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ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
SENESCENT INDUSTRY COLLAPSE REVISITED
S. Lael
Brainard and Thierry Verdier
Massachusetts Institute of Technology
WP#3628-93-EFA
November 1993
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
SENESCENT INDUSTRY COLLAPSE REVISITED
and Thierry Verdier
S. Lael Brainard*
Massachusetts Institute of Technology
WP#3628-93-EFA
*
**
MIT
Sloan School and
CERAS
and
November 1993
NBER, Cambridge USA.
DELTA-ENS
Paris and
CEPR
London.
M.I.T.
LIBRARIES
SENESCENT INDUSTRY COLLAPSE REVISITED
Abstract
One of
the most robust empirical regularities in the political
persistence of protection.
economy of
trade
is
the
This paper explains persistent protection in terms of the interaction
between industry adjustment, lobbying, and the political response. Faced with a trade shock,
owners of industry-specific factors can undertake costly adjustment, or they can lobby politicians
for trade protection and thereby mitigate the need for adjustment. The choice will depend on
the returns
from adjusting
relative to lobbying.
can be shown that the level of
tariffs is
By
introducing an explicit lobbying process,
an increasing function of past
tariffs.
it
Since current
adjustment diminishes future lobbying intensity, and protection reduces adjustment, current
protection raises future protection. This simple lobbying feedback effect has an important
dynamic resource
allocation effect: declining industries contract
fully adjust. In addition, the
and Hillman (1986)
The paper
is
model makes clear
more slowly over time and never
by Gassing
that the type of collapse predicted
only possible under special conditions, such as a fixed cost to lobbying.
also considers the symmetric case of lobbying in
growing
industries.
INTRODUCTION
I.
One of the most
of trade
is
the persistence of protection.
in explaining current protection levels in
instance, in their study of the pattern of protection that
Kennedy Round of
the
GATT, Marvel
liberalisation, after controlling for industry
Rounds, Baldwin (1985) found
were
greater
characteristics,
growth
rates,
was
growth
its
in the
that
an industry was more
level of protection preceding
Similarly, in studies of both the
levels of protection,
and import penetration
an industry.
U.S. following the
rates, industry concentration,
that industries received
pre-liberalisation
emerged
and Ray (1983) found
successful in resisting liberalisation the higher
advantage, and buyer concentration.
economy
Empirical research by a number of authors suggests
of protection are significant
that past levels
For
robust and least discussed empirical regularities in the political
more
the
comparative
Kennedy and Tokyo
post-liberalisation protection the
even after controlling for labor force
ratios.
In empirical tests explaining
corporations' positions on 6 trade initiatives during the 1970s, Pugel and Walters (1985) found
that the
demand
for protectionism
was
strongly increasing in the industry's initial tariff level,
controlling for import penetration and variables reflecting exporting strength.
This paper offers an explanation for the persistence of protection in terms of the
interaction
between industry adjustment, lobbying, and protection. The story
results are quite striking.
is
simple, but the
Faced with a trade shock, owners of industry-specific
respond by undertaking costly adjustment.
Alternatively, they can lobby politicians for trade
protection, and thereby mitigate the need for adjustment.
reflect the relative profitability
capital can
The choice between
of adjusting versus lobbying.
the
two
will
In equilibrium, the level of
protection will depend on the intensity of lobbying and on the value politicians place on lobbying
1
revenues relative to the welfare cost of the intervention, and will in turn affect firms' marginal
By
adjustment decisions.
Helpman (1992),
it
introducing an explicit lobbying process similar to
can be shown that the level of
Grossman and
an increasing function of past
tariffs is
This relationship works indirectly through the adjustment process:
tariffs.
since current adjustment
diminishes future lobbying effectiveness, and protection reduces current adjustment, current
protection raises future protection.
This simple lobbying feedback effect has an important
dynamic resource allocation
declining industries contract
would
contract less than they
effect:
in the
more slowly over time and
absence of protection.
Hillman
Several papers have studied protection and lobbying in declining industries.
(1982) examines political-support protectionist responses to declining industries by adapting the
regulatory capture framework of Stigler (1971) and Peltzman (1976) to an international trade
context.
He shows
that the derived protection
does not
fiilly
compensate specific factors
import-competing industry for the adverse terms-of-trade shock.
Long and Vousden (1991)
extend the analysis to a general equilibrium Ricardo-Viner framework, and discuss
partial
compensation
result is affected
owners and by the way
tariff
by the degree of
revenues are redistributed.
analysis is static and the political support function
Dynamic
is
risk aversion
how
this
of the specific factor
Both papers share the feature that the
specified exogenously as a black box.
aspects of protectionist policies have also been investigated.
Several authors
have analysed circumstances under which the adjustment path under protection
suboptimal in the absence of lobbying.'
in the
is
socially
In contrast, Gassing and Hillman's (1986) analysis of
See Matsuyama (1987), Tomell (1991), and Brainard (1993). These results generally hinge
on a dynamic inconsistency problem.
'
senescent industry collapse explicitly considers the effect of lobbying on industry dynamics.
Gassing, Hillman model differs from the one presented below in two important respects.
the Gassing, Hillman analysis hinges on an ad hoc tariff response function, which
in the level
politician
of labor in an industry, whereas
and specific factor owners
in
we
derive
it
explicitly
is
The
First,
increasing
from interaction between a
Secondly, the Gassing, Hillman model
an industry.
predicts that initially resources will shift gradually out of an industry in response to an adverse
trade shock,
to
some
point at which protection
This discontinuous adjustment behavior
collapses.^
tariff
up
response function, which
smooth path of decline
in
is
ad hoc.
abruptly terminated, and the industry
is
is
attributable to an inflection point in the
In contrast, the
response to an adverse shock.
model presented below predicts a
In an extension,
we show
that results
similar to those of Gassing and Hillman require an additional assumption, such as a per period
fixed cost to lobbying.
The model
industry.
is
designed so that
it
can be applied symmetrically to the case of a growing
We examine this case in another extension
to
make
the point that the disproportionate
share of protection afforded to mature industries in countries such as the
by a
bias in the political process than
by pure economic differences.
US
is
We
better explained
also discuss the
implications for general equilibrium.
The paper proceeds
interaction
as follows.
Section
II
constructs a general, two-period
between a trade-impacted industry and a
politician.
Section
III
model of the
extends this model
Lawrence and Lawrence (1987) also develop a model in which labor adjustment in a
is discontinuous.
However, there is no political intervention in their model.
The discontinuity is attributable to the combination of lumpy capacity reduction with monopoly
behavior on the part of labor.
^
declining industry
to a discrete time, infinite horizon
and the
politician.
framework by simplifying the
FV extends
Section
the
model
interaction
between the industry
to consider industry collapse.
V
VI concludes.
considers growing industries and the implications for general equilibrium. Section
TWO-PERIOD MODEL
n.
