
strictly convex, this conclusion would be invalid.
14
Figure
Given
(9)
,
1
it is a simple matter to compute the Nash equilibrium
subsidies. The Nash equilibrium policy levels of the stage two subgame
without prior government commitment are
si
(10)
"
a, (F +
for i,j = 1,2; i *
j.
[N
3)
D
+ X " N ]
i
*
s,
[0t
*
and
"
(N
where
s2
i
+ 2)C
+
i
(N
i
+ 1)C
Under the reasonable economic condition that the
second square bracketed term in
(10)
is positive,
i.e.,
that the demand
intercept is sufficiently large relative to marginal cost,
from
(10)
]
J
it
follows
that the cartelization motive is never dominant in the country
with the more concentrated industry and is dominant in the country with
the less concentrated industry only when
case,
the
overall effect
is
to
|
N.^
-
N
.
|
> 1.
Even in this
depress price unless costs
higher in the country with the more concentrated industry.
price is made less variable, regardless of cost differentials.
talcing the resulting quantities,
Moreover,
This can
from
(10)
into
and substituting into
(7).
The
be seen by substituting the equilibrium policy levels
(6),
are much
price that results from the Nash equilibrium policies, p**, is given by
15
a +
(id
(N 2 +
p** =
l)c 1 +
(N x
+ l)c 2
irfl
This price can be contrasted to the Cournot equilibrium price in the
absence of any government interference.
obtained from
by setting
(7)
In the ensuing
s
= s = 0.
2
1
section
This latter price is readily
consider the decision to commit to
I
policy in stage one or delay the policy choice until stage two.
a
As the
benchmark against which commitment can be judged, consider the expected
payoff from choosing to delay given that the rival government has also
chosen to delay.
the
To do so,
first consider the equilibrium payoffs in
second stage subgame without prior government commitment.
These
payoffs are obtained by substituting the equilibrium policy levels from
(10)
into
(8)
to yield
n* =
(12)
r(F +
for
i,
j
=
1,2;
i
*
(N.
+ 2)c.
+
(N.
+ l)c.]
2
b
3)
Then,
j.
+ 1] [a -
[N.
taking expectations with respect to
yields
(13)
E e n* =
r-
for i,j = 1,2;
IV.
(F +
3)
*
j.
i
Commitment
In
this
government
of
[N.
b
Versus
section
I
country
i.
+ 1] { [a U
Delay
and
focus
on
Since
(N.
+ 2)0,
Optimal
+
(N.
stage
one
decision
governments
are
assumed
the
stage one decision on having observed m..
2
+
Var
Commitment
simultaneously in stage one, the government of country
section,
+ l)c.]
i
by
to
the
move
cannot base its
For the remainder of this
let m. denote the government of country i's point expectation
6
}
as to the play that the government
of country
j
will pursue in stage
one.
Case
From
Commitment By the Rival Government
1;
r
(9)
country
a
when N. +
s»
,
1
= N.
In
.
Moreover, it is evident that this
laissez-faire policy in stage one.
constitutes the optimal stage one commitment.
that
1,
d
=
1
.
delay is
country
In all other cases,
r
is not constant.
s.
strictly preferred to commitment
since for every realization of
i,
policy that might be chosen before
happens to coincide with
Case
Hence, the government of
is indifferent to committing or delaying in this case given
i
.
of
can duplicate its optimal stage two decision by committing to
i
country
the government
this case,
is
8
for
when d. =
Thus,
the
government of
outperforms any fixed
s.
observed,
unless this policy
s..
Delay By the Rival Gove rnment
2;
When
d.
=
and N. *
N.
+
1,
the government of country
i
knows
that it can affect the unit subsidy chosen by the government of country
j,
since
country
a
s.
i
is not constant in this case.
Hence,
if the government of
chooses to commit to a policy in stage one, it will do so like
Stackelberg leader in the tax-subsidy game played between the rival
governments.
order
In
facilitate
to
understanding case
2,
I
intuition
the
of
the
reader
first consider the case where Var
in
is very
small and provide a graphical analysis which is conducted assuming Var
= 0.
Without loss of generality, take
Subcase
1;
U,
> N_ in what follows.
Downward Sloping React ion Functions
When N x = N 2 the
tax-subsidy
sloping for both governments.
In
reaction
this
case,
functions
are
downward
Stackelberg leadership
17
entails increasing the subsidy beyond the level that would obtain in the
equilibrium of the stage two subgame without prior commitment.
along
j's
function
reaction
tax-subsidy
is
II.
