f\
dewey
HD28
.M414
Strategic Trade Policy
with Incompletely Informed Policymakers
S. Lael Brainard*
and David Martimort"
September 1992
Working Paper No. 3469-92
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
Strategic Trade Policy
with Incompletely Informed Policymakers
S. Lael Brainard*
and David Martimort"
September 1992
Working Paper No. 3469-92
First Draft July 1991
Massachusetts Institute of Technology Sloan School and National Bureau of Economic Research.
Institut
We
d'Economie
Industrielle.
are grateful to Jean-Jacques Laffont, Julio Rotemberg, Jean Tirole, and Kala Krishna for helpful
discussions, to the Ecole Polytechnique and the National Science Foundation for research support, and to
two anonymous referees and participants
at a variety
of seminars for helpful comments.
Strategic Trade Policy
with Incompletely Informed Policymakers
Abstract
Ever since the inception of research on
strategic trade policy,
economists have warned that the
informational requirements are high, and unlikely to be met in practice. This paper investigates the implications
of incomplete information for a simple, rent-shifting trade policy of the type proposed in Brander-Spencer
(I98S).
It
finds that asymmetric information undermines the
intervention,
due
precommitment
to the requirements of incentive compatibility.
distortion in the optimal subsidy,
which may be so great as
efficient firms, given a zero-profit participation constraint.
effect,
by reducing the incentive
of unilateral government
This "screening" effect induces a downward
to require a tax rather than a subsidy for the least
Second, in contrast to the full-information case with
strategic substitutes, the introduction of a rival interventionist
precommitment
effect
government reinforces rather than countervails the
for the domestic firm to misrepresent
its
private information.
Finally, the paper introduces a novel nonmtervention-profit participation constraint to take into account the
special relationship
between firms and policymakers
in trade; in this case, the
government
targets the efficient
firms with f>ositive subsidies, and eschews intervention altogether for the least efficient firms.
JEL
Classification Nos.:
F13, L51
Introduction
I.
This paper analyses the implications of incomplete information for strategic trade policy.
It
revisits in
incomplete information context the simple but powerful point made by Brander and S|>encer (1985)
oligopolistic industry, unilateral
The
analysis
government intervention can
motivated
is
by the observation
that
US
policymakers are often quite acute in trade policy. In the
shift rents
-
that in
an
an
by providing a strategic advantage.
informational
for example,
asymmetnes between firms and
when
firms petition for antidumping or
countervailing duty investigations, the investigators rely on proprietary information frequently provided by the
Even senior
petitioners.
officials within the
information used in mjury investigations
'Professional statisticians
mformation presented
'If
-
you look
at the
the
ITC has
and the only way you can get
definitely has the
power
targeting
is
to see the sort
Bovard ( 199 1),
is
that the
For instance. Commissioner Cass has
stated,
"
Another high-ranking ITC
official
has been quoted,
do business, we have industry analysts who get information from the industry
that information is to
most obvious
in the case
be on a friendly basis with the industry... The industry
comes out of
the
ITC (Bovard,
p.
217)."
The
potential for
of infant industries, where the cost structure of emerging
evolving, and possibly unique to each enterprise. But
may be compromised by
Commission express concern
of judgments drawn by most commissioners from the
p. 207).
to censor the information that
informational asymmetries
enterprises
to
International Trade
inadequate and biased.
would be appalled
to us (quoted in
way
is
US
it
also afflicts mature industries,
where
efficient
long-standing relationships between regulators and managers that serve to obscure
information from central authorities.
Ever since the inception of research on
strategic trade policy,
economists have been warning that the
informational requirements are enormous, due to the sensitivity of f>olicy recommendations to the particularities of
the market,
and unlikely
to
be met in practice.
'
This warning has been borne out in practice, as even attempts to
evaluate the effects of trade policies in oligopolistic industries ex post have encountered severe informational
'
See Grossman (1986) for a clear statement of
this concern.
1
So
obstacles.-
affect policy,
far,
however, there has been
research on the specific
ways
and on modifying policy recommendations to account for such
This paper
pomt.
little
is
a
first
step
m
addressmg these
issues, taking msights
that informationai failures
failures.
from regulation theory as
little
spillover from the incomplete-information regulation literature into trade theory.*
because trade policy differs from regulatory policy
One important
in several
is
m
power almost always reduces welfare,
the domestic firm raises domestic welfare
whenever
it
is at
This
starting
far there
is
m
part
important ways.
difference between trade and regulation
regulation the exercise of market
its
But so
Regulation theory has explored informationai asymmetries extensively in recent years.'
has been
might
the government's objective.
in trade the exercise
While
in
of market power by
the expense of foreign consumers.
In this paper,
we
highlight this difference by assuming the firms produce purely for export.
An
intervention
firm pairs.
important consideration in trade policy, unlike in regulation,
on the part of a foreign government. This
In this paper,
recent theoretical research
A
we compare domestic
calls for analysis
is
of games
the potential for countervailing
in contracts
among government-
surplus under unilateral and bilateral intervention, building on
on competition between principal-agent pairs with incomplete information.^
third important distinction involves the
the sufferance of the govenmient.
firm-government relationship.
The firm has no
recourse;
it
In regulation, the firm exists at
must accept regulation or
exit the industry.
contrast, in trade, firms are generally considered footloose, or capable of redeploying their assets in a
policy environment.
We
-
'
more
Moreover, firms frequently are themselves the instigators of interventionist trade
attempt to capture these features in a transparent framework.
See, for example. Dixit (1988), Baldwin and
Knigman
(1988), and
In
friendly
policies.
Our complete information benchmark
Krugman and Brainard
(1988).
This literature analyses relationships between regulatory authorities and regulated firms, interaction between
various interest groups and regulatory agencies, and regulatory hierarchies in the context of imperfect information.
In these models, attainment of the social optimum is usually compromised by the potential for allocative distortions
due to informational rent-seeking. See, for example. Baron and Myerson (1982) and Laffont and Tirole (1986 and
1993).
Exceptions include regulation of transfer pricing within multinationals (Prusa (1990), Raff (1991), and Gresik and
Nelson (1991)), and incomplete information between governments about domestic protectionist pressures (Feenstra
and Lewis (1991)).
*
'
See Gal-or (1988), Caillaud, Julien, and Picard (1990), Katz (1991), and Martimort (1992).
is
a simple trade policy designed to shift rents, along the lines of Brander-Spencer.
several
ways
to incorporate imperfect information
we
First,
We
modify
in
and highlight the essential features of trade identified above.
analyze the difference in the firm-government relationship between regulation and trade by
introducmg a novel participation constraint.
In the
Brander-Spencer analysis,
which
not clear whether the government
a standard zero-profit participation constraint with a nonintervention-profit
by comparing the optimal policy for
participation constraint,
it is
Here we distinguish between these two cases explicitly
uses the firm as a precommitment device, or the reverse.
effectively gives the firm residual rights of control.
Second, followmg Laffont and Tirole (1986), Gruenspecht (1988), and Neary (1991),
framework about the sharing of
rents
there
is
The government maximizes domestic
between the govenmient and firms.
surplus less the cost of net transfers to the finn.
In contrast to the analysis in both
solve for the optimal complete-information policy without restricting the
we
we assume
This resolves a crucial ambiguity in the Brander-Spencer perfect information
a cost of raising public fiinds.
Lastly,
framework
this
Neary and Gruenspecht, we
number of instruments.
incorporate asymmetric information in the form of adverse selection; firms are assumed to have
private information about their costs.
This paper
is
only a
However, even
information.
first
in the
step toward an understanding of strategic trade policy under incomplete
simple framework developed here, the presence of informational asymmetries
changes the results in several interesting ways.
intervention
is
undermmed by
profit functions, the
enhances
its
information.'
strategic advantage,
We
term
Second, a two-dimensional policy
is
precommitment
effect
of government
Lacking precise knowledge of the firms'
to the local firm in a
and preventing the firm from deriving distortionary rents from
The informational asymmetry induces a downward
precommitment and
that the
government faces a tradeoff between manipulating the payoffs
nonintervention-profit constraint.
"Local"
we show
the requirement of incentive compatibility.
distortion of the optimal subsidy,
way
its
that
private
which may be
with a zero-profit participation constraint, and to
severe enough to force the subsidy below
*
First,
with a
this the "screening" effect.
is
required to target both the distortion associated with strategic
that associated with informational rent-seeking.
used to denote the firm whose production
is
3
With asymmetric information, the range of
located within the jurisdiction of the trade authority.
tools available to policymakers
is
even more important than under complete infonnation because different tools
present the firms with different opportunities to extract distortionary informationaj rents.' Here, the optimal fwlicy
can be implemented as a menu of contracts specifying a per-unit subsidy and a lump-sum tax as a function of the
firm's reported cost.