We
start
with an industry that
specific factor in the industry,
The
labour.
variable factor
specific factor.
industry
amount
is
x,
occurred.
(where
a price taker on international markets.
is fixed,
and a variable factor
x>0
=
y,-x„
the next period, y,+i
.
implies contraction).
E
{1,2}, the stock of
specific factor input, output is
which
is
There
is
a cost of adjustment,
production cost, C, which
is
is
will refer to as
employment
in the
employment by some
assumed equal
<t>,
employment
which
</>'(Xt)>0
assumed convex and increasing
is
to adjust
also just equal to the stock of
amount of adjustment:
Domestic demand, D,
we
a
is
Production takes place after the adjustment has
increasing function of the
absence of intervention
t
Each period, the industry chooses
y,.
that
There
supplied competitively, and any rents accrue to the owners of the
is
Given the fixed
q,
which
is
At the beginning of each period
given by
employment,
is
to the net level
at the
assumed
to
in output:
beginning of
be a convex,
There
and (t>"ix^>0.
of
is
also a
C'(qi)>0, C"(qt)>0.
a decreasing function of the domestic price, p„ which in the
just equal to the
that the international price is constant
0.
Section
exogenously given world price, p„
,.
We will assume
over time, with the exception of a discrete jump
at
time
Prior to that time, both the international price and the domestic price are constant at pb,
which
is
consistent with an equilibrium
employment
level, y„°.
The employment
such that the marginal cost of production equals the price: C'(yw'*)=Po-
4
At time
level is chosen
0, a
permanent
shock
in the international
of employment
market causes a decline
at the outset
of period
and the industry must contract
new
in
1,
in the
world price
yi=yj', exceeds the
to p„
< po.
new long run
Thus, the stock
equilibrium level,
order to bring the marginal costs of production
down
to the
international price.
Adjustment:
In the absence of lobbying, the industry does not receive any protection, since there are
no market imperfections.
In this case,
its
adjustment program
is
defined as
:
(1)
where p
The
first
is
the discount factor of the industry, and profits in period
are defined:
t
order conditions are:
-Py^^^'^i -^i) * 9{-Py,^C'(y, -X, -Xj)] =^'{x,)
(2)
-P^^C'{y,-x^-x^)=^'{x^)
In each period the industry trades off the marginal return to adjustment against the marginal cost.
Solutions
of
Xi*>Pw)=X2'(yi,Pw)-
this
system
can
Solving the two
convexity assumptions establishes that
international
price
0<3x,/3y,<
level,
p„,
first
Xi=x,*(yi,p„)
as:
is
and
X2=X2(yi-
order conditions under the usual concavity and
period adjustment,
in
the
initial
x,*,
an increasing function of
increasing in the initial stock of employment,
y,.
is
decreasing in the
employment
and therefore the second period employment stock,
1,
is
first
written
and increasing
addition, second period adjustment, X2,
value of X2'
be
yj*, is
y2,
The
stock,
yi,
new
with
increasing in y,. In
and thus the equilibrium
full
impact of the world
price p^
on
X2* is
a priori ambiguous:
through decreases in x/
the direct effect is negative, while the indirect effect
If the direct effect
is positive.
outweighs the indirect
smaller price shock results in lower adjustment in period two: 3x2*/3p»
demand and
<
effect, then
0. In the case
a
of linear
quadratic costs, the direct effect dominates and the optimal adjustment levels are:
(1*4>(1+P))
^i=(Po-Pj-
(1
(3)
+<!>)
Lobbying
is
P*
^
X2 = (Po-Pj
Thus, adjustment in each period
+
increasing in the size of the price shock.
:
Next we assume the industry has the option of lobbying
The domestic
price
is
to influence the
domestic price.
the product of an endogenously determined ad valorem tariff, &„ and the
exogenous world price: p,=(l +^t)Pw.f Following Helpman and Grossman (1992),
lobbying process as a contribution
level of the tariff
of the
tariff,
t
^(Pry,'^,)
each period, the industry can influence the
to the
incumbent politician as a function
are:
= Pr(yr^,)-c(y,-x,)-^(xyF,(p,j>j
restrict consideration to differentiable
does not provide any contribution
if
The policymaker values both
(5)
the
or equivalently, of the two prices, F(R,p„). Given world price p„, and employment
(4)
degrees.
in
by offering a schedule of contributions
adjustment, x„ profits in period
We
game where,
we model
We
assume
there
lobbying contributions, and assume that the industry
is
no protection: F,(p»,,p„)=0.
social welfare,
W,
and lobbying contributions
that the utility function is linear in both elements:
G(p„y,^,) = pw^(P„yA)^(i-P)^,(Pr^H)
in different
where the weight on welfare,
/3,
lies
between 1/2 and
1.
Welfare
is
the
sum of consumer
surplus, industry profits and tariff revenue:
W(p„yrX) = [Diu)du *
p,(y,-x,) -
C(y,-xy^ix)
^ (p,-/)J[D(p,)-(y,-A:,)]
Pt
This objective function
is
the partial equilibrium,
dynamic analogue of
that
developed
Grossman and Helpman (1992).'
In the interests of simplicity,
features of political interaction,
especially competition between political parties.
Grossman, Helpman point out, evidence
to incumbents,
and frequently contribute
simplification has
period
>
ignores a host of interesting
But, as
lobby groups disproportionately make contributions
to candidates after they
have won, suggests
this
some empirical credence.
The timing of
the
game
is
as follows:
period 2
1
>
Industry
Government
Fi
p,
In each of the
that
it
in
> ...|.
Industry
two periods,
>
>
Industry
Government
Fj
X,
the industry first chooses
> ..^
Industry
X2
P2
its
contribution function,
F„ the
politician
then chooses the domestic price, p„ given the contribution schedule, and finally the industry
chooses the level of adjustment,
x,."*
'
The welfare weight parameter,
*
Qualitatively similar results obtain if instead the government
a, in
Grossman, Helpman
is
just equal to /3/(l-/3) here.
is
assumed
schedule as a function of the contribution, and the firm then chooses
employment
level simultaneously.
its
to
choose a price
contribution and
The second period lobbying game:
Solving backwards, the industry chooses Xj to maximize T(p2,y2,X2), yielding
first
order
conditions:
-p,^C%-x^)=^'ix^)
(6)
which gives
Xj as a function of
employment
x^ = xl(y^j>^
(7)
Second period adjustment
domestic price
level),
is
with
stock, yj,
—
^(P2.y2»X2*),
which
and of
is
<0 and
first
period adjustment, since
pj:
0<— <1
a decreasing function of the second period
adjustment from (7) into the profit function in
-
and domestic price,
tariff (reflected in the
y2= yrx,. Plugging
the optimal
r'(^,y-^
(4), yields the indirect profit function,
decreasing in the employment stock,
y2,
and increasing
in the
domestic
price, p2.
