WPTC 0410
i ional Agricultural Trade and Policy Center
INVASIVE SPECIES MANAGEMENT THROUGH TARIFFS:
ARE PREVENTION AND PROTECTION SYNONYMOUS?
By
Ram Ranjan
WPTC 0410 December 2004
WORKING PAPER SERIES
i~fr
UNIVERSITY OF
FLORIDA
Institute of Food and Agricultural Sciences
"j_
INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
THE INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
(IATPC)
The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multidisciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:
* Serve as the Universitywide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nationwide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.
Invasive Species Management through Tariffs: Are Prevention and
Protection Synonymous?
Ram Ranjan'
Postdoctoral Associate
International Agricultural Trade and Policy Center,
Food and Resource Economics Department, University of Florida.
Abstract
This Paper designs a political economy model of invasive species management in order to
explore the effectiveness of tariffs in mitigating the risk of invasion. The revenueinterests
of the government together with the interests of the lobby group competing with the
imported agricultural commodity, that is believed to be the vector of invasive species, are
incorporated in a Nash Bargaining game. The government, however, also considers the
impact of tariffs on long run risks of invasion and decides optimal tariffs based upon its
welfare in the pre and postinvasion scenarios. Along with the size of the lobby group,
which is a function of the slope of the demand and supply curves, the weights assigned to
the various components in the government welfare function too play a key role in
influencing the extent to which tariffs could be an effective policy tool for invasive species
management.
JEL CODES: H23, Q17, Q58
KEYWORDS: Invasive Species, Political Economy, Tariffs, Bargaining, Interest Groups
1 G097, McCarty Hall B; P.O. Box 110240; Gainesville FL 326110240
Email: rranjan(gifas.ufl.edu, Phone: (352) 392 1881 Ext. 326, Fax: (352) 392 9898
Introduction
There options available to manage invasive species comprise prevention,
monitoring and control. Recently, there have been some suggestions regarding the use of
tariffs as a preventive measure by influencing the import of goods believed to be vectors
of invasives. Costello and McAusland (2003) use a trade model to show that while
tariffs may lower the rates of invasive species introduction, they may also cause higher
damages from infestation due to increased domestic production. Using another trade
model, McAusland and Costello (2004) look at the role of tariffs combined with
monitoring efforts in managing invasive species. They find that while it is optimal to
employ tariffs for managing invasive species, higher infection rate does not necessarily
call for higher tariffs.
While it is important to understand the effectiveness of tariffs in preventing
against invasion and damages, it must also be recognized that the use of tariff itself is
guided by a multiplicity of factors, not all them aimed at invasive species control.
Tariffs have primarily been used to protect domestic industries and to generate revenues
for the government. The role of tariffs in mitigating risks of invasion cannot be looked
upon in isolation of these other roles, as the effectiveness of tariffs in mitigating the risks
of invasion could be significantly compromised by these multiple, and often conflicting,
objectives.
The role of interest groups in influencing public policy has been a subject of
concern lately, as new incidences of invasive species, specially the ones that have
potential of harming humans, animals and plant species alike, have led to questionable
management strategies. Recent outbreak in the US of Bovine Spongiform
Encephalopathy (BSE), commonly known as the mad cow disease, has caused
widespread concerns over its impact on the beef industry from international trade
restrictions and subsequent demands for ban of imports from countries thought to
potential sources of BSE. Besides causing damages to the domestic beef industry, there
are significant risks of the disease passing on to the humans (in the form of BSECJD).
When the disease has hosts that span multiple species, potential exists for
conflicting interests among groups affected by it. There are similar other cases where
import competing domestic agricultural industry may lobby to impose tariffs on imported
agricultural products in the disguise of mitigating invasive species threat.
This aspect of influencing public policy has been a subject of intense research in
the past, albeit, at a more general level where several domestic lobby groups seek to
protect their interests against competition from imports. However, not much has been
done so far to apply such political economy models to understand the interestgroups'
influence on invasive species management. Yet, a lot remains to explore in terms of
understanding the role of interest groups that are directly affected by invasives and their
interaction with the government, especially over a long time horizon.