The
publicly observable announcement of a subsidy serves as a credible
expand the firm's output, just as
m
Brander-S(>encer, while the
Third, the introduction of a rival interventionist
lump-sum
govemmeot
The
to
transfer serves as a screening device.
actually enhances the effectiveness of the
domestic government's intervention under incomplete mformation, rather than nullifying
case.
commitment
it
as
m the full-information
foreign agency problem mitigates the domestic agency problem, since the contract between the foreign
government and foreign firm reduces the temptation
for the domestic firm to misrepresent its private information.
This "competing contracts" effect reduces the "screening" distortion, and thus reinforces the precommitment effect,
rather than countervailing
Lastly,
we show
it
as under full information.
that
when
firms have residual rights of control, the optimal fxilicy
intervening for the least efficient firms. This yields the intuitively appealing result that only the
receive subsidies, and that subsidies are always nonnegative.
In this case, the likelihood
is
to refram
more
efficient firms
of intervention
for bilateral intervention than for unilateral intervention, because of the countervailing effect
from
is
greater
from competmg
contracts.
Section
firms,
II
develops the benchmark case with complete infonnation.
and the government's objective function.
It
describes the
It
game between
then specifies the firm's participation constramt for both the
nonintervention and zero-profit cases, and solves for the optimal unilateral and bilateral policies.
introduces an informational asymmetry
The
m the
form of adverse selection between each government and
firm's incentive compatibility constraint
is
defined, and the optimal policy
profit participation constramt for both umlateral
and
bilateral intervention.
is
Section
'
Obviously,
costlessly,
m
cbangmg
several of the central assumptions.
a world with unrestricted
lump-sum
by threatening a sufficiently large negative
It
transfers, the
transfer.
III
local firm.
its
derived for the case of a zero-
Section IV modifies the optimal
umlateral and bilateral policies to mcorporate the nomntervention-profit participation constramt. Section
the implications of
the
V
discusses
discusses the case where the firms' decision
government could induce
truthful revelation
variables are strategic complements, the robustness to changes in the specification of the informational asymmetry,
and the connection between contract observability, renegotiation, and precommitment.
n.
Section VI concludes.
Cotnplete Information
Game
i.
We
assuming
between the Finns
develop a simple international duopoly model, adopting the device used by Brander and Spencer of
that a single
(vastly simplified)
home
model of
This could be taken as a
firm and a single foreign firm export to a third market.
US
and
EC
air
frame manufacturers competing for exports
in the
Canadian market, for
instance.
The firms
is
assumed
take simultaneous quantity decisions in a one-stage
game with
differentiated products.
linear for the sake of simplicity:*
(1)
Piili><lp
where h denotes home, and
o
=
— 1i*^i
We
f foreign.
choice variables are strategic substitutes.
'"* when j=f and the reverse
restrict attention to the case
We
also
assume
that
where d
is
uniform density function
shift variable).
of
The
f(a)
on
realization
tractability,
[a,a\ (alternatively, the
of a
is
assumed
to
model specification permits
according to a
interpretation of
be publicly observable and verifiable
by per-unit subsidies imposed
in either market,
quantities simultaneously, after having observed the realization of a, and
The assumption of
a, distributed
a as a demand
in this section.
In the
both firms' profit functions are assumed to be affected symmetrically by the same shock.'
In addition, firms' profits are affected
^
negative, such that the firms'
b^-2d^>0.
Both firms have synunetric marginal costs given by a random variable,
interests
Demand
linear
demand
is
s,,
for
i
= h,f.
announced subsidies.
Firms choose
Quantities are
not important for the case with a zero-profit participation constraint.
nonintervention-profit participation case, however, the results are sensitive to the form of the
demand
In the
function.
We
discuss this further in Section IV.
'
V
Similar results
would be obtained by assuming only
for further details.
that the firms'
shocks are positively correlated.
See Section
These are straightforward
detennined as the Nash equilibnum of the Cournot game.'"
to
compute
the
as
intersectioD of the best response schedules:
Max^
(2)
i=h when j=f and the reverse
{Pf<li<Q)-<3*s^q,
associated with the unique equilibnum:
(3)
.^s^.o)
-
^^
a-o*
b*d
yielding profits of:
n,(SpSj,a) = -qj^s^j,a)^
(4)
Government Objective Function
ii.
We
next introduce a domestic government,
the budgetary cost of net transfers to the firm.
amount
The assumption of
c.
the sectoral intervention,
We
costly public funds
where
is
who
attempts to maximize the rents of the domestic firm less
assume
{s(ff),t((T)}
Given the
would simply impose a per-unit subsidy.
we assume
that the
s,
and a lump-sum reimbursement,
realization of costs and the
government faces no constraints
t,
way of
the
lump-sum
transfer.
of output does not enter into the contract directly, consistent with the precommitment mechanism.
It
imposes.
is
Moreover,
firm's output
'°
assumed
m
rational, so that
it is
it
straightforward to
addition to the subsidy,
it
If firms first
form of the
choose
profit function
m
its
optimal
The
level
However,
the
correctly anticipates the firms' optimal output responses to the subsidy
show
that if the
government were able
would choose the same
The assumption of Cournot competition and
(1983).
in
as a function of the realized cost
aimounced value of the subsidy, each firm chooses
After receiving profits, the firm reimburses the government by
government
by an
turns out that the optimal can be obtained with a two-dimensional contract of the form
stipulating a per-unit subsidy,
parameter, a.
output.
It
1
an ad hoc way of capturing the general equilibrium effects of
In contrast to the Neary and Gruenspecht models,
instrument choice.
of public funds exceeds
raising revenues incurs administrative costs or creates distortions in other sectors.
In the absence of such a cost, the government
Its
that the social cost
be justified as
m
Kreps and Scheinkmaim
and then compete with each other
capacities can be expressed as
on the domestic
level of output as the firm.
strategic substitutes can
their production capacities,
to contract
Cournot competition
m
in prices, the
quantities.
reduced
Thus,
we
can express the objective function of the domestic government as the domestic firm's rents less
the budgetary cost of net transfers to the firm:
Max ,^(,,^^„
(5)
where
earned by the
U^(ff) is the rent
The assumption of
home
t/^(a) -(1 *c)[5^(o)<7,(a) -f^Co)]
firm:"
costly public funds can be justified in a variety of ways.
It is
consistent with the
assumption that the government attempts to minimise a weighted social welfare function, in which the weight put
on the government's budget,
into the
1,
exceeds that put on the firm's rent, w.'^
framework presented above simply by
Alternatively,
it
may be more
setting
balance
'
'
We
its
to
= 1 +c.
persuasive to interpret the assumption of costly public funds as capturing the
general equilibrium consequences of sectoral targeting.
government seek
I/w
This assumption could be incorporated
maximise domestic
According to
this interpretation,
both the domestic firm and
profits, but their objectives differ insofar as the
govenmient also has
budget in expectation. This interpretation would yield the same objective function as equation
mclude
Sf
as a placeholder
(S),
to
with
whenever we are defining general functional forms m order to avoid repeating
is
under unilateral intervention, and the optimal foreign subsidy
equations, with the understanding that this term
under
'*
bilateral intervention.
Caillaud
et. al.
(1985) discuss the relationship between the assumption of costly public funds and a weighted
social welfare function.
on the expected budget constraint, which
c interpreted as the multiplier
independent of
aP
Participation Constraint
iii.
There
is
an ambiguity
incomplete information
is
Brander-Spencer, fuU-informatioo model that turns out to be
in the
Although
introduced.
of a firm can serve as a precommitment device,
the firm as a
precommitment device, or the
clear in their
it is
it is
model
that
not clear whether this
Moreover,
reverse.
With incomplete mformation, however,
matter.'''
is
this distinction
in the
is
critical
once
government mtervention on behalf
achieved by the government taking
B-S model,
this distinction
becomes important, since firm
does not
interests conflict
with government interests over mformational rents.
A number
game on
agent to play a
"
B.