Fully anticipating the industry's employment response, the politician chooses the tariff
to
maximize
G(p2,y2,X2*).
The
first
order condition yields an expression relating the marginal
industry contribution to the domestic price level:
®
The
'v^T^*.-M D'ip^)
first
term in equation
(8) is the
marginal deadweight loss of the
tariff
weighted by
/3/(l-^).
In order to induce the politician to choose the domestic price level, p^, the trade-impacted
industry has to propose a contribution schedule that exactly compensates on the margin the
associated social welfare loss, weighted by the politician's preference for contributions.
level of tariff protection increases in the marginal contribution
politician
assigns
to
welfare,
under
the
assumption
8
that
and decreases
the
import
in the
demand
The
weight the
function,
M(y2,P2)=D(p2)-y2+X2.(y2,P2),
is
not overly convex in the domestic price.
values only social welfare, the tariff
The lobbying
When
the politician
is 0.
contribution schedule of the industry in period 2
is
then derived by
integrating (8):'
(^)
^2(P2^>v.y2) =
-A/("-/'w) D \u) +
|au
P..
Anticipating the politician's tariff response, the industry chooses
its
contribution in period 2 (or
equivalently the domestic price) so that the marginal cost of lobbying just equals the marginal
benefit to the industry
from increased protection:
iy,-4) -
(10)
^^^f^^^
dP2
which can be restated
in the usual
Ramsey form (Grossman, Helpman
^i-Pw)
(11)
where Mjipi)
is
import demand.
the import
demand
(1-p) ^y^-H)
in period
employment
and concave in the price
P2, the sign
2 and €M(p)=-M'(p)p/M(p)
In the Grossman,
in that period P2*(y2)-
of b^'lby2
is
the
it
lobbies.
lobbies and
Here,
this
For a program
same
is
the elasticity of
when
it
is
p2, as a
that is well-defined
as the sign of the expression:
Helpman general equilibrium framework, each
includes a constant in addition to this integral, which
when
1
Equation (10) defines the equilibrium second period domestic price,
function of the stock of
^
_
(1992)):
industry's contribution
equal to the difference between
its
return
does not, given the equilibrium contributions of the competing
term does not appear since there are no competing lobbies.
.
dx;
(11)
'~<p.-pj
1-
1-p
dy.
which
is
first
first
of second order for small
is
tariffs.
The
first
is positive.
As long
term in
The second
as the first term
sufficiently large relative to the second, the equilibrium level of protection in period
an increasing function of the employment stock,
adjustment undertaken in the previous period,
is
order condition in (10).
order effect of y2 on the output level, qj, and
term has an ambiguous sign,* but
is
dp^dy^
derived by totally differentiating the
brackets represents the
\
^^
y^^
x,.
two
is
^"^ therefore a decreasing function of the
In particular, in the linear-quadratic case
it
straightforward that:
(12)
P(l+4>)/',+<t>(l-P))'2
,
(13)
Pi =
-
(P(2+<|>)-1)
In this case, the second term in equation (11)
contribution, F2, does not depend directly
is
on
is identically
yj,
equal to zero, the second period
and B^'ldy2
an increasing function of the stock of employment
>
at the
0.
Second period protection
beginning of the period, and
therefore a decreasing function of the adjustment undertaken in the previous period.
The
first
period lobbying game:
Continuing backwards, the industry's
*
It
first
period adjustment level
is
chosen, taking into
cannot be signed without some additional conditions on the derivative of marginal costs.
In particular,
it
can be shown that for convex marginal production and adjustment cost functions,
The larger the industry, the less sensitive
3^2*/^P25y2
in domestic prices in period 2.
is
positive.
10
is
the adjustment to changes
account
its
effect
on the
level of protection
program for the industry can be written
and adjustment
as:
MAX^^ p,(y,-x,)-C(y^-x^)-^(x,)
(14)
The maximization
in period two.
Using the envelope theorem for the second period
+ p [n '(/j^Cy, -x,),y, -x,)]
profit function
and equation
(7), the first
order
condition for x, can be written as:
dF.
(15)
= i>'(x,)
-Pi^C'(y,-x,)*p ^^(y,-^,)]
^2.
The
is
first
two terms represent
the marginal gain
from adjustment
in period 1,
while the third term
the marginal adjustment cost saved in period 2 due to adjustment in period
represents the strategic impact of adjustment in period
2. Its sign
depends on
[d^
1
1.
The
on the lobbying contribution
Xz'/dpjdyJ. In the linear quadratic case,
it is
last
term
in period
equal to zero.
At the
equilibrium, the marginal direct and indirect returns from adjustment are balanced against the
marginal cost of adjustment in the current period.
For a well-defined concave problem,
defines the optimal adjustment level, x,*, as a function of the initial stock of
this
employment and
the domestic price, p,:
(16)
;cj
= JCi^i/jj)
with
—
!-<0
and
0<—^<1
Combining equation (16) with the condition derived above
that
the second period tariff
first
straightforward:
and the lower
is
the higher
is first
Continuing
an increasing function of the
is
period tariff
The
result that
intuition is
the domestic price in the first period, the less the industry adjusts,
period adjustment, the
farther
3p2*/3y2>0 yields the
backwards,
anticipating the effect of this price
the
more
the industry lobbies in period two.
government chooses the domestic
price,
pi,
on the industry's subsequent adjustment and lobbying
11
behavior in period 2, and taking as given the contribution schedule, F,, proposed in that period.
Assuming
the policymaker has the
optimization problem
^^^
same discount
rate as that
of the industry, the policymaker's
is:
Max^^ PI^(Pp)'i^;)Hl-P)F,(p,^,)+p[PJr(p;(y2);y2^*)+(l-P)F2(p;(y2);p,,y2)]
Using the envelope theorem with respect
to the optimal price
and adjustment
in period 2 yields
the first order condition for the politician:
(» dF,(p,j?J
_
(Pi-Pj
D'(p,)
(1-P) ay.
dPi
the equilibrium protection level, the lobbying contribution in period
terms
at the
margin.
The
first
term
second term reflects the loss of
in equation (18) is the usual static
tariff
revenue
implied by reduced adjustment in period
dF,
1
/ ^
.\
ax;
-P(P2-PJ
(1-P)
dPx
At
Av*\ Bxl
(
p
1.
in period
The
third
l^J
must balance three
1
deadweight
loss.
The
2 due to the increase in production
term
is
the strategic impact of period
1
protection on the lobbying contribution in period 2.
Integrating equation (18) yields the optimal
of the industry.
constraint.
The
first
period lobbying contribution schedule
industry chooses the optimal tariff taking the contribution schedule as a
Again, using the envelope theorem, the
first
order condition
is:
dF^(p^j)^y^)
(19)
yi-xi(j>i,yi)
=
dPi
which defines the equilibrium
stock, y,.