This paper seeks to explore the role played by domestic lobbying in influencing
import of certain goods believed to be vectors of invasive species. While the modeling
framework follows the lobbying concept as first formalized by Grossman and Helpman,
it differs from the existing political economy models in several important regards. Only a
single lobby group (the importcompeting agricultural sector, in particular) directly
affected by invasive species is considered here. While there may exist several other
lobby groups, the interests of this particular differ from the rest in that it seeks not only to
protect against imported goods, but also against their hazards, which could even span the
rest of the economy. In order to keep the analysis simple, it is assumed that its interests
do not conflict with the rest of the existing interest groups, thus allowing the government
to deal with them separately. This allows a more detailed modeling of the Nash
bargaining game between the agricultural group and the government. Specifically, the
long term impacts of tariffs are explored where the government incorporates the post
invasion scenario in its bargaining objectives. This is an important feature of the invasive
species management problem that needs to be incorporated in the political economy
framework. Postinvasion scenarios may completely differ from preinvasion scenarios
in terms of the lobby groups interests, their ability to make contributions, the weights that
the government assigns to rest of the economy, etc. Consequently, long term interests of
the government may lead to policy outcomes that are completely different from those
arising from oneshot interactions with the lobby groups. Yet, due to cumulative nature
of risks of invasion (accumulating over time and economic activity), if tariffs are imposed
for protection against invasives, their long term impacts are the ones that are of particular
relevance to the society.
The paper, first, explores one time interaction between government and the lobby
group by modeling a Nash bargaining game between the two. Tariffs serve as the control
instrument that could affect the risk of invasion by restricting import of foreign goods
competing with the lobbying industry's goods. Not any less significantly, tariffs also
contribute towards government revenues and producer surplus of the lobby group.
However, the flip side of tariffs is the increase in price of the domestic good in
consideration, thus causing a reduction in the consumer surplus. Following the literature
on political economy of tariffs, the government is expected to incorporate in its welfare
the weighted benefits of the producers and consumers of this commodity, besides its own
revenues and the contributions it receives from lobby groups. The rest of the economy
in this model is indirectly featured as the reverse of the weights assigned to this particular
group of producers and consumers of the commodity. It is therefore reflected in the
weights the government assigns to its own revenues as it would eventually use these
revenues to affect its chances of survival by spending on the rest of the population (and
other interest groups). The model then proceeds to consider the dynamic aspect of the
bargaining game, wherein the benefits from optimal policies following an invasion are
considered in the preinvasion policies. Several scenarios are considered in the post
invasion situation that range from elimination of tariffs to continuation of bargaining but
with various levels of damages to the producing sectors. The implications of such
situations on optimal tariffs are considered. The role of weights assigned to the lobby
group and the consumers along with the market strength of the lobbyist is found to be
decisive in influencing the level of tariffs and thus the risk of invasion.
Model
Let the demand curve facing an economy for a certain good (q), believed to be a
vector of potential invasives, be given by:
(1) p = a pq
where p is the price of the commodity and q the quantity demanded. The domestic
supply of the same commodity is given by:
(2) p = O + q
Assuming the domestic economy to be small so that it is not able to influence the world
price of the commodity, p", the residual demand for import of the same commodity will
be given by the difference between consumer demand and domestic supply as:
a p" pw 0
(3)
P 8
The domestic industry producing the good lobbies for tariffs on imports by offering a
contribution C to the government. The government's welfare function includes producer
surplus of this domestic industry, the consumer surplus of the people consuming the good
and its own revenues GR besides the contributions C. The government uses its revenues
and the contributions to increase its prospects for future survival by spending it directly to
improve its popularity or indirectly by distributing amongst the entire population.
The government puts a weight of a on the producer surplus, b on the consumer
surplus and (1ab) on its own revenues and contributions. Let r be the tariff imposed
on the import of this commodity and pt the price of the commodity after tariffs. Further,
noting that for a small economy tariffs are fully converted into an increase in domestic
prices:
(4) = p p
The Producer Surplus in presence of tariffs:
(P '+ Z )2 OPS (pW + Z )2
(5) PS = (p, with (p = +ve
23 Or 23
Consumer Surplus in presence of tariffs:
(a p" r)2 9CS O(a p" r)2
(6) CS = , with = ve
2/7 cr 2/7
Government Revenue in presence of tariffs:
7 apR 7P+ T with
(7) GR =  ) ( )( with
P 9 1
GR ( )(  TI + p + ve
Or v P 5P 8j
The next step involves sharing the bounties of tariffs between the government and
the lobby group through a bargaining game that maximizes the product of their surpluses.