To
of papers
mdustnal organization analyze the pnncipal's
budget deficit
its
precommit by "hiring" an
that the
government has
in the targeted sector,
which we denote
overall resource constraint (as, for mstance, in Dixit-Grossman (1984)), the government
an opportunity cost, C(B),
OO,
ability to
These papers effectively assume
the pnncipal's behalf."
see this, supf)ose the government chooses the size of
Assunung an
where
m
C" >0.
m other
sectors of any funds that
The government's
objective
is
to
it
maximize the firm's
minimise the opportunity cost to other sectors of the budget
mcurs
allocates to the targeted sector under consideration,
profit net of subsidy
payments, and
deficit:
o
Max^^^J^,^ [[^^(s^(.a)^/,a),a)-s^(a)q^is^ia)^/,a),a)]/[o)da-C(B)
a.
subject to
(where E,
the expectation operator over a), subject to the firm's incentive and participation constraints.
is
LaGrangean of
this
program
The
is:
o
L
=
f[U,(o)-{l*c){s,{a)q^(s,(oUjia),a)-t,(o)mo)da-C(B)*cB
a.
where
c
is
the multiplier
on the budget constraint (c>0), which
is
derived endogenously from the
first
order
conditions:
c = C'(B)
B
Then our formulation
'*
However,
is
just a reduced
this distinction is
firms
is
move
in the spirit
for this
more complicated problem.
important in a full-information context
(1988) or Carmichael (1987), or
constramt
= E,(5^(a)4^(V)^/<'),a)-r^(a))
form
when
there are fixed costs, as
of these models,
all
of which
shift the
before governments.
" See Tirole (1988)
for a clear exposition of this literature.
8
when
firms play Bertrand, as in Gruenspecht
m Brainard (1990). The nonintervention participation
balance of power in favor of firms by assuming that
complete residual rights of control;
is
wholly appropriate
this
in regulation,
it
can induce the firm to participate as long as the firm breaks even."
where
assumption can be incorporated
the firm has
This
no recourse other than exiting. In the model developed here,
in a zero-profit participation constraint
(ZPC):
U^(a)iO
(6)
In trade,
behalf.
however,
it
may be more
accurate to think of firms inducing governments to intervene on their
This assumption more nearly approximates the footloose character of firms in traded goods industries, or
the trade policy process in {wlitical systems
where firms
formalize this by assuming that the firm can refuse to participate
if
it
We
described in the introduction.
initiate intervention, as
would earn
less
under intervention than
in the
absence of intervention. Define profits when neither government intervenes under unilateral intervention as K^a),
and profits when the
rival
government alone imposes the optimal subsidy under
^rC")
Then
=
Sj=^ for m=u\
-t«i(0'S>"'^^^
s.=sfa) for
the domestic firm's nonintervention-profit participation constraint
f^)
this is a fairly
plausible results, since
novel approach
it
in principal-agent theory,
limits the size of
lump-sum
(NPC)
is
m=b
expressed:
for m=u,b
t/j{o)2Ji"(o)
Although
bilateral intervention as 'K^(a):
it
has the additional attraction that
transfer that the
government
it
leads to
more
extracts.
There are a few alternative interpretations of the formulation of the govenunent's problem with the NPC.
It
can be interpreted in more traditional terms as a Hicks-Kaldor social welfare function, where there
redistribution.
Alternatively, in a setting
where firms
initiate protection, the transfer
if
"
Under
this scenario,
firms expect to do at least as well under intervention as in the free market equilibrium will they
investment in access.
In Gal-Or, with
asymmetric information, principals must leave a rent to the firm.
9
a cost to
can be thought of as a fixed
cost to gaining access to policymakers, and subsidy payments as the return to gaining access.
only
is
make
the
Intervention Eguilihnum with Complete Information
IV.
We
solve for the optimal policy under complete mformation as a benchmark.
govermneat establishes a per-unit subsidy and lump-sum reimbursement
In this situation, the
to solve (S) subject to participation
constraint (6) or (7), after observing the realization of a.
It is
straightforward to prove that the participation constraint must bind for each realization of costs in the
complete information case.
raise welfare
clearly this
to the contrary,
If,
it
did not bind for some values of a, then
would not have been an optimum
(8)
p>ossible to
in the first place.
i
under intervention regime
transfer
is set
i
down,
for all values of
under intervention regime
(')
m
Here the transfer leaves the firm
just indifferent
r.
In the case of the
NPC
for
m=uM
case as
(J(<j):
between
define the optimal
i=h/
between nonintervention and intervention, for
all
values of a.
In
a decreasing, quadratic function of a.
is
Differentiating the objective function with respect to
on the optimal subsidy
ZPC
as (^a):
t^''(a)=nJ[sjia)^jia),a)-Kl'(a)
both cases, the transfer
in the
just equal to the firm's subsidized profits, leaving the firm exactly indifferent
participating under intervention and shutting
transfer for firm
m
for m=u,b, i=h/
r;"(o)=7:.(5,(a)^/a),o)
The lump-sum
v*"/
would be
by reducmg the firm's rents by a small amount, without violating the participation constraint. But then
Define the optimal lump-sum transfer for firm
lump-sum
it
s.,(a)
yields the
same necessary and
sufficient condition
for either participation constraint:
i=h when
5,(ff)=
Settmg s^a) equal to zero
in the unilateral case yields the
(H)
I
=f and the reverse
following expression for the optimal
s;'(o)=(a-o)-
home
subsidy:
dHb*d)
Hb^-Td^)
The optimal umlateral subsidy
is
a linear, decreasing function of a.
10
Notice that the subsidy
is
positive for
all
values
of the cost parameter, implying that targeting
the domestic firm to
This
to contract.
strategic
is
expand
its
is
efficient
over the entire interval." The optimal subsidy induces
output to the Stackelberg leadership level, and corresjwndingly, the foreign firm
The government
precisely the result derived in Brander-Spencer.
advantage because
it
has
full
precommitment power with
is
able to give
its
firm a
information and no coimtervailing
full
intervention.
The
precommit.
When
ability
When
it
of the domestic government to raise domestic surplus depends
intervenes unilaterally, the government enables
on
its
ability to
firm to commit to an expanded output level.
both govenmients intervene simultaneously, neither government can give
precommitment.
its
firm an advantage through
In this case, the optimal subsidies are symmetric in equilibrium:
(12)
The
its
critically
'^
,;»(«) = s-\o) = (a-o)
of both firms above the free-market
bilateral subsidies raise the equilibrium quantities
surplus in both economies falls relative to the free market equilibrium.
although welfare in both countries
govenmient anticipates
that
its
is
higher
when
i=h/
There
is
Coumot
level,
and
thus a classic prisoner's dilemma:
neither govenmient intervenes, both intervene because each
rival will intervene if
it
does not.
Notice that in both the bilateral and imilateral case, the form of the participation constraint affects only the
sharing of surplus between the firm and the government through the transfer.
It
has no effect on the equilibrium
quantities or aggregate surplus.
Next we show
in.
that the introduction
of incomplete information changes these results significantly.
Adverse Selection
Returning to the case of unilateral intervention,
The
distribution of
a
is
realization of their costs.
" Assuming
common knowledge
While each firm
is
for both
fully
we
introduce incomplete information about the level of a.
govenunents and firms, but only firms know the true
informed about both firms' profit functions, the govenmient
that a-<j> 0.
11
is
Thjs would be the case, for instance,
not able to observe the effect of the shock on either firm's profits.
if air
frame manufacturers had precise mformation about the effect of an mput price shock or a demand shock on their
own
profits,
and (assunung similar technology) on those of
their nvals, but the
domestic government had access
oniy to the consolidated financial statements required for tax purposes.
We assume
that the
government
is
not able to contract on other informative variables, such as the foreign
firm's output or prices, either because the sales terms are secret, or because such contracts could not be enforced
due
Since the govenmient does not observe or cannot verify the realization of a,
to venfiability problems.'*
profits, foreign output, or prices,
it
bases
policy on a report from the firm,
its
a.
The government
of per-unit subsidies and lump-sum transfers, conditional on the firm's reported costs,
We
further
assume
that the contracts are publicly observable,
information, the potential for renegotiation has no effect.
in
effects
and asymmetric mformation
{S|,{<^,t^(o)}.
and cannot be renegotiated. With complete
we
We
rule
it
out in order to distinguish clearly between
discuss the implications of allowing renegotiation
Section V.
Such an assumption can be
justified
establish a reputation for nonrenegotiation.
repeated
game with
industries.^
Alternatively, the
First,
it
may be
Reputation would be important
govenunent and/or the firm might have an
were incurred
" Clearly,
variables
if sufficient
knowledge of
on several counts.
if
a firm in a single industry," or in several one-shot
large fixed investment
'*
effects.
menu
With incomplete information, however, renegotiation
through secret contracts can have precommitment value. Here,
precommitment
offers a
for each
interest to
the government were engaged in a
games with finns
in a
variety of
interest in avoiding renegotiation if a
roimd of negotiation.
were observable and
their relation to the
government's
in the
verifiable, the
government could use them
in
conjunction with
unobserved variable to solve the information problem.
Ratchet effects from sequential contract offers can be ruled out by assuming that the firm's costs are drawn
mdependently each period.