(20)
first
period protection level as a function of the
For a well-defined concave program, the sign of 3pi/3yi
^1*
^^i(PnPw»yi)
ay,
dp^ avj
1-
12
is
the
initial
same
employment
as the sign of:
The
term, which represents the direct effect of the
first
protection,
period
1
is
positive.
The higher
and the higher
,
the declining industry
is
when
stock.
The
positive,
is
the tariff.
the initial level of
The second term
and the policymaker.
linear-quadratic case and
Thus, 3pi/3yi
is
initial size
and protection
employment, the higher
reflects the
is
relatively impatient this
in period
larger is the initial shock, the larger
is
1
is
output in
lobbying interaction between
to sign in general.
It is difficult
the policymaker
of the employment stock on
term
However,
is
increasing in the initial
in the
also positive.
employment
the initial protection level and the larger
is
is
future protection.
m.
INFINITE HORIZON
We now
MODEL
extend the model to the infinite horizon case, simplifying in two ways.
in order to obtain explicit solutions,
cost and
demand
we
focus on a linear-quadratic version of the model, with
functions given by:
.2
Second,
assumed
politician
2
order to derive an explicit path of adjustment for employment and domestic prices
in
we
over an infinite horizon,
is
to
choose
its
simplify the structure of the stage game.
adjustment level and
then chooses a tariff level to
framework,
this
each period, but
its
is
the
Each period, the industry
contribution schedule simultaneously.
maximize
utility.
Compared
to
The
the two-period
timing assumption assigns greater commitment power to the industry's action
this is offset
by the
alternating sequence of
Both the industry and the politician are assumed
variable
First,
employment
stock,
whose evolution
13
is
to
moves
in
an
infinite
employ Markov
horizon context.
strategies.
The
described by the simple equation:
state
(22)
Then
= yrx,
y,.,
the politician's value function
Vp)
(23)
=
is:
Max^ [PW[p^y,)-(l-P)F,(p,^J+8F^(y,^,)]
Given the relationship between the domestic price and the contribution
politician's first order conditions, the industry
level
embodied
in the
maximizes
its
strategies,
the politician's protection decision
value function by
its
choice of
contribution and adjustment levels:
With
this
affects only
Therefore,
timing structure and
Markov
the contemporaneous levels of the contribution and
the politician's problem
Choosing the optimal
can be simplified to a
F(p„p„)= (p,-p»)V2a
Faced with
permitting the
this tariff
first
maximization problem.
level of protection as a function of contributions yields the
on the relationship between the marginal contribution and the
Integrating yields
static
employment adjustment.
,
where
a=
same condition
tariff level as in
equation (8).
(l-/3)//S.
response function, the industry's problem simplifies considerably,
order conditions to be expressed as a second order difference equation.
Substituting y,-y,+i for x„ incorporating the politician's tariff response in the industry's value
function, and differentiating with respect to the contribution yields the condition:
(25)
y
=
^'-PJ
while differentiating with respect to the employment level yields:
(26)
Combining
p^ = -p<t>y,,2+(l+4>(l + p)))',,i-4)>',
(25) and (26), and using the initial condition that the
14
employment stock
at
time
is
y„, (and setting the coefficient
on the larger root
to 0) yields the industry's optimal adjustment
path equation:
(27)
,^ ,
where the root
is
(28)
Po-
M'
(l-a))
^"
(l-a)
defined:
i^a)
-
l-fl^»(l^P)-V(t-fl)'^2(l-a)<t>(Up)-4p4>^-Kt>^(f^
2<t)p
and
0<b(a)<
1
for the restrictions
on
/3
adopted above, and b'(a)>0.
This path can be contrasted with the adjustment path in the free market equilibrium,
which
is
obtained by setting the politician's weight on welfare to
(29)
y, =
Comparing
the
1
(a=0):
(Po-pJHOy^p,
two expressions reveals three channels through which lobbying
adjustment path. The equilibrium stock of employment
is
affects the
higher each period because lobbying
reduces the rate of adjustment and reduces the cumulative amount of adjustment that takes place,
and these two effects more than offset the decrease
reduction in the price shock.
level of
employment
to welfare.
is
The
in the coefficient, po -Pw/(l-a),
rate of adjustment is slower,
higher, the greater
With lobbying, employment
is
is
due
to the
and the long run equilibrium
the politician's preference for contributions relative
adjusted
15
downward smoothly,
at
a decreasing pace.
.
eventually converging to a level that
The two paths of adjustment
The path of
are
permanently above the efficient level of employment.
is
compared
in
Figure
1
the associated equilibrium tariff can be derived
first
order conditions with the adjustment path of employment:
The
level of protection declines
smoothly and gradually with employment over time, reflecting
the effect of past protection through the current stock of
higher at each point of time, the larger
advantage (measured by Po/pw).
and Young (1989).
new
adapt to the
The
by combining the industry's
This
is
employment.
Further, the tariff
the initial adverse shock or shift of comparative
closely related to "the compensation effect" of
is
is
larger the initial shock, the
more
Magee
the industry must adjust in order to
international environment, and the larger are the incentives to lobby for
protection to mitigate the need for costly adjustment.
rV.
SENESCENT INDUSTRY COLLAPSE
Our
result differs
declines smoothly up to
markedly from
some
result is attributable to the
to
concave
explicit, the
at
that
of Cassing, Hillman,
point, after
which
shape of their
tariff
some threshold
level of
framework above makes
it
response function, which switches from convex
By making
some kind of
variable contribution, then the industry
the tariff formation process
discontinuity
the industry's lobbying activities to yield a point of collapse.
the lobbying process each period required the
find that the industry
suddenly loses protection and collapses. This
employment.
clear that
who
16
in
In particular, if participation in
payment of a fixed
would lobby only
would be required
cost,
C,
in addition to the
as long as the intertemporal return to
Such a fixed cost might be associated with operating an
lobbying offsets the fixed cost.
information network, maintaining political connections, or paying lobbyist's fees.
Recall that with a zero fixed cost, the industry always lobbies, and adjusts gradually to
a level of employment, p^/(l-a) above the free market level, p„.
introducing a fixed per period cost
return to lobbying
never finds
it
is
is at its
maximum
to
levels, the industry lobbies
market
rate.
At time
lobbying and loses
its
market return
fi-ee
For a fixed cost
in
at
exceeds the
time 0, when
finite
number of periods,
T(yo).