One Time Bargaining Game
In order to share the rewards from tariffs between the lobby groups and the
government, a Nash bargaining game is played between the two, which aims at
maximizing the joint product of their surpluses. The government's and industry's
surpluses are the difference between their welfare before and after tariffs. Government
welfare from tariffs is given by:
(P 0 )2 (a _t 2 ba(t p t pt 
(8) a ++(1ab) (p_ ) ( )_( +C
28 2/7 P
Bargaining constraint for the government, defined as the gain to government from tariffs
compared to no tariffs, is given by:
(9)
a f b +(1ab) p)L) ( ) +C a(P2 +b( p)2
28 2, 8 29 2 l
Bargaining constraint for the producers, defined as the gain to producers from tariffs
compared to no tariffs, is given by:
(10) (P 0)2 02 C
The first stage of the Nash bargaining game maximizes the product of the government
and producer surpluses with respect to contributions by the industry to the government:
(11)
Max c
a )2+b +(1ab) (p ) ( )( ) +Ci a +b )2
26 28 2P ( 256 2p
\{(p )2 _(p _0)2_
29
Proposition 1:
1.1 For the range of tariffs ni i/hin which bargaining constraints are satisfied,
contributions are increasing and convex in tariffs as long as
a > b 3,9+3,5 3,+25
a>   + L 
4 + 23 4 + 23
1.2 Bargaining constraint for the producer surplus is concave in tariffs as long as
38+P 23+/
a < 3 b + 2+ and convex other wise.
2(1 + 3) 2(1 + 3)
1.3 Bargaining constraint for the government is concave in tariffs as long as
38+ P 23+ P
a < b + and convex oheWi ni i\e However, the bargaining
2(1 + 3) 2(1 + 3)
constraint for the government always lies below that of the producer.
1.4 For a given tariff level, higher the weight on consumer surplus, higher would be
the level of contributions.
1.5 For a given level of tariffs, the higher the weight on producer surplus, the higher
would be the level of contributions.
Proof 1: If the two bargaining constraints are satisfied, first order condition with respect
to C would maximize the product of government and producer welfare when:
(12)
( 2a b) + + (2a + b 1) (p b(a p )2
1 28 28 2,
2(1ab) a b)ap pW+rz0 b(a_ pW)2
P b 2,/
The contributions vary with the level of tariffs selected by the government as shown by
their first and second order partial derivatives below:
(13)
2a (p + ) b(a p r)
aC 1 8 P
P+ve
dr 2(1 a b) az ap pw+z + 1 1
S( ab){ (1 a b)r{+}
P 8 P p
02C (1 l2a b) b 1
+ \+ & +ve
ar2 2(1 a b) 3 + +
(14) if
a > b 3+35 3/7+25
a>  + 
4/ + 52 47 + 52
The second order partial derivate of the contribution function shows that it will be convex
as long as the above relation between the weights is satisfied2. But, the first order partial
derivative reveals that contributions could be falling in tariffs. However, in order to rule
out this possibility, let us look at the contribution function as derived in equation (11). It
can be easily deduced that the contribution is zero at a level when the tariffs are zero.
This implies that the contribution function passes through the origin on the plane
involving contributions and tariffs. As a consequence, only places where the contribution
can be falling and still be convex would be when contributions are negative. This would,
however, imply that the bargaining constraint for the producer has been violated. Figure
below shows the contribution function for a certain combination of parameters.
INSERT FIGURE 1 HERE
Proof 1.2: The bargaining constraint for the producer is usually concave in tariffs. This
can be shown by taking the partial derivate of the producer surplus function with respect
to tariffs:
5) 2 2 (pW )2 (1 + 2a + b) + (2 2a 3b)
arZ2 2 2P5(a + b 1)
2 The contribution function would be concave only at very high weights on consumer and producer
surpluses that are close to 1. Though, not readily apparent from the above condition in (14), this fact can be
numerically verified.
Note that concavity of the bargaining constraint implies that the gain to the producer from
tariffs initially increases but eventually falls with tariffs. As the weights are increased,
the surplus to the producer from bargaining shrinks, eventually turning to zero. Further,
it can be verified that the bargaining constraint is zero when tariffs are zero3. From the
above, a relation between a and b for concavity could be derived as:
33+ P 23+ P
(16) a< b +
2(/ + ) 2( + 3)
Note that as long as the weights lie within the line specified by the above equation, the
bargaining constraint would be concave.
Proof 1.3: The bargaining constraint for the government is usually concave in tariffs.