Since
diminishing in
s^,
Either
leadership in this case entails additional profit shifting.
government may emerge the leader.
Leadership point with
government 1 as the leader
Figure
Subcase
2:
When
2
Natural Follower and Leader
N1
=
N2 +
1
government in country
1
the
is
tax-subsidy
function
reaction
perfectly inelastic.
this
In
Stackelberg solution of the tax-subsidy game with country
of
the
case,
the
as
the
2
leader coincides with the equilibrium of the stage two subgame without
prior commitment.
to
committing in
That is,
stage
one
the government of country
or
delaying until
2
prefers to delay.
is indifferent
stage two.
introducing the least bit of noise into the model,
country
2
Then,
by
the government of
Hence, there does not exist an equilibrium
of the model where the government of country
2
is the leader.
there is an equilibrium where the government of country
1
However,
institutes
a
18
positive
subsidy
in
stage
one
to
as
so
instituted by the government of country
2
reduce
the
subsidy
level
in stage two.
Leadership point with government
2 as the leader coincides with Nash
lilibrium of the stage 2 subgame
Leadership point with
government 1 as the leader
Figure
Subcase
3;
When
3
Cooperative Follower and Leader
Nl
>
N2 +
government in country
tax-subsidy
the
1
is upward sloping.
1
reaction
function
In this case,
of
the
there are two
candidates for Stackelberg equilibrium and they may be Pareto ranked!
When the government of country
2
is the leader it reduces its subsidy
from the level that would obtain in the equilibrium of the stage two
subgame without commitment.
2*s
commitment
relative
government of country
leader.
1
to
both countries benefit from country
Thus,
the
no
commitment
case.
Indeed,
the
may prefer to be the follower than to be the
This occurs if l's isoprofit curve through 2's leadership point
does not cross 2's reaction function.
argue that leadership by
2
is focal.
When this is the case, one might
19
Leadership point with
government 1 as the leader
Leadership point with
government 2 as the leader
is focal Nash equilibrium
Figure
4
Increasing the Noise of the Demand Intercept
The above graphical analysis is valid when Var
9=0
and remains
IF
valid for Var
9
small,
since
For larger values of Var
Let
s
Sj^
country
denote
i
in
9,
optimal
the
stage
one
EqFI
.
|
(s.
is continuous in Var 9.
= s.(s.))
delay may become
a
tax-subsidy choice
Stackelberg leadership point for government
i.e.,
s
i
for
the
given that the government
decided to delay its policy choice until stage
game,
more attractive option.
is independent of Var 9,
2.
i
of
government of
country
Note that
in
the
for some i,
j
=1,2;
j
= s', Sj = Sj(s"))
> E e n*
From
(9)
* i.
(8)
and
is the
because of the linear-quadratic
The graphical analysis remains valid as long as
E e n.i (s.
has
induced policy
structure of the model.
(14)
Sj^
j
it follows that
20
Ni
r
i
EQlI.Ms.fSj = s.(s.)) = h(s.) +
(15)
4(N i +
From
for some function h.
E e n* =
(16)
—r(F +
for some constant
k.
1
(17)
(F +
for
i,
j
= 1,2;
3)
j
* i,
[N. + 1]
Var
9,
b
3)
Thus, when
.
z2
b
'
it follows that
(13)
+
k.
Var
2
1)
[N, + 1]J
L
Ni
>
j
4 (N
t
2
+ 1)
'
it must be that when Var 9 is sufficiently large
the perfect equilibrium of the game entails both governments delaying
their policy choice.
satisfied when
N,
Note,
= N
2
.
that these conditions can only be
however,
In all
other cases,
the overall equilibrium
necessarily entails some government committing to its policy choice in
stage one.
except in the case where countries have the
In other words,
same number of firms, this model predicts a leader-follower relationship
between governments.
i,
Also note that when
(17)
is not satisfied for some
this same i is the leader in the focal equilibrium of the policy game
without uncertainty.
The intuition behind this
leader in the focal equilibrium,
j
observation is that when
s
i
a
policy
in
stage
variability of country i's aggregate output falls as
the
the
In this case,
actually increases the variability of the
product price by committing to
commitment,
is
tax-subsidy reaction function is
negatively correlated with the random, demand intercept.
the government of country
i
a
result of such
covariance between price and country
output rises, i.e., expected profits rise as well.