Up
and contracts gradually, cushioned by the resulting protection.
this interval lies
t(.), it is
and
an intermediate range between these two
and receives protection for some
T(yo), the industry lobbies
The rate of contraction on
lobbying and the
If the fixed cost
a smooth
is
relative to the steady state value, the industry never lobbies
simply adjusts according to (29).
time
steady state, C<ap„^/2, then the industry
identical to that in equation (27).
difference between the return
to
its
of
below the per period
optimal to stop lobbying and receives protection permanently. There
adjustment process, which
employment
If the fixed cost is
is fairly clear.
when adjustment has reached
Intuitively, the effect
between
that
under permanent protection and the free
no longer worth paying the fixed
political influence.
cost, so the industry stops
Domestic protection collapses
to zero,
and adjustment
accelerates in a discontinuous manner.
The appendix proves
these results and specifies the relationship between the time,
fixed cost, C, and the other parameters of the model.
The proof proceeds by defining
t,
the
the value
function for a single period of lobbying followed by no lobbying, and then solves forward
recursively to determine the optimal
number of periods of lobbying before
lobbying. This value function for optimal temporary lobbying
17
is
compared
the switch to
no
to the value functions
for
permanent lobbying and for unprotected adjustment, and the resulting inequalities define the
ranges for the fixed cost relative to the intertemporal return from lobbying.
GROWING INDUSTRIES AND IMPLICATIONS FOR GENERAL EQUILIBRIUM
V.
Growing
Industries
The case of growing
framework, with rather
there
is
may be accommodated
industries
startling results.
Start
a permanent price shock at time
t,
by assuming there
quite simply in the above
is
no fixed
cost.
Suppose
such that po rises to some level, p„.
that
In the free
market economy, the industry will want to raise employment each period, to adjust to the steady
state level
yw=Pw>yo.
so that
employment adjustment
growing industry
analysis of lobbying in a
is
will
be positive
in equilibrium.
The
exactly symmetric to the case of decline, as are the
maximizing levels of contributions and employment adjustment each period. Proceeding through
the
same
steps as
for the declining industry in the infinite horizon
expression for the equilibrium stock of employment in period
(31)
y
=
''
where the
_P.w
(1-fl)
^^
\{\-a)
it
would
in the free
yields an
t:
-PoWy
characteristic root is defined as in equation (28).
grows more rapidly than
framework
When
it
lobbies, a
growing industry
market, at a rate increasing in the size of the price
shock, and the steady state level of output exceeds that in the free market by an amount that
increases with the politician's preference for contributions.
This
suggests
that
the
empirical
evidence
that
disproportionate share of protection in countries such as the
declining
US would
industries
receive
a
be better explained by
a bias in the political process than by pure economic differences. There are a variety of reasons
18
why
the political process
may be
biased against growing industries.
First,
there
may be
important differences in the cost of lobby formation for fledgling as opposed to mature
industries.
In the model above,
intertemporal return
is
we
simply assume that an industry lobbies whenever the
positive, thereby ignoring the critical issue of lobby formation.
more
research in political science suggests that industries are
likely to
overcome
However,
the free rider
problems of lobby formation when they have large committed resources and established unions.
In addition,
growing industries are characterized by rapidly changing market structures and a
high likelihood of future entry, while declining industries are more likely to have stable market
structures with a reduced threat of domestic entry.
dissipated with entry
The
may make lobby formation more
declining industries with clearly identified players and
greater risk that future rents will be
difficult in
growing industries than
more predictable
in
rents.
Secondly, in the presence of imperfect capital markets^, liquidity constraints on lobbying
activities
may be more
be the case
if
binding in a growing industry than in a declining industry.
incumbent domestic firms
in
This would
mature industries have more accumulated cash
reserves from past retained profits relative to investment opportunities than do firms in emerging
industries.
To
illustrate the effect
of a liquidity constraint, assume that firms must finance both
investment and contributions from current profits.
The
industry's maximization
program
is
modified to take into account the liquidity constraint as follows:
'
Imperfect capital markets
may
exist
because either
it is
not possible to borrow to finance
lobbying, or investors are less optimistic about an industry's future growth path than are industry
participants
due
to
asymmetric information.
19
(32)
Vp,X)
- Max^^^^^
(i-xyvp,^,,k,^,)
2
where
\ is
the multiplier
on the
2a
2
interval,
if
it
binds at
all.
employment only through
VJ-^;
Since the unconstrained equilibrium profit
liquidity constraint.
level rises monotonically over time, the constraint
When
^
must bind
the constraint binds,
it
initially
and over a continuous
affects the equilibrium stock of
the characteristic root:
bCUyL^
^ =
where
^-
L, =
24>pL,
-^
(lU,)
'
Thus, a binding constraint lowers the industry growth rate relative to the unconstrained lobbying
path.*
However, the growth
equilibrium value
is
the
rate remains
same as
above the free market
that for unconstrained lobbying.
paths for the unconstrained lobbying equilibrium,
constrained
rate,
and the long run
The equilibrium adjustment
lobbying equilibrium, and
unconstrained free market equilibrium are compared in Figure 2.
In addition, a fixed cost in the lobbying process might create a bias against growing
Suppose, as above, that the fixed cost does not depend on the size of the industry.
industries.
If
an industry ever
starts to
lobby,
it
will not subsequentiy stop lobbying, since the return to
lobbying never decreases in a growing industry.
to wait before
it
the first period,
*
It is
constraint
starts
it
lobbying.
If the
Thus, an industry chooses
how many
periods
per period return to lobbying exceeds the fixed cost in
lobbies permanentiy, and conversely if the fixed cost exceeds the return to
not possible to solve for L, explicitiy. However, by combining (33) with the liquidity
it
can be shown that b
conditions, such that b
is
is
declining in
L
decreasing over time.
20
and
that
L
is
rising over time
under sensible
lobbying
lobbying.
at the steady-state level
If the fixed costs lies in
optimal number of periods until
cost,
of employment under lobbying, then the industry never
some intermediate range, then
it is
large
enough
the industry waits for
that the return to lobbying
starts
some
exceeds the fixed
and begins lobbying.
Implications for General Equilibrium
These
results ignore potential spillover effects
of lobbying across sectors, which
central consideration in understanding the effect of lobbying
on dynamic resource
industries with declining competitiveness.
in a static general equilibrium
The
away from
results derived
framework, where protection
a
allocation.
whereby the equilibrium
In a general competition for protection, there are a variety of channels
pattern of protection might result in a diversion of resources
is
infant industries toward
by Grossman and Helpman (1992)
spills
over between interest groups
through consumption, suggest that mature sectors would gain protection at the expense of infant
industries in a competition for protection if the infants
industries for
in a
any of the reasons cited above or
model where there
is
were
less well organised than
if the infants initially
a limited supply of a
common
mature
were smaller. Similarly,
factor of production, or the import-
competing sector produces an input used by the exporting sector, the equilibrium pattern of
protection might result in resources being directed
away from
industries, distorting adjustment in both directions.
growing industries would grow more slowly
in a
equilibrium.
21
the growing industries to mature
If the distortions
were
sufficiently great,
lobbying equilibrium than in the free market
VI.