This can be shown by taking the partial derivate of the consumer surplus function with
respect to tariffs at the level when optimal contributions are accounted for as:
(17)
a 2 I_ )2 t2 t t (p, w_ 2 (a w, 2
S a +b +(lab) (p'p") ( )( +C a +b
r pT2 28 2,8 a 28 2fi
(1 + 2a + b)f + (2 + 2a + 3b)3
2,8
Note from above that the slope of the constraint would be lower, the larger the values of a
and b. This would imply that as the weights are increased, the gains from revenue
increases, thus increasing the bargaining surplus. Rewriting the above as a relation
3 Therefore, it is possible for the bargaining constraint to be concave and yet be nonpositive as weights
are increased significantly, even before it becomes convex. Consequently, it is possible that bargaining
breaks down even when the constraint function is concave.
between weights on consumer and producer surpluses we get the same relation as the
producer's:
(18) a< b +
2(/ + ) 2( + 3)
Finally, also note that the bargaining constraint for the government always lies beneath
that of the producer. That is, the constraint is more binding over the range of weights on
consumer and producer surpluses for the government. This can be easily deduced from
the fact that the second order derivative of the bargaining constraint, as given by (15) is
always higher in magnitude as compared to that of the government, as given by (17).
Intuitively, the producer is not directly affected by the weight on the consumer surplus as
compared to the government which is directly and indirectly affected by both the weights.
INSERT FIGURE 2 HERE
Proof 1.4 : An increase in weight on consumer surplus would lower the government
revenues for any given level of tariffs as weights on government revenues would fall and
so would the weighted consumer surplus. Whereas, an increase in weight on consumer
surplus, for any given level of tariffs would leave the producer surplus constant.
Therefore, maximizing the product of surpluses would require that relatively increased
surplus to the producer be shared with the government thus increasing contributions.
Proof 1.5: For any given level of tariffs, an increase in the weight on producer surplus
would lower the weighted government revenues as ((1ab) would fall), but leave the
producer surplus intact. This would raise producer surplus relative to government
revenues, thus increasing contributions.
Government as the Stackelberg Leader
In the next stage of the game, the government, acting as a Stackelberg leader,
selects the level of tariffs in order to maximize its surplus. In a one period game,
government maximizes its benefits (GB) with respect to tariffs:
(19) a +b I +(1ab) (p p) ( )_( ) +C
28 2,8 P
Taking the first order condition, the optimal level of tariffs can be derived as:
a (2b + a 1) p )
(p" ) (a 2)
23 2P
(20) r =
(1 b) b 1 1
+  (1 a b)( + )
28 2/7 / 3
In the above equation, the denominator is the second order partial derivate of the
government's benefits, GB with respect to tariff. When a and b are small enough, GB
will be a concave function. More specifically, it could be verified that as long as the
bargaining constraint for the government is satisfied (as given by equation 18), the
concavity of GB would also hold. A large denominator in the derivate would mean that
the GB is falling (or rising ) fast with respect to tariffs, thus lowering tariffs.
So far the optimal level of tariff selection only involves maximizing the joint
profits of interest groups and the government. In order for tariffs to be justifiable on the
grounds of mitigating the risk of invasive species, the government must incorporate the
consequences of invasion into the bargaining game. However, since risk of invasion is a
cumulative process primarily affected by economic activity over a sustained period of
time, any such effort at modeling risks into tariffs must be done in a multiple time frame.
In the next section, risks of invasion are explicitly modeled as being affected by the level
of imports which in turn are affected by the level of tariffs. The government still plays
the bargaining game with the lobby group as a one shot game in each period, however,
being the Stackelberg leader it must incorporate the consequences of tariffs on risks over
a longer time horizon.
Multiple Periods
We deviate from the literature on political economy models at this stage by
making the model dynamic. The government's objectives extend beyond a single period.
Therefore, it must keep in mind the consequences of its current actions on future risks of
invasion.
Following Clarke and Reed (1994), the risk of invasion is modeled using a
survival function S(t) to represent the country's likelihood of surviving an invasion at
time period, t. Let T be the moment of invasion. The cumulative probability distribution
associated with invasion is denoted F(t), where F(t) = Pr(T < t). The survivor function
captures the probability that an invasion has not yet occurred in time t, and represents the
upper tail of the cumulative probability distribution4:
(21) S(t) = Pr(T > t) = 1 F(t).
Even though the risk of a particular invasive species are affected by such broad measures as prevention,
and monitoring, here we consider only the incremental risk reduction from tariffs that reduces the import of
this particular commodity.