In a
long-term contracts because there
^ Models
dynamic framework of
is
some
this nature, the
government
is
probability implicit in the discount rate that
not credibly able to write
it
will not get reelected.
along these lines assume that the government's time horizon exceeds that of firms, either because the
government
is
longer-lived, as in Fudenberg, Levine (1989), or, as
discount rate, and the
game between
the
government and firms
12
is
m
Schmidt (1991), because
of "conflicting
interests.
it
has a lower
Incentive Compatibility Constraint
i.
With incomplete infonnation, the optimal fwlicy must
truthful
m
revelation,
constraint,
Suppose
information.
addition to the participation constraint.
useful to
it is
satisfy
an incentive compatibility constraint to induce
Before specifying the mcentive compatibility
examine firm behavior when faced with the optimal full-information policy, given private
in the unilateral case that the
government assigns the full-information contract {s^ff),t^(o)}
A
for
w = n,z,
report
The
a,
when
the firm reports
given policy
its
while
in the
in the
NPC
a.
Define the value
to the
domestic firm with true costs a of making
{s^((^,t4(o)}, as U^Cff.ff):
firm's optimal choice of report
Then
costs as
ZPC
case,
is
A
the value of a that
A
maximizes
case, the firm's optimal report
\Jjia,a).
is:
it is:
-
a=
0*0 ^
>a
2
In both cases, the firm optimizes
by misrepresenting
its
costs as higher than the true value.
decrease in the lump-sum tax associated with higher levels of reported costs
from the decrease
in the value
of the subsidy, given that true costs are lower.
similar results obtain in the case of bilateral intervention.
it
more than
As
is
common
It is
This
is
because the
offsets the effect
straightforward to
on
profits
show
that
in the imperfect information literature,
will turn out that the transfer plays a critical role as a screening device in the presence of incentive compatibility
problems.
Under imperfect information, any proposed policy has
the firm's report.
The
to satisfy an incentive compatibility requirement
revelation principle enables us to restrict attention to the class of direct
13
mechanisms
on
for
which
truthful revelation
is
Thus:
optimal.-'
o
Then \]\a)
is
argmax
e
simply the firm's informational rent when
U^(d,a)
^
mcentive compatibility constramt
its
is
satisfied:
f/»(o)«f/,(o.o)
By
restricting attention to equilibria for
which contracts are piecewise-differentiable, we can express the
first
order
condition for the firm's revelation problem as:
Va
(14)
da
Combimng
as.
(14) and the definition of U^(.) yields:
——^
5^(0)
(15)
da
And
da
.
.
^
.—
.
*>
^
^
= -9»(^A('')'^/<')'<')7i--r
"
r -
(i
f,
—
^/"^
^-77-^^
(^_j)
the local second order conditions are satisfied for:
r- ,0
^^^11.^^
(16)
da
The
da
{b*d)
\
,
justification for the restriction to piecewise differentiable subsidies is straightforward.
A
standard
revealed preference argument establishes that the optimal subsidy, s^{a), must be decreasing to be incentive-
compatible, given a differentiable foreign government subsidy, s^a), such that:^
(17)
^
1-
(b*d)
The condition
^'
^^'Ko
da
that s^(ff) is decreasing in turn implies that
Myerson (1982) shows
\(a)
is
that in a bilateral principal-agent structure,
piecewise differentiable almost everywhere.
it is
a Nash equilibrium in reports for the two
agents to reveal their private information truthfully, as long as collusion between the two agents
ref)orting state
of the game, and each agent
this implies that the
domestic firm chooses
is
is
ruled out in the
associated uniquely with one principal. In the context considered here,
its
optimal repwrt knowing that the foreign firm reveals truthfully under
bilateral intervention.
^ Martimort (1992) provides a more general justification for the assumption that
He shows that when T(Sfc(ff),sXff),ff) satisfies an aggregation property, such that:
the agent's rent
is
decreasing.
ait,(.)/&
=
as.
dn^QIda
the incentive problems of the rival prmcipal-agent pair can be treated analogously to independent hierarchies, for
which
the agent's rent
must decrease
in a,
and impiementatibility implies decreasing subsidies.
14
However,
it
should be noted that there
may
which these conditions on
exist nondifferentiable equilibria for
s,(ff)
do
not hold.
Optimal Policy with Unilateral Intervention
ii.
The government chooses
By
its
we
substituting for the transfer,
^^^^
*''"..(.).£/.(.)
policy to maximize domestic surplus, less the cost of net transfers to the firm.
can express the objective function in terms of the subsidy and the firm's rent:^
/
k^»(<')^/<»).'')-^*(«)«A(<')'^/<').<')-^^*«')]«:<')^''
subject to the incentive compatibility conditions in equations (14) and (15), and the
ZPC
in equation (6).
We
first
solve for the optimal policy ignoring the second order conditions in (16), and then check to ensure that they are
indeed satisfied at the optimum.
The government's problem can
thus be expressed as the Hamiltonian:
—
^i{s,,(o)^Jia),a)-s^f.o)q^^.s^(a)^Jia),a)-—
-U^(.a)]f[<})
(19)
which
is
concave
in sji.)
for the unilateral case,
and
and
Uji.),
and where X(a)
is
the multiplier
on the incentive
constraint.
Setting
s^a)=0
differentiating with respect to LP* yields the first order condition:
iM£)=_L.y^o)
(20)
da
1+c
Recalling that firms are tempted to overreport the value of a
in order to save
efficient type if
on the
it
transfer to the government,
binds for any type, U^(o)=0.
we
when
faced with the fiill-infonnation optimal policy,
expect the participation constraint to bind for the least
This implies that X(a) = 0, which enables us to solve for the
multiplier:
^
Tb(.)-Uh(.)
is
substituted for
to a single control variable.
t^(.),
based on the definition of U^(.), in order to simplify the government's problem
This substitution
is
commonly employed
15
in the regulation literature.
i(a)=-^ [Aa)do-
(21)
l*c
Differentiating with respHJct to
s^(cr)
J^
(l*c)(a-2j
yields the following expression for the optimal unilateral subsidy:
Thus, the optimal subsidy
linear
is
and decreasing in
a,
and
is
^**'^
^
for a"=-
5;(aX"(a)-a'(a-fl)
(22)
"^"-^
distorted
below the
full -information
value of a except the most efficient by an amount that mcreases in the distance from
a.
subsidy at every
In the presence
of
incomplete mformation, the government must distort the optimal contract in order to mduce the domestic firm to
produce efficiently consistent with
its
true costs.
Notice that for a sufficiently great divergence between a and
the least efficient firms.
Call the value at
(23)
a"
o
may
the
which
fall
home
on
either side of
a.
Define a
''
a, the
subsidy actually becomes negative for
this takes place a":
d^
,(l+c)
(a-g)=(a-a)I
= min{<j",
a}.
For the range
aKa",
the effect of the subsidy
is
to raise
quantity above the free market level, but by less than the full-information subsidy, and to discourage
foreign production relative to the free market equilibrium, but by less than the full-information subsidy:
with equality holding
is
to reduce
home
at a.
For the range
in
which the subsidy becomes a
tax,
a "<
<T<.a, the effect
of intervention
output relative to the free market equilibrium, which induces an expansion in foreign output.
Thus, for sufficiently high values of the cost parameter, the screemng effect actually dommates the precommitmeat
effect,
and optimal policy serves to strategically disadvantage the home firm.
In either case, the
government chooses a schedule of
transfers that gives higher rents to
low cost firms as
an inducement to produce efficiently, and leaves other types just indifferent between operating under intervention
and shutting down.
In effect, the optimal policy trades off the external objective of strengthening the domestic
firm's strategic advantage against the internal objective of minimizing allocative distortions associated with the
domestic firm's informational rent-seeking.
Clearly, the optimal subsidy satisfies the local second order conditions for truthful revelation in eqiuUion
(16).
Moreover, the form of the optimal contract
-
a subsidy that
16
is
piecewise linear
in a,
and a transfer
that is
piecewise quadratic in a
-
ensures that the local second order conditions are sufficient for a global
maximum.
Optimal Policy with Bilateral Intervention
hi.
In the bilateral case, each government
is
assumed
to
choose a menu of transfers and subsidies as a function
A
of the local firm's cost report,
a.
The governments announce
their trade policies simultaneously.
assumed reciprocally observable, but nonrenegotiable. The two firms, having observed the
governments' policy announcements, simultaneously choose their report
decisions.
to the
and both
government, and make their output
to
maximize domestic surplus
less the cost
of net transfers to the local firm,
subject to the incentive compatibility and participation constraints of the local firm.
the truthful revelation restriction can be applied to both firms.
first
realization of a
Again, neither govenmient can make the subsidy contingent on the rival firm's output, profits, or prices.