Though the
one.
i's
a
aggregate
21
discussion
previous
The
summarized
is
following
the
in
proposition.
Proposition
2
policy game
:
The nature of perfect equilibria for the three stage
depends
on
difference,
the
N1
N2
-
and on Var
,
9.
The
perfect equilibrium correspondence is described below.
When
a)
N.,
= N_,
there exists y such that for Var
equilibria of the overall game.
government of country
1
government of country
the
second of
reversed.
2
commits to
a
the
policy in stage one while the
delays its policy choice until stage two.
There exists v,
unique equilibrium of
y there are two
In the first of these equilibria,
equilibria,
these
9 <
y_
the
the
leader
and
follower
such that if Var
< v,
overall
game.
this
In
9
y
< Var 9 < v.
y_
are
there is a
equilibrium both
governments delay their policy choice until stage t w o.
is also a unique equilibrium when
>
roles
In
If
y
< v,
there
In this equilibrium,
one of the governments commits to a policy choice in stage one.
b)
When
game.
N.
« N.
+
1,
there is
a
unique equilibrium of the overall
In this equilibrium the government
of
country
i
policy choice in stage one while the government of country
commits to
a
j
delays its
9
< v* there
policy choice until stage two.
c)
are
When N i > N. +
two
equilibria
1,
of
there exists v* such that for Var
the
overall
equilibria, the government of country
while the government of country
two.
2
game.
1
Here,
government of country
first
of
these
delays its policy choice until stage
in contrast with
i
the
commits to a policy in stage one
In the second of these equilibria,
are reversed.
In
the leader and follower roles
(a)
,
the equilibrium where the
commits to its policy in stage one may be focal.
When Var
9 > v*,
there is a unique equilibrium of the overall game where
the government of country
commits to its policy in stage one
.
Conclusion
V.
In this paper
the
i
I
have argued that
critical issue in understanding
a
strategic interplay between rival governments competing in trade
policy is the timing of government commitments.
When governments are
capable of adjusting the flexibility of their policies,
the outcome is
likely to be asymmetric in the sense that one government will adopt
a
rigid policy with strong commitment power while its rival will adopt
a
more
policy which
flexible
environment.
responds
better in
a
changing economic
The model predicts this asymmetric outcome except in the
case of high noise and an equal number of firms in both countries.
Two results were obtained in analyzing the stage two subgame that
seem worthy of some additional comment.
country
1
When the number of firms in
differs significantly from the number of firms in country
2,
it was shown that the tax-subsidy reaction function for the country with
the less concentrated industry is upward sloping.
In
addition,
this
tax-subsidy reaction function is negatively correlated with the demand
shock.
It
is
worth asking whether these results are robust to more
general demand and cost structures.
First, observe that these two results are adjuncts when there is a
unique
Cournot
equilibrium
equilibrium is stable.
the
of
Second,
third
stage
subgame
and
this
recall that when viewing these results
in the joint output space, the crucial determinant was the slope of the
locus
of
functions,
tangencies
between
on the one hand,
the other hand.
i's
isoprofit
curves
and
j's
reaction
and the slope of i's reaction function,
on
23
i's isoprofit curves were
In the analysis provided in the paper,
unaffected by
a
change in the number of firms operating in country
because of the constant marginal cost assumption.
i,
Were firms to operate
under rising marginal cost, these isoprofit curves would be affected by
The resulting shift in isoprofit curves would tend to
such a change.
support the conclusions of the paper even when demand is nonlinear,
long
the
as
standard
assumptions,
that
i's
marginal
revenue
as
is
diminishing in both i's output and j's output, hold.
Recall that in the paper it was argued that an increase in the
number of
firms
operating in country
reaction function more elastic.
structure of the model.
i
makes
i's
aggregate,
output
This is a consequence of the quadratic
It is not possible to sign the resulting change
in the slope of i's reaction function as the number of firms operating
in country i increases,
for more general demand and cost structures,
because these effects depend on third derivative properties of demand
and cost.
However,
operate in country
more
or
less,
i,
with
it
is
evident that when
a
large number of firms
the aggregate, output reaction function coincides,
the
competitive
reaction
function.
the
Thus,
desired relation between the number of firms operating in country
i
and
the elasticity of the aggregate, output reaction function must hold over
some range,
under standard assumptions governing demand and cost.
conclusions of my model are valid in
attention is restricted to this range.
a
more general framework,
The
when
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