In each time period it is assumed that the country faces a certain probability of transition
into the postinvasion state, denoted A(t). This conditional probability, A(t), is also
referred to as the hazard rate. The cumulative probability is given by:
(22) F(t) = e e(t
where
(23) p(t) = (q(r(s)))ds
0
and
(24) g(t) = A(q(r(s)))
where A(q(r(s))) is the hazard rate affected by reduced imports from tariffs. The
probability of surviving until any time period t without being invaded is, e (t'. The
unconditional probability of invasion in an exact period t is the probability of both being
invaded in period t and not having been invaded prior to that period:
(25) A(q(r(s)))e "(.
Let the hazard rate be defined by:
(26) A(q(r)) = + p 'yr
In the above formulation, y is the factor that affects the effectiveness of tariffs on hazard
rate reduction. The first term under brackets is the point of intersection of the demand
and the supply curves and implies zero residual demand. Note that when y is 1, tariffs
must equal a + p" in order for the hazard rate to be completely zero. This would
,8+s
happen when the residual demand for imports is zero. However, the risk of invasion does
not necessarily have to be linearly dependent upon the tariffs and consequently the
quantity imported. As mentioned above, in presence of complementary policies aimed at
risk reduction, even a marginal reduction of imported quantities from their status quo
may lead to significant or complete reduction in risks5. This would be made possible by
having the value of y to be more than 1.
In the scenario of an invasion, several situations may arise that would adversely or
positively affect government's revenues from tariffs and contributions from lobby
groups. A forward looking government would seek to maximize its long run expected
benefits from tariffs and bargaining in the presence of risks. Government's long run
objective function can be defined as6
Maximize with respect to tariffs r :
(27)
(a )2 (a +(1ab) (p P) ( ) ( ) +C +AV
28 2 P/7
Alternative specification of risk evolution may be where: A = pw y}. This specification would
be more applicable when the commodity of concern is the only host to the invasive pest and even if the
imports are reduced to zero, significant risks remain in the form of invasives arriving through other means.
In that case even the domestic production of the commodity adds to risks and the hazard rate is reduced to
zero only when there is no production of that good at all.
6 Note hat all the variables in the objective function would have a time argument but are ignored for
purposes of simplicity.
where V is the discounted sum of value derived from optimal policies in the aftermath of
an invasion. This value function would depend upon specific scenarios that follow an
invasion. We discuss some of these scenarios below.
Scenario I: Elimination of Tariffs upon Invasion
In the simplest case consider that the postinvasion scenario leads to elimination
of tariffs7. Let V be the discounted and weighted sum of consumer and producer
surpluses in the aftermath of invasive species establishment. The value function in the
post establishment scenario can be derived as:
a b
( 0')2 + (a pw)2 (1a b)d
(28) V 2 2, er
r
where d is the per period damages from species establishment to the rest of the economy,
r is the rate of discount and 0'is the new intercept of the domestic supply curve,
assuming pest infestation leads to an increase in private fixed costs to the domestic
firms8. The government's long run objective function, after substituting for the
contributions as a function of tariffs from above, can be written as:
(29)
7 International Sanitary and Phytosanitary regulations may call for tariff elimination if the pest has already
been established.
8 It is also possible that the supply curve is shifted to the right causing changes in both its slope and
intercept. Implications of such a possibility are considered later.
(r+p" )2{} +(a p)2{ }+(p,)2(2a+b )+(c )2 b+
46 4, 48 4P
Max, a )2 b _,)2 a b)t dt
(p p) + (a p( ) (1ab)d
oap" r +p"O. (1ab)r 2( 2
P S 2 r
Subject to the equation of motion for the hazard rate as given above by (26). The current
value Hamiltonian is given by9:
(30)
2 1b b 2a+b1) W2 b
(r+p 0) { }+(a r )2{ }+(p 0)2( +(ap)2 +
43 4,8 49 4,
a b _e) +
W a(P ((pW )2 + (a p)2 (1 ab)d
a p _r+p" 0 (a b) 2+ 2e c t
P 3 2 r
a1( + p r)
p+3
where / is the shadow price of cumulative risks, u/, and refers to the cost of decreasing
the cumulative risks marginally by an increase in tariffs. First order condition with
respect to tariff leads to:
l b 1( 1 1+ (a p")b 1ab (apw) (p" 0)
_+ 2 a +p ) 2 2 ( 8
(31) 25 26 ( b 26 26 2 P 6
a 2 b
(pa 0') + (a p)2 (1ab)d
26 2,
r7 e" =f1e
r
Notice that reducing the cumulative risks reduces the chance of invasion and thereby
pushes farther into the future the gains to be had in the postinvasion scenario. Post
invasion value could either be positive or negative depending upon whether the damages
9 The current value Hamiltonian would be concave in tariffs, thus ensuring a maximum, as long as the
government's benefit function is concave. It was shown earlier that concavity would hold as long as the
weights on consumer and producer surpluses do not exceed a certain threshold as defined by equation (18).