Both governments are assumed
the
Subsidies are
and second order conditions described
the Hamiltonian
defmed
condition for which
is
the condition
derive the corresponding
home
symmetric subsidies indeed
this
and (16) apply to each of the two firms, and
each govenmient separately.
As mentioned
in the discussion
approach depends on piecewise differentiability of %(.), a sufficient
on the foreign subsidy
subsidy,
in footnote 21,
proceed here as in the unilateral case, so that
in equations (14), (IS),
in equation (19) applies to
of the incentive compatibility conditions,
We
As explained
s^(.), in
in equation (17).
Assuming
the symmetric equilibrium, and then
this condition holds,
go back
to
check
that the
satisfy equation (17).
Differentiating each government's objective function with respect to U^(a) yields the condition
multiplier in equation (19).
we
With the
rent decreasing in a, the constraint
transversality condition, \(a), thus implies that equation (21) holds.
must bind
a
at
Differentiating the
if
it
on the
binds anywhere.
home government
The
objective
function with respect to s^{a) yields:
ib*d))b^
*
b(b*d)
(W)\a-ii/.
ib*d)
Proceeding similarly for the foreign government yields an analogous equation.
da
)
The symmetric equilibrium
is
obtained by solving both equations simultaneously, yielding a differential equation for the symmetric subsidy, with
a singularity at
a=
ff.
In the case analysed here,
where d < 0,
17
there exists a imique solution,
which can be expressed
in
terms of the full-information optimal subsidy
(^)
a'=
s,(a)=s, (o)-a''(o-2)
straightforward to verify that
It is
the optimal subsidy
linear
is
optimum by an amount
and decreasing
may be
sufficient to
case as
in the bilateral
is
positive, since
in a,
;
d<0
and lr-2d*>0.
As
and distorted downward
that increases in (a-g) for all values
with the screening effect
subsidy
a^, is
.u
as:
relative to the
And
of a on [a.oj.^
push the subsidy below
0.
in the unilateral case,
we
find that
complete mformation
again, the distortion associated
Define the cutoff value of a for which the
o^:
(25)
o* =
(a-2)=(a-a)
a
I
a\b^-d^-db))
Again, a*
o<a^,
may
the
fall
on
either side of
symmetnc
a,
depending on the spread of the distribution. Define a ^=iiun{a^,d).
subsidies are positive, and both firms expand their output relative to the free market
equilibrium, but by less than under complete mformation.
and both firms contract output relative
However, with
(although
it
to the free
market equilibrium.
bilateral intervention, there is
does not eliminate
it
altogether).
For a^<a<(r, the symmetric subsidies are negative,
an additional effect that countervails the screening effect
The competition
in contracts
governments loosens each firm's incentive compatibility constraint, due
bilateral
equations (23) and (25) reveals that the range of types for which the subsidy
bilateral intervention, or o"
< a*.
Thus,
^ See Martimort (1992),
^
•^
It
Indeed, from an ex post point of view,
for a
is
precommitment
information. Asymmetric information mitigates the prisoner's dilemma, and
tax.
more complete analysis of the
it
impact of the
positive
is at
least as great
eliminate
may appear
it
on the
solution, including the case
This result depends on the assumption of strategic substitutes.
18
under
of incomplete
interval
where
that intervention is not the
where d>0.
should be noted that the lineanty of the solution derives from the structure of the model;
V.
m
the introduction of a rival
effect in the presence
may
rival
and unilateral intervention
m sharp contrast to the complete-information case,
contract between the foreign government and firm reinforces the
becomes a
between the incompletely informed
to the expansionary
Comparison of the threshold values of a under
subsidy on rival output.^
the subsidy
For
The case of complements
is
it is
not assumed.
discussed
m Section
dominant strategy.
It is
straightforward to verify the approach taken here by checking the second order conditions on each
firm's problem.
Each firm
quadratic in a.
condition
is
The expressions
is
for the optimal subsidies are linear in a, implying that the optimal transfers are
thus maximizing a quadratic function of a,
sufficient for global optimality.
second order condition in equation (16)
IV.
ZPC.
far,
we have been
decreasing
is
second order
in a, the local
is satisfied.
The assumption
effectively treating firms as the agents of their respective governments,
that firms are willing to operate
rents leads to the conclusion that
as a
Since the optimal symmetric subsidy
that the local
Nonintervention-profit Constraint
So
the
which ensures
In this case, intervention
on the
under intervention as long as they make nonnegative
asymmetric information undermines the government's
precommitment device. Indeed, the
effect
part of a rival
may be
by adopting
ability to use the local firm
so extreme that intervention creates a strategic disadvantage.
government can have the beneficial
effect
of loosening the incentive
compatibility constraint of the local firm.
As discussed above, however,
residual rights
in a trade context,
it
may be more
of control, or of having additional bargaining power vis-a-vis the government.
can be incorporated by adopting the
compatible mechanism that does
NPC
at
in
equation (7). In effect, with the
least as
more
accurate to view the firm as having
NPC, we attempt
well as nonintervention (which
is
itself
This consideration
to find
an incentive-
an incentive-compatible
mechanism)."
i.
To
Government Objective
isolate the part
This
V^(ff)= U^(ff)-T^(r).
^
Nonintervention
is
of the firm's rent
new
state variable
also characterized
govemments, which would be important
if
that accrues to
it
because of asymmetric information,
we
define
evolves according to the equation:
by the absence of any need for communication between firms and
were admitted, since communication provides
the potential for collusion
scope for collusion.
19
(26)
-KsAo)
da
The government's program
H
is
1-
for
{b-d)\b*d)
then:
{a^j(o),K,(a),ti(a),X(o)) =
/o)^7i^(5^(a)^^o),a)-nj^(0^^a),o)-5/o)<7^(5;^(a)Ay(o),a))---^^'j(o)
,27x
d
-l(o)J&j(a)l-
where
K'
do
(b*d}
X((t) is the
on the incentive
multiplier
constraint, and ^(ff)
is
^/f')
->i(a)K,(a)
the multiplier
on the participation constraint
(and the local incentive compatibility conditions are assumed to apply only to those values of a for which the optimal
subsidy
differentiable).
is
It
is
reservation value
is
m
common
assumed
is
evident from the
prmcipal-agent theory to assume that the participation constraint
NPC
in
commonly, mversely
either constant, or, less
Equation
(7),
from the
ZPC
we
case,
government should reduce the reward
\a the distance
government
from
to refrain
ii.
However,
a.
exogenous; the
Here, however, as
related to the rent.
both the rent and the reservation profits are decreasmg in a, so that
not obvious where the participation constraint binds (or equivalently, which subset of firms
Intuitively,
is
is
it is
just indifferent).^
expect that efficient firms are tempted to claim higher costs, so that the
to cheating
by
in contrast to the
from intervening
distorting the subsidy
ZPC
case, with the
downward by an amount
NPC
it
turns out that
it is
that increases
optimal for the
for sufficiently high cost firms.
Unilateral Policy
Solving (27) for the optimal policy in the case of umlateral mtervention subject to the >fPC yields the
following proposition:
*
Lewis and Sappington (1989) were the first to analyze this type of problem in their study of countervailing
work more closely related to the model presented here, Faggart (1991) modifies the Baron-Myerson
model to mcorporate a constraint that regulation must leave the firm no worse off than under monopoly. The results
incentives. In
are broadly consistent with ours
that with general inverse
(we were unaware of them
demand
nonmtervention always obtains for the highest cost
elasticity
demand, there
is
until after
our analysis was completed).
Faggart finds
functions there are alternating regimes of intervention and nonintervention, and
levels.
In the cases of linear (analysed here) and constant
a continuous range of intervention followed by a continuous range of nonintervention,
similar to our findings.
20
Proposition
1
Defuie
and
cf,
s'Xa),
as in equations (22)
"
cr
and
nonintervention-profit constraint under unilateral intervention
s'(a)
(28)
the optimal subsidy that satisfies the
given by:
is
on
[sL.o'i
on
(d",o],
s'(a)
,
Proof
Appendix
Even with a stronger
1
participation constraint, asymmetric information distorts subsidies
weakens the precommitment
the
Then
(23).
NPC,
IS
it
effect
of intervention.
However, when firms are given
never optimal to tax the output of even the
necessitate a positive
lump-sum
least efficient firms.
result that the optimal incentive-compatible policy is to subsidise the
intervention for the least efficient firms, in order to gain the
maximal
most
and thus
residual rights of control with
A
per-unit tax,
transfer in order to satisfy the participation constraint,
compatibility, encouraging efficient firms to report costs above their true value.
downward,
The IVPC
would
violate incentive
thus yields the appealing
efficient firms most,
strategic benefits
which would
and
to
eschew
from intervention, without
inducing misrepresentation.