CONCLUSION
Motivated by the strong empirical regularity that the best predictor of future protection
is
past protection, this paper has analyzed the adjustment path in declining industries under
By
endogenous protection.
developed
in a static
introducing an explicit political objective function similar to that
framework by Grossman and Helpman
adjustment costs, the paper shows that the level of
tariffs is
into a
dynamic model with convex
an increasing function of past
In this model, industry adjustment and lobbying are substitutes: the
the greater the protection
more
effective
it is
in
it
receives and the less
lobbying next period.
it
adjusts,
Lobbying
price shock, or equivalently of the gap between the
is
and the
more an
tariffs.
industry lobbies,
less the industry adjusts the
an increasing function of the
initial level
initial
of employment and the long run
equilibrium level.
The paper
finds that in the absence of nonconvexities in the lobbying process, the paths
of lobbying and adjustment are smooth. The industry contracts employment gradually over time
to a level that is
permanently above the free market level by an amount
value the politician places on lobbying contributions relative to welfare.
sharply with the Cassing and Hillman finding that there
to
an inflection point
in the path
in
an ad hoc
tariff
This result contrasts
a point of collapse, which corresponds
response function.
Here,
we
derive a similar collapse
of protection by introducing a per period fixed cost into the lobbying function.
the fixed cost lies in a range defined
lobbying
is
that increases in the
at the initial level
by the difference
of employment and
industry lobbies and receives protection for
in returns
between lobbying and not
at the steady-state level
some
finite
under protection, the
number of periods and then abruptly
stops lobbying, resulting in a collapse in protection and accelerated adjustment.
22
When
The
rate of
adjustment under temporary lobbying
lies
between the adjustment
rates
lobbying and no lobbying, and the associated long run employment level
is
under permanent
just the free
market
equilibrium.
Ultimately,
the
question
To
of whether
is
investigations
comparing adjustment paths across
small
number of
industries
and
protection
do not address
industries.
smooth
are
or
no systematic
the best of our knowledge, there have been
discontinuous
empirical.
adjustment
Several articles that investigate a
this issue directly.
However, our purpose was
to
investigate the conditions that determine the adjustment path rather than to establish the validity
of a particular path.
In addition, the paper
growing industries
will
grow
shows quite
faster
clearly that in a partial equilibrium
under endogenous protection unless there
against growing industries in the political process that
results are suggestive for general equilibrium,
makes lobby formation
where such a bias
in
sectors.
23
is
some
costly.
bias
These
combinaton with a resource
constraint or a vertical relationship between infant and mature industries
dynamic misallocaton of resources between
framework,
would
result in a
Figure
1
ADJUSTMENT TO NEGA TIVE SHOCK
110
100
90
c
I
B
80
70
60
50
40
O
C/3
30
20
10
"\^
I-
Figure 2
ADJUSTMENT TO POSFTIVE SHOCK
250
pw/(l-a)
200
p
S
150
B
o 100
o
o
«-»
50
Q
I
I
I
I
I
13
I
2
I
I
I
I
I
I
I
I
I
I
I
I
I
II
I
6
4
5
Time
25
I
8
7
10
9
Appendix
Assume
cost,
C, in each period.
lobby in any period after
when
it
F(p„p„) to the politician, the industry must pay a fixed
that in order to offer a contribution schedule
Assume
t.
We
also that if the industry does not pay the fixed cost at any time
start
does not lobby, and when
it
by defining the value functions of the industry when
some
lobbies for
number of periods and then
finite
it
t,
then
it
cannot
lobbies permanently,
stops.
Dilutions and notations
I.
1)
Define Vo(y) as the value fimction of the industry without lobbying:
(1)
with z
V^O-)
=
=Max,^^4p^z-^
y-x. Because the function h(z,y)
Lucas and Stokey (1989) establish
= p^
-2^/2
-
-^^
. p
nz)]
4>{y-zf-l2 is strictly
that there is a unique, continuous,
and
concave and quadratic,
strictly
results
from
concave value function Vg(.)
defined on the interval [0,yo] that satisfies this equation.
2) Further, define V,(y) as the value function of the industry with permanent lobbying
After optimization on p, this value function
V (y)
(2)
The same
= A/a.,, ,
result establishes that V,(y)
Moreover, V,(y)
It is
=
V,°(y)-C/(l-p),
is
is
on
the interval [0,yo].
equivalent to:
z-lll^ -^^I^
[;,
-C
p
V (z)]
a well-defined, continuous and strictly concave function
where W°(y)
also useful to define an operator,
is
T„
on
[0,yo].
the value function of permanent lobbying with zero fixed costs.
that associates to
any continuous function V(.) on
[0, y,] the
new
function (T,V) defined by:
(3)
T,V(.)
is
iTV)iy)-.Max,^^^^
is
b.Z-^
the value of lobbying in the current period followed
clear that V,(.) is the unique fixed point of this operator
26
-^
"C*
P
V(z)]
by the value function V(.)
on the
set,
in the following period.fl
QO,yo], of the continuous fimctions on
[0,yo]
(i.e.
(T.VJ = VJ.
that for
any
initial
R
continuous function
In addition, define the
3)
to
Define [TJ" as the k*
iterate
V on
of the operator T.:
[0,y°], the
T.'
^ T. o T. o T,...o T..
It is
well
known
sequence of functions ([TJ'V) converges uniformly to V,(.).
two 'unconstrained' operators,
Tq'
and T°„ on the
set
of
all
functions from
R
as:
(4)
(roV)(y)=Max^
inV)(y)=Max^
(5)
Again drawing on
results
[p^Z-^-^^yZ^
* pV(z)]
[p^Z-^1^-^^ -C
pV(z)]
from Lucas and Stokey (1989, Theorem 4.14 and
defined above and h(z,y,a)=p^ -(l-a)z^/2
-
p. 95),
because the functions h(z,y)
^(y-z)^/2 are strictly concave, quadratic in (z,y) for
all
OSa< 1,
the
operators To" and T", have unique fixed points, Vp'(.) and V,*(.) respectively, defined on R, which are well-defined,
quadratic, strictly concave functions in y.
The optimal adjustment paths
z(0,y) and z(a,y) associated with Vg' and
V,° are linear and increasing in y, with a slope less than unity, such that:
V
y
Va€
^
p„,
p„
^
[0,1)
and
V
z(0,y)
y
^
V y ^ p„ y ^
^y;
Pw^l-a.
P./l-a
Consider the restriction W^" of W^' to [p„ yj.
^
z(a.y)
It is
2d
z(0,y):S p,.
^
V
y;
y
^
y
P./l-".
^
z(a,y)^ Pw'l-a-
clear that the fiinction:
v-y
(6)
V(y) =
Kly)
satisfies the fixed point
restriction
property of Vq on CIO,yo] and
of V,' on [p^/l-a,
y^],
it is
If
is
y
I [p..
yj
therefore equal to Vq.
a simple matter to verify that:
2p^y-(l-a)y'-2C
if
(7)
2(1 -p)
y
6 [0.