Bilateral Policy
iii.
Bilateral intervention
similar to the
ZPC.
First, the
mtroduces additional effects from the competition between contracts with the NPC,
competition in contracts weakens the participation constraint, which affects the level
of the lump-sum transfer, but not the size of the subsidy.
Second,
it
moderates the effect of the distortion due to
asymmetric information, by loosening the incentive constraint (again, assuming strategic substitutes and the foreign
subsidy
is
decreasing
precommitment
But with the
in
a).
Similar to the
effect, leading to
NPC,
case,
the effect of competing
contracts
reinforces
the
higher output, but does not fully offset the asymmetric information distortion.
as in the unilateral case, there
that the per-unit subsidy is
ZPC
is
a range of nonintervention under bilateral intervention, such
nonnegative over the entire interval.
Proposition 2
Define
s''(<t),
a
'',
and a* as
in
equations (24) and (25). Then the optimal bilateral subsidy that satisfies the
21
NPC
is
given by:
s^a)
(29)
on [sLO^'
i»(a)=|
on (d*,ol,
,
Appendix 2
Proof
An
is
important corollary
is that
the introduction of the nvaJ contract broadens the set of efficient firms that
targeted in equilibnum, because the competition in contracts loosens the incentive compatibility constraint.
Corollary
a''<a^
for
a"<a
Appendix 2
Proof
Recall in the full-information case that there
that the
dominant strategy
is
always intervention.
is
a prisoner's
dilemma
In sharp contrast,
structure to the bilateral
game, such
under incomplete mformation with a strong
participation constraint, bilateral nonintervention for the highest cost firms obtains endogenously as the
equilibrium of the
game
in contracts.
For more
efficient firms, both
Nash
governments intervene with positive subsidies
in equilibrium, similar to the complete information case, but at a lower level of subsidies.
Similar to the analysis with the
that the local
second order conditions are
with the
NPC,
V.
Alternative Assumptions
i.
so the proof
is
in
both the unilateral and bilateral cases
it
is
optimum. Global optimality
is
more complicated
satisfied at the
straightforward to verify
to verify
elaborated in Appendix 3.
Renegotiation
Throughout,
As long
ZPC
we have assumed
as renegotiation
is
that renegotiation is impossible.
ruled out, observable contracts can
do no
This assumption
if secret
by no means innocuous.
better than unobservable initial contracts.
a result, the government's ability to precommit by delegating action to the firm
asymmetry. However,
is
is
As
compromised by the informational
renegotiation between the government and the firm were permitted after the private
22
information had been realized,
that obtained
would be possible
it
for the
He shows
of uncertainty.
mformation,
it
when
that
secret renegotiation
committing the domestic firm
is
to sufficiently
possible.
secret ex post renegotiation,
and
reservation utility level in such a
to the initial contract,
such that each firm
is
is
jxjssible after the agent has learned its private
to contracts with inefficient ex post
high output to discourage foreign production, as long as there
is
is
a
realized; such a contract is credible because of the
in information.
Caillaud, Julien, and Picard (1990)
rents
a contracting stage preceding the
For instance, the principal could sign a public contract
potential for secret renegotiation after the private information
commits
game with
commit ex ante
possible and optimal for the prmcipal to
is
outcomes where no pareto improvement
asymmetry
some precommitment power above
by delegation.
Dewatrip>ont (1988) considers renegotiation in a umlateral
realization
to capture
government
is at least
make a
strategic substitutes, the
way
that
knowing
it is
that
committed
it
With
similar point in a bilateral principal-agent framework.
observed
to a
initial
contracts serve to alter each agent's
more aggressive output
level.
Each principal publicly
will be renegotiated after the private information has been realized
as well off as under the observed initial contract,
and surplus net of informational
higher.
ii.
The
Alternative Information Structure
results presented here are robust to other specifications
distributions other than the uniform that satisfy the
similar results, as
would
monotonic hazard
of the information structure.
rate property {d\F((j)/f(a)]/da> 0),
would
yield
a formulation in which costs are imperfectly correlated across firms (as, for example, in
Gal-Or (1988)). Alternatively, asymmetric models could be developed
firm's costs differently.
For instance,
For instance, domestic costs could
differ
in
which the uncertainty could
from foreign by a
factor of (1 +t),
affect each
where
t
might
represent a transport cost.^
^ An
interesting extension
would be
to
model each government as having access
to a different type
of information
about the local firm, which would correspond to different political frameworks, or different mechanisms of control.
23
Consumption
lii.
We
have imposed the
interaction between
at
Home
artificial
precommitment
convention
effects
that both firms are
and asymmetnc information from complications associated with
consumer surplus. An obvious extension would incorporate production
In this case,
downward
the mformational
if
exporting to a third market, to isolate the
asymmetry applied
to
for the
home market
as well as for export.
both types of production, the government would distort
subsidies on the firm's total production in order to minimize allocative distortions from informational
rent-seeking, while using the reimbursement as a screemng device.
be accomplished
in these
circumstances by using two distinct subsidies.
compnsed of two marginal
We
it is
possible that screening could
leave the investigation of policies
tools in the context of incomplete information for future research,
due
to its
complexity.
Complements
Strategic
iv.
Alternatively,
Eaton and Grossman (1986) show
that
with
full
information, the optimal policy
firm's decision variables are strategic complements, whereas
difference in policy prescriptions
is
it is
is
an export tax
when
a subsidy in the case of strategic substitutes.
the
The
attributable to the difference in sign of the cross-partial second derivative. This
difference in the sign of the optimal policy in the case of complements carries over to incomplete information, but
here
it
OF>erates
through the firms' incentive compatibility constraints.
Martimort (1992) analyses strategic complements (d>0)
He shows
with competing principal-agent pairs.
equilibrium, which makes
However, by assuming a
is
difficult to
linear
is
demand
the range of types
changes.
* The
As
is
is
framework
a continuum of symmetric separating subsidies in
unilateral
and
bilateral intervention.-"
function and a uniform distribution, as in the model developed above,
This
set includes in particular
one equilibrium
a linear fimction of a, which can be computed using the approach in Section
notable because the optimal policy
when
is
compare equilibrium outcomes under
possible to compute the set of equilibria explicitly.
optimal subsidy
is
it
there
in a general incomplete information
robust to
some modifications of
III.
in
it
which the
This equilibrium
the informational structure.
broadened by increasing a while maintaining a uniform distribution, the
set
For instance,
of equilibria
the range broadens, only the linear equilibrium subsidies continue to be decreasing in a, hence
lack of uniqueness
is
attributable to the assumption of
24
symmetry.
remaining incentive-compatible, and thus an equilibrium.
This unique linear solution
is
a tax for both the unilateral and bilateral intervention cases.
Companng
these
linear policies to the optimal policies under full information esUblishes that the optimal tax is distorted
upwards
under incomplete information, because of the incentive compatibility constraint. Thus, the optimal policy
is
restrictive relative to the full-information case.
bilateral intervention,
overly
In contrast to the substitute case with incomplete information
and
with complements the governments' contracts reinforce rather than coimtervail each other,
because they raise the rival firm's temptation to cheat. Each government attempts to reduce the local firm's output,
but the resulting contraction exacerbates the rival firm's incentive constraint.
production
image of
is
restricted
more severely under
that in the case
As a
bilateral than unilateral intervention.
result, in the linear equilibrium,
The
of substitutes; with complements, each firm's contraction
is
intuition for this is the mirror
met by reciprocal contraction,
thus exacerbating rather than mitigating the incentive compatibility constraints.
VI.
Conclusion
This paper
information
is
is
likely to
far
from conclusive; imderstanding
be a complex
task, requiring a variety
strategic trade policy in the context
of asymmetric
of models to address a number of different questions.
Nonetheless, the simple model developed above suggests several interesting insights.
First,
the effect of the informational
govenmient intervention. Second,
asymmetry
is
to lessen the
in contrast to the full-information case, the introduction
govenmient reinforces rather than countervails the precommitment
offset the distortion
informed
precommitment
effect,
of a
effect
of imilateral
rival mterventionist
although not sufficiently to completely
from the informational asymmetry. This mitigates the prisoner's dilemma associated with
bilateral intervention,
and may eliminate
it
informational asymmetry distorts the optimal subsidy
altogether for sufficiently high levels of costs.
downward
in all cases,
and
this distortion
to require a tax rather than a subsidy for the least efficient firms, given a zero-profit constraint.
participation constraint gives the firm residual rights of control, the
25
fully-
Third, the
may be
sufficient
Fourth,
when
government eschews intervention
the
for the least
efficient finas,
and subsidies are always nonnegative
At minimum, these
for social welfare
in equilibrium.
results caution that profit-shifting trade policies
when governments
may have
undesirable consequences
are even partially ignorant about firms' profit functions.
mformationally-constrained social optimum requires a complicated
and lump-sum transfers, which may be impracticable
m
menu of
contracts combining per-unit subsidies
actual trade policy contexts.
26
Attainment of the
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APPENDIX
Proof of Proposition
We
start
1
1
by defining the Hamiltooian for the government's program:
H
{a^,(o).K,(o).n(a).i(o)) =
Ao)
— Fj(o)
n^(5^(a)^y(o),a)-n;^(0^y(o),o)-54(o)(7j^(s^(c)^y(o),a))-—
(1)
-iiia)V,(o)
{b*d)
da
where:
(b-d)Hb*d)
*
\(a)
*
ti(a) is the
*
s^a)=0
is
the multiplier
on the participation constraint
for the case of unilateral intervention.
The Hamiltonian
concave
multiplier
on the incentive constraint
in Vh(a).
is
concave
and in
in \J.a)
Further, after optimizing over
s^Cff).
Given these conditions, and given a
finite
number of discontinuities,
necessary and sufficient for optimality (Seierstad-Sydsaeter (1987)):
*
X(a)
*
|i(ff) IS
is
piecewise continuous on subsets
continuous on subsets
[a,ffJ,[<Tk,fft+|],...,[o'„,(^
[a,ffJ,[<rk,ffk+i],...,[<ra,o]
In addition:
(2)
= -Ks,{a)
da
—t^
da
(3)
for
all intervals
=
Ao)-V.(a)
1+c
-;
on which sAa)
^l(a)
i
(4)
\i(a)V,ia) =
1
s^((r),
is
continuous
the Hamiltonian
is still
the following conditions are
3//(oj^(o).K,(a).A.(a).0)
^
.J.
^
as.
'*
The boundary conditions
are:
i/K,(a) is/r«. i(a)=0
(g)
is^M, X(o)=0
i/Kj(o)
We
contain
0.
next determine 0, the subset of values of a on which V^(a)
Then
a.
Call a,
V^(<^
= sup
is free,
<
Then, using
a.
>
with V^(^
The boundary condition
0.
can be computed on
(3), X(cr)
=
is
Start
0.
then X(<^
by supposing
=
does not
that
0, and, in addition, /i(o)
=
[ai.oi as:
X(o) = -^
(7)
l*c a -a
Optimising with respect to the subsidy over
W
this interval yields the
5;(o)=j;'(o)+a»[a-o]
which
decreasing over
is
must be positive on
sj(ff)
Clearly,
o.
^a) >
Next, notice that
subset.
Suppose
if (1
s'^a) for
V\(ffJ
which from
\(a)
is
This
firms
whose
>
>
(1) implies that s^(<7j
decreasing.
We
that a,
s"J(a) is positive (a-ff>0),
decreasing on the subset
must equal
<
<
a^,
is
a
a.
= on
this
((T„(ri).
We
S|,(a)
which Vt(aJ = Vh((ri) = 0, and V^(ff)>0 on
for
such
But
s^(aj.
conclude that
on [2,2+e] the subsidy
NPC. Thus, we can conclude
CTj
which
[a,, a],
that:
V\(ffJ
is
this
would contradict
an interval of
in turn implies that V^(2) is free.
costs lie
V|,(ff) is
Moreover, since
contains a subset with a non-empty interior, equation (2) implies that
could then find two values of a in (a„(Tj, a^ and
ii)
t [2,0].
So we can conclude
contains two values a, and
that
a
all
This implies that the rent
[ff|,ol.
contradiction to V^(a,)=0 and V^((^>0.
that
following subsidy:
If instead,
s^(ff)
that V,,(£) is free,
[a.oj.
Q = [a^,
associated with the
and
the incentive compatibility condition
the govermnent could do better by giving
ZPC, which exceeds
that associated
that the participation constraint binds
with the
on some subset
[<%,o].
Next we integrate over
[ff.ffo]
to find:
(0-2)
X(o)=-
(9)
l*c(o-2)
The optimal
subsidy, s ^a), equals s^a) on this interval.
discontinuous, there exists 0^
^ O
such
Define
0^,
such that for any value a^
at
which \(a)
is
that:
Allowing for the possible discontinuity of X(a)
at the
c
value
Oq,
for
a above a^
we
have:
(o-a)
X(a)=-^^^^*Po*M(o)
(11)
l*c(o-2)
where:
M(a)»r°ji(t)df
is
such that M(ff)=0 on
[ff.ob],
and M(ff)
decreasing above
is
ff,.
Optimization with respect to the subsidy on [ooM leads
(12)
^Po*M(a)]
Using the definition of
(13)
sj,
we
=
—
1
dn{s^(a),0,o)
a[i/o)<7/i^(a),0,o)]
^
(0-2)
as.
**
l+c
and
s
/i((T),
^
(o-a)
(b^-2d^
1
L
[5j(o)-i»"(a)]
b(b*di
S(<^)=0 on [ao.ol. M((t) will be negative and decreasing above Oq
negative and decreasing above this value.
of
A(a -2j
obtain:
[p.*M(o)] =
With 00 =
to:
=
a
"(a),
because s^ff)
is
Straightforward differentiation of M(ff) yields the corresponding value
and confirms the switch of regimes
at
a^^a
".
APPENDIX
2
Proof of Proposition 2
We
look for a Nash equilibrium in contracts.
Thus, the
home government
takes as given the subsidy
schedule announced by the foreign government:
on
iy(o)
(1)
sAa)
on [d*,a]j
I,
We
start
by vending through straightforward computation
b*d
[fl.o*]
=
that:
da
so the necessary condition for implementability (equation (16) in the text)
is
that s^(a)
is
nonincreasing.
Further,
given:
(")
the
i/(a)
same necessary condition implies
With
holds only
are
bilateral intervention,
when both
contmuous
ma.
foreign subsidy,
=0
V
o 6 [d*,o]
that s^(a) is nonincreasing
we cannot apply
on [a
^,d\.
the general theorem used in
Appendix
1
directly. This
theorem
the objective function and the function describing the evolution of the state variable, V^(.),
In the case
s )(a), is
of bilateral intervention, the objective function
is
continuous in a (because the
continous), but the evolution of V^(.) changes at the point where the foreign subsidy goes
toO:
d dSf(a)
Ks^ia)
b+d da
for a <
a*"
^
da
a
-KS),{a)
Thus,
to
be rigourous,
we
rent evolves continuously,
i.
a
proceed by considering small perturbations of the government's program, for which the
which permits use of the same technique as
in
Appendix
1.
By computing
subsidy for the perturbed problem, and taking the limit as the perturbation becomes small,
the optimal subsidy for the perturbed
problem converges
J*(o)
(2)
to
s \(a):
on [2,6*]
^»(<')
^
on
[a''^],
we show
the optimal
that in the limit
Start
by definixig k
as:
it
=
do
Consider:
on
[Sl.a''--]'
n
(3)
*.(«)
nk[d^-a]
[d*--.d*]
[d*,o]j
Notice
1c„(<t)
need not be differentiable.
Then we have:
k
(4)
on
(d'^j
[0
Next
[ji,5*]|
liin,_ kjio)
we
government's perturbed problem, whose solution will be denoted
state the
It
(5)
sjia):
^
.
'
-
dV^(.o)
= -i&,(o)|l--^*,(a)
*
do
V^io) ^
Define 0„ as the subset of values of a for which \(a)=0, and the domestic government does not intervene.
as in
Appendix
we
1,
can prove that Q„ contains
a,
and
that Q„ is
an interval, Q„=[a„,(^ for some a^<
incentive compatibility condition that the subsidy must be nonincreasing.
constraint
on the
determine
s„(.)
Again,
state variable are
and
now
continuous in a,
we
a,
Just
using the
Since both the objective function and the
can apply the same methodology as in Appendix
I
to
a^.
call the possible discontinuity
as the integral of the multiplier
of
X(ff) at
on the participation
(t„,
^,= X(a*J-X(aJ, and
constraint.
define
M(a)
as in
Appendix
Optimising with respect to %(a) yields:
1
'
b*d
1
(6)
(o-flj (b'-d^y
we have
(where
M„(ff)
=
used the definition of
and 0^=0.
For a "-l/n
(7)
s''( a)
< a<
as long as s„(.)
is
positive.