(I
-a)
v,(y)
K(y)
if
27
y^l (l-a)
.
yj
Similarly, defining V,°'(y) as the
Vo(.) and V.(.) are therefore differ^itiable,
(8)
and using the envelope theorem
yields:
P^-il-a)y*pV^'(y)
(12)
if
-<i>(y-z!.(y))
From
if
y
e
y^]
[0,
{TV^'(y)
and
(4)
(5),
y
t
\yo
yj
,
unconstrained optimal adjustment without lobbying, z(0,y), and with permanent lobbying, z(a,y),
are determined respectively by:
(13)
z(0,y) = {z
(l-*)
It
z(a,y) = {z
I
p^-z*<t>(y-z) = -p\^(z)}
p^-z(l-a)*<t>(y-z) = -pVj(z)}
I
follows directly from inspection of (10), (13), and (14) and the fact that on [O.yJ
z(a,y)
>
>
Hence, p^(l-a)
in (8)
z'.(y)> z(0,y), for
yo'
>
Using
p,.
and (12), one concludes
V.'(y)
In particular,
>
we
Now
5)
this,
y
G
for all y
Vo'(y)
on
[0,yo].
Let
z,'(y)
<^^)
Then
t""
iterate
is
and V,'(y) obtained
increasing in y.
of the T, operator applied to Vj.
is
For
all
t
^1
and
all
y
G (O.yo],
one may
a differentiable, strictly concave, piecewise quadratic
be the solution of the following unconstrained program:
arjV^(y)=Max^^,
z,'(y) is
V(,'(y), (T.Vo)'(y)
G [CyJ
construct ([TJ'Vo)(y) recursively, given that ([TJ''Vo)(y)
fiinction
Vo'(y) that:
[O.yJ
and comparing the expressions of
conclude that (T,Vo)(y)-V(,(y)
consider the
>
that:
>
(T.Vo)'(y)
all
V.'(y)
[h(z,y,a)
-C*
p([rj'-'V^(z)]
the solution of the following equation:
(1®
z:
Because
([T.]'"'Vo)(y) is
= {z
I
P^-z(l-a)*<IKy-z) = -p(lTJ-'V^\z)}
concave and piecewise quadratic, (16) shows
increasing function in y with a slope less than unity.
that z',(y)
^
y
if
and only
if
y ^y",.
In addition, z',(0)
that for all
>
Hence, one may rewrite (ITJ'V(,)(y)
29
0.
y
in [0,
So there
as:
is
y,,],
z'.(y) is a linear,
a unique point, y'„ such
p^y-^^z^-cMiTj-'VoXy)
(17)
y
if
« [0. )'."]
aUV^(y)
iirjv^iy)
Using the envelope theorem,
a simple matter to see that ([T,rVo)(.)
it is
>«[>,', y^
if
differentiable, strictly concave,
is
and
piecewise quadratic on [0,y^ and:
P^ -(^-a)y*p({TX'y^'iy)
(18)
if
-<t>(y-zjy))
Now we
z.'-'(y)
show by forward recursion
<
z.'(y)
<
z(a,y)
Our discussion of (T.Vo) showed
notation).
show
Assume
first
< V*'(y) <
<
and ([TJ-'Vo)'(y)< ([TJ'V„)'(y)
that this property is true for
t>
t+ 1, we need
z(a,y)
t
[0, >,']
1.
Then
only show
it
is
tS 1:
y.
V.'(y)
for all
z(0,y)
clear that for all
y
=
t^r,
e
[O.yJ and
t^r.
with the previous
2?,(y)
y",.,
all
<
y',< p^/(l-a).
To
that:
from ([TJ'-'Vo)'(y)<
concave function in
y f:\y', y^
t=l (where
and ([TJ'Vo)'(y)< ([TJ-'Vo)'(y)
part of the assertion follows directly
fact that ([TJ'V(,)(y) is a strictly
if
the following property for
the property is also true for
that the property is true for
z'.(y)
The
y
([r]'v^'(y) =
The second
<
V;(y).
([TJ'V(,)'(y)
<
V,'(y), equation (16),
part follows directly
from
and the
(18).
Thus, the previous discussion establishes:
Lemma
1:
For
all
y GfO.yJ, for
1^1.
all
i)
The value funaion ([TJ
it)
([TJ
Hi)
f\{y) <tjiy) <z(a,y)
n.
The problem of lobbying with
yo)(y)
-
y()(y) is differentiable
{[TJ-' Va)(y)
We are now equipped to
is
and
strict fy
concave.
increasing in y.
for ally
^
[O.yJ and t>0.
Fixed costs
solve the problem of lobbying with fixed costs.
30
In any period
when
the industry
The value
has lobbied in the previous period, the industry chooses between lobbying and not lobbying.
industry v^th an initial size y, of
problem then
If the
argmax of
after a finite
Lemma
2:
periods of lobbying followed by no lobbying
is
an
simply ([TJ'Vo)(yo). The basic
is:
Max.^o
(A)
t
to
([TJ'Vo)(yo)
this
problem
oo, then
is
number of periods and
For
all ya
>
permanent lobbying will prevail. Otherwise, the industry stops lobbying
loses protection.
We
start
by showing the following lemma:
pjl-a,
we have ([TJ)V^yo) ^
i)
Iffor
some
ii)
Iffor
some f^l.we have VJy^)
f2.1,
^
(rrj'')Vo(ya), thenfor
(n'J^()(y(), thenfor all
k>
allk>
0,
we
0.
we
also have ([TJ**" V^^iy^
also have VJyo)
<
(fTJ*^
<
Vo)(yo).
Proof:
Consider
i)
t
^ 1,
such that ([TJ'Vo)(yo)
[P*.
yj,
we
conclude that for
Ip*',
yj,
we
get:
all
y in [p^,
([TX'VoXy)
y,),
^
([TJ'-'Vo)(yo).
([TJ'Vo)(y)
<
Since ([TJ'Vo)(y)-([T.]-'Vo)(y)
is
([TJ-'VoXy). Therefore, as ^^',(y)
increasing on
>
p*"
for y in
= h(Min[C(y),y],y,a)-C * (>([UV^{Min[z':'(y),y])
^^5^
<
Hence,
T,'*' Vo(yo)
have for
all
ii)
Consider
<
^
Using a similar argument,
T,' ygiyo)-
y in [p~,yo],
t
h(Min[C(y),y],y,a)-c + paU-'v^iMin[C(y),y])
1
,
([TJ'^'OVo)(y)
such that V.(yo)
that for all y in [p*',yo), V.(y)
<
<
^
([TJ'*''-')Vo(y).