The
(o-a)
d
(!*<:)
(0-2)
(i>+d)
to simplify the expression).
a ^
,.«,) = .
c
we
For a<(j
''-1/n,
we
obtain s^{a) = s\a), with
obtain:
V)-.^a-^^](^|l-a**a)
rationale for restricting attention to nonnegative subsidies
is
the
previous section, since a negative subsidy would imply an increasing rent, V^(a). This restriction
as
/?„ is
nonpositive, and MJ^a)
Clearly, one candidate
is
negative and decreasing about the value
would be one
*,(a*--) =
n
5.(a*) =
sjia)
The
last 3
s,(a) is
decreasmg on
s\d'-h
Indeed,
as in the
justified as long
ff„.
we
can check
that:
>
n
c
t'
<
Jt
<
of degree 2 in a
s„(ff) is
equal to
for a unique value, a„
e
(a
''-1/n,
a
*").
Moreover,
this interval.
we show
that
Combining equations
(6)
one can find expressions for M,(a) and /3,=0, which justify the switch of regimes
and
at
(7) yields:
M.('')«11~^(«')
(8)
which s„(aj = 0.
-A(6*-fl)-
propositions allow us to say that
Next,
(T„.
is
for
is
same
1
(0-2)
(fc*-dY
b*d\*c
(a -2) In
Rearranging:
M(o)
(9)
where
ipjia) is the
expression on the right hand side of equation (26), and g,(a)
side multiplying M„(a).
to
=
be decreasing over
a.
It is
is
the expression
consistent for both M„(a) and (pjia) to be negative for ff>
Note
first that:
6
a^.
on the
left
hand
Moroever, M„(ff) has
(10)
do
<
da
and second
that:
,S,(c)-<P,(<j)-
5M,(o)
(11)
ao
da
do
^.(•'^
where:
4
since g„(.)
is
affine in
cr
on [a
''-1/n,
*,(")
a
^].
An
easy computation allows us to check that:
(12)
-nkX-
Hence, on [a
Lastly,
''-1/n,
on the
a
**],
the numerator in equation (11)
interval [a ^,d\, s,(a) is equal to 0,
(13)
is
negative and the overall expression
and MJ^a)
is
straightforward to check that M„(a)
Next,
we determine
negati\
then given by the decreasing function:
is
b*dl*c
(A^-dY
continous at a
(a -a)
*".
the limit of sj^a) as n goes to infinity,
s^o)
(14)
on
which
is
equal to
s
^
lsL,o'i\
li™,- ^.(o)
lo
Co*,"],
Define r„(s) as the value of the objective function in equation
objective function given a subsidy,
inequality implies that for all
(V„(.), s)
(15)
is
Aa4,(a) =
(o-fl)
It is
<
^
(a-2)(i>+<i)(l+c)
da^
s,
s.
For
all s
and
all n,
r(s)< Hs^J). Consider
[ino)-y,ia)y{a)da
=
/ a
-a.
and r(s) as the value of the original government
Next
r„(s)< r„(sj.
we show
that in the limit this
(V(.), s{.)) as an admissible pair for the
an admissible pair for the problem (PJ such that
r,(5)-r(5) =
(S),
V(^ = V„(^.
We
iy'(o)-v',{a)]da =
problem
have:
j\^Uo)[k-kJia)]-^do
(P),
and
Using the definition of
we
k,(.),
obtain:
jj^j.,,^,4-,)^ da
,.,-r,., =
(16)
Hence:
(17)
Or.
(18)
d
k
|r(5)-r(5)| i \s\.
2nb*d
where
|
s
|
.
is
bounded by the radius of the
The
the admissible subsidies.
s,
for
any arbitrarily small
Finally,
it is
t.
last
A
ball containing the
shows
inequality
would
similar proof
straightforward to check that r(.)
(19)
r(5^-r(f/)
=
that for
is
compact
set (that
n big enough,
we assume
we have
also establish that |r„(sj-r(sj|
continuous;
we
|
sufficiently large) of
r„(s)-r(s)|
<e,
<£
uniformly in
for sufficiently large n.
can write:
da
/[Tt,(5,(a)4/(o).a)-Tr^(f/(a)^/(a),o)-(K,(o)-F(o))]^
(a -2)
or:
(20)
r(5j-r(i/)
=
Hence, for n big enough:
(21)
predicted limits.
|
Combining
r(sj-r(s ^| <c.
|r,(o-ni/)l
for sufficiently large n.
So,
ll^h -Jk-^Wo)-i;(a))Wo
[[n,(s^(a)^;(a),a)-n^(s/(a)^,\a).a)-
5
Thus, both the right and
we have proven
that s
^
is
the last
two
results yields:
|r.(5j-r(5^|*|r(0-r(5/)| ^ 2e
left
hand sides of the inequality, r(s) <r(sj, converge towars the
a best response to
s
r-
Proof of Corollary
to Proposition
Proposition
1
2
established that the optimal policy
is
nonintervention over the interval
[cr
".oj,
for
Proposition 2 established that the optimal policies result in bilateral nonintervention over the mterval [a
a ^<a.
The Corollary
intervention.
This
is
states that the
range of nonintervention
equivalent to the claim that a ''<a
Using the definition of
ff
"
from equation (23)
C"
(a-d")
Similarly,
from equation
(25), define
^»
(23)
,
C'
it is
clear that
CkC*"
C
^'
(1^^)
b\b^-2d^)
c
as:
as:
(q*-g) ^
d\\ *c){b*d){b^-d^-db)-cb^d\
cb\b^-ld'^)
(a-o*)
Then,
^,a], for
greater under unilateral relative than bilateral
in the text, define
=
s
"'<cr.
^.
^°'~^
(22)
is
ff
(for the relevant case,
where a
"
<a
and
<a * < a),
which
in turn implies that
ff
"
<a
''.
APPENDIX
Proof of Global Optimalitv
for the Agent's
NPC
in the
Case
Unilateral Case
I.
Consider a firm with costs a
claimmg
it
Problem
3
be
to
receives
a. the
[a,o
"J.
If
argument bemg the same as
no protection, so
Now
m
it
gets ir(0,0,(j),
consider a firm with costs a
the firm claims to be
ZPC
in the
whjch
below
is
[a,
a
"],
it
can do no better than by
a firm claims
be
ere [a ".a],
between reporting a and
ere [a ",0^,
If instead the
case.
to
{J{a,a), the participation constramt.
The firm
in [a ".oj.
ff £
is
indifferent
A
smce both
result in
ir(sS(o),0,ff]-T"(o).
no protection.
Notice
Suppose mstead
that
it
claims a
[5,0"].
t
We
must prove
that T(0,0,a]
that:
(1)
(a)=
at
/
But
(2)
so
-^
n[s:(d')fi,o]-n[s,\d)fi,o]=[-^
\ at
we have
only to check
that:
&;«
(3)
/
dn[s^it)fi^]
<kdt
/
a<a " <
ff,
i.
***
,
But since
-<b
aSi,
and
<0
ds^,da
since profit
is
increasing in the subsidy, which in turn
is
decreasing in a, this
10
last inequality is true.
^
Bilateral
II.
Case
Consider a firm with costs a in [a,a
a for the same reasons as
T[0,s,''(a),ff],
Now
leave
it
is
below
ZPC
case.
If the firm reports
If instead the
at
[a, a
""],
firm reports ae [a
it
'.oj,
can do no better than by reporting
it
receives no protection, yielding
U(ff,ff), the participation constraint.
consider a firm with costs a ia[a
with no protection.
A
-t ''((^
which
in the
*].
Suppose instead
^,a\.
that
it
It is
indifferent
ae
reports
[s.,
a
between reporting a and a
""],
and
it
+ T[s^''((^,0,a].
We
must establish
that this
obtains
number
is
no greater than
ir(0,0,a].
i\,yJ^^^l^l^!lflM^
"
I
as.
dt
So we want:
'
ds,\t)dn[s,\t)^f\t),t]^
(5)
But notice that because a>a'°,
s''(ff'')=0,
and
dnj)
as^(t)d7:[s^(t)fij]
^
*l
^ .
ds,,da
So
(7)
[ff "".oj,
A
(4)
(6)
in
an[5;^V).0.q] ^
3n[^^W/(d*).d*]
^
We
can write:
as both
&/(0
dn[sl;(t),0,o]
dn[s^(.t)Af(t)j]
ar
as.
as.
(9)
as,*(r)
dt
where the
right
term
is
positive.
'i
7<
dn [s,\t)jtf\zU] as/(z)
dn [s.^tU'dU] 1
i
cb^a$.
ar
dSf^da
Integrating this last inequality between
12
r
aand a
*"
leads to the desired condition.
Date Due
Lib-26-67
MIT LIBRARIES
mil
III
II
I
II
I
nil
III
3 9080 02238 6087