([TJ'Vo)(yo).
As
we
^
can show by recursion that for
Result
i)
V.(y)-([TJ'Vo)(y)
is
have for
all
y in [p*,yo],
V.(y)
^
for y in Ip'-yJ,
<
([TJ'"^%)(y), and result
31
ii)
we
also
we
we
conclude
get:
<
([T^'V^iy)
Using a similar argument, we can show by recursion
([TJ'^'VjXyo).
k>
increasing in [p'.yo],
([TJ'Vo)(y). Therefore, since z(a,y)>z'.(y)>p''
h(Min[z(a,y),y],y,a)-C + paTJV^(Min[z(a,y),y])
<
all
follows immediately,
VCy) = h(Min[z{a,y),y],y,a)-C * pV^(Min[z(a,y),y])
Hence, V.iyo)
([Tjv^iy)
follows immediately.
that for all
k>
we
also
Lemma
2
implies that if problem (A) has a finite solution, there are at most two points r and
i)
can be the solution. H^ice, unless y^ belongs to a
that
there is at
most one
finite solution T(yo) to
set
problem (A). Note
V,°(y)-C/[l-p].
3
t
<
Temporary lobbying
00
we
costs,
that
Lemma
2
rewrite ([TJ'Vo)(y) as ([T,°]'
and only
will arise if
>
such that ([TJ'Vo)(yo)
oo
of isolated points y (such that ([T,]'Vo)(y) = ([TJ'*')Vo(y))
holds for
i)
all
C> 0.
Defining T,° as the operator T, associated with zero fixed costs, and recalling that V,°
permanent lobbying with zero fixed
t+ 1<
V^Xy)
-
C[l-p']/[l-p]
,
is
the value of
and V,(y) as
if:
V.Cy,)
or equivalently:
3
It is
t
<
oc such that
Vo(0)= (T.oVoXO)
By
<
clear that V(,(y)
=
V.°(y) for
all
y
>
u,
=
is
Lemma
Proof:
3
<
t
^<C/[l-p]< ^„. This
contradicts
Lemma
Since
it is
2
3
<
it is
<
V.°(y) for
clear that Vo(y)
([T,°]'^'Vj)(y) for all y
- ([T.'']'V„)(yo)]/p'.
3: The sequence of points (uj,
Suppose the contrary:
increasing in y,
([T,°]"Vo(y))
>
<
y>
0. Also, since
([T/JVoXy) for
Finally,
0.
all
we
all
y>0.
can conclude that the
monotonically converging to V,°(yQ) from below.
[V.^Cy,)
equivalent to the condition:
([T.TVo)(yo)]/p'.
Then by recursion
0.
and ([T.'']Vo)(y)-Vo(y)
([T,°]'V5)(y(,) is
Let us define
-
[V.°(y„)
recursion one can also see that ([T,°]'Vo)(y)
sequence of points
is
C/[l-p]>
t
oo such that
is
3t
the condition,
C/[l-p]>
<
u,
oo
<
u,+,.
such
that:
3
t
<
oo
such that ([T.]'Vo)(yo)
>
V.(yo),
u,.
a decreasing sequence
such that
implies that
Then
(ie.
u,
S
u,^,for all
Then one can choose
([T J'Vo)(yo)
> V.(yo)
I
ciO).
a level of fixed cost
C
such that
and ([TJ*'Vo(yo))< V.(yo). This
ii).
a decreasing, positive sequence, (uJ, converges towards a limit
guarantees that this limit
is strictly
positive:
32
u^O. The
following proposition
Proposition 1: If VJp")
>
Vgfp"),
In this case, the adjustment path
>
Proof: Given that V.'(y)
Therefore, by recursion,
([TJ'Vo)(yo),
that for
which says
^
any yo
protection
A
p,
is
that
it is
apJ/2, then there
is
permanent lobbying and permanent protection.
given by y,+,=z(a,yj with the initial condition
\„'(y) for
Vy G
C<
i.e.
all
y
(p", y,],
G
[p", yj,
>
V.(y)
^
V.(pJ
Vo(pJ impUes
([TJ'Vo)(y) for
all
y^.
that
Vy G
[p.,
Thus, for
12:1.
yj, V.(y)^V„(y).
all
tSO,
always beneficial for the industry to continue lobbying. Consequently,
p^(l-a), there
is
permanent lobbying and protection.
are such that y,= z(a,y,.,), and p,=
p''
The
adjustmrait process
y,
V,(yo)
>
we conclude
and domestic
+ az(a,y,.,).
corollary follows directly from this proposition:
Corollary 1: For all
We
are
now
t
SO and all C ^
apJ/2
>
u,
,
C/fl-p].
Hence u = Lim
u,
S
apj/2[l-p]
>
0.
able to state our main result:
Proposition 2:
i)
If the fixed cost
C
is
such that C/fl-pJ
^
u, then there is
permanent lobbying and protection never
collapses,
ii)
If the fixed cost
C is such
that C/[I-pJ
>
u, then there exists
enjoys temporary protection for T(y^ periods, after which
Hi)
When protection
trade
is
a unique time j(y^ S
it
stops lobbying
,
such that the industry
and protection
temporary, the adjustment path during the lobbying periods always
lies
collapses.
between the free
and permanent lobbying adjustment paths.
Proof:
i)
If
C
is
such that C/[l-p]
Hence, permanent lobbying
ii)
If
C
is
is
^
u, then for all
t,
C/[l-p]
<
u„ which
is
equivalent to V.(yo)
>
([TJ'Vo)(yo).
optimal.
such that C/[l-p]
>
u, then, because u, is decreasing (except in the case
of isolated poinU such that ([TJ'Vo)(y)
=
([TJ'+'Vo)(y)), there exists a unique
33
t
such
where
that:
yo belongs to a set
u,
=
[V."'(yo)-{[T.TVo)(yo)]/p'
([TJ'Vo)(yo)
t,
>
V,(yo).
that reaches the
Obviously, then
>
C/[l-p] and C/[l-p]
u,^,
=
[V/(yo)-([T.°]'Vo)(yo)]/p'.
Moreover, since the sequaice ([TJ'VoXyo) amverges
sup ([T.r'VoXyo).
it is
>
By Lemma 2
this point, T(yo), is
Then
for all
t'>t+l,
to V.(yo), there is a point, -riy^
unique for almost every yo
>
>
p^(l-a).
optimal for the industry to lobby for riy^ periods, and th»i to stop lobbying. Thus, there
is
temporary protection for riy^ periods.
iii)
y.-n
This follows immediately from
Lemma
1
and the
iii)
fact that at
time
t
along the adjustment path,
= Min(y„z'.(yO).
An
immediate corollary
Corollary 2: If ({TJVo}(yg)
<
is:
Vj/yJ, then there
is
no lobbying and no protection along the adjustment path.
34
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34
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