to the rest of the economy d (which are assigned a weight (1ab) ) exceed the combined
sum of gains to the producers, consumers and the government. In the case when the
invasive species of concern may have significant economy wide impacts, the post
invasion value would be negative, implying that the shadow price of cumulative risks be
negative. When the postinvasion value is positive, an increase in tariffs would still be
warranted as long as the preinvasion value exceeds the postinvasion value. The optimal
path of tariffs would be decided by the noarbitrage conditions derived below:
(32)
S1b ) b 2a+b 1 )2 b
( _+p" 2_pw2Y w l 2? )+(a pw +
4) 4, 48 4,/
b+a b
= (pW" 0)2 + p)2 (1a b)d
a b. )+ z (P 0 Q a b)z( b 25 28
ap'r r+p (1ar 28 2
P 8 2 r
Letm = le" where m can be thought of as the conditional shadow value of cumulative
riskso. Then
(33) th m=e" +le"i
Substituting for i from above we get:
(34)
10 Clarke and Reed (1994) define this manipulation as the shadow price conditional on the fact that the
event associated with risk has not yet occurred.
rt +
1 b b 2a + b 1)2 b
( + P 8)2 +(a p)2 ) + (pW )2 (w +(a z2 +
48 48 48 4P8
m= a b
S:a (pW0')2 + (a p)2(1ab)d
apWr r+pWO} (1ab)r 2 (p 2/3
P 8 2 r
+rle" +le'A
Rewriting the above we get:
(35)
r + {r{
m=
,ap
r
+
7
1b b 2a+b1 b
) {}+(  p )2 {} + (p )2 ( a )+( P )2 +
45 4P, 45 4P,
W a(P" 0')2 + (ap)2 ( a b)d
r T + p }((1 a b)z 25 28 ep
J 2 r
b b 1 1 1b (a p )b 1ab (a pW)
+(1 ab)(+ ) +(p )() + (
25 2, JP 25 2, 2 P
(p )2 (apW)2 (1 a b)d
22 2 ert
r
The shadow price of conditional risks is a function of tariffs and also of key parameters
such as the weights a and b. In order to understand how the shadow price of cumulative
risks varies with tariffs we derive its partial as:
( 83 h r +A 1b b 1 1
(36) = +(1ab+
r y7 28 2/3 P JJ
The term inside brackets is nothing but the curvature (or the second order derivative) of
the instantaneous benefits function. From the above equation, it is evident that the
derivative would be negative when the curvature of the instantaneous benefit function is
eU +
rt
S+
(p 0).
8
concave. This would happen when weights on the consumer and producer surplus are not
too high and therefore satisfy the concavity constraint as derived before. The expected
value in the post invasion scenario in absence of revenues is lower than the benefits in
the preinvasion scenario. Therefore, it pays to lower the chance of getting into that state
by raising tariffs. As a consequence, shadow price of cumulative risks would be falling
as tariff increases, because as tariff increase, the expected postinvasion value falls due to
reduced risks. Figure below shows the graph of for a low combinations of the
weights on consumer and producer surpluses1.
INSERT FIGURE 3 HERE
Steady State
Steady state implies / =0, which would happen when the hazard rate is zero. Solving
ctd +/
P
pa +
which, one can derive the steady state level of tariffs as r = Note that
when y is more than one, it is possible for g = A(r) to be zero even before the tariff
levels reach their maximum possible level at which the residual demand for imported
goods is zero. While the existence of such a steady state is a possibility, it would happen
under extreme scenarios where very high costs from invasion or very low gains to
consumer surplus prompt maximum possible tariffs. Consequently, further steady state
1The time path of tariffs could be derived from equations (32) and (35), however, they get too complex
for a qualitative analysis.
analysis is ignored here. Instead, we do a brief numerical simulation to explore the role
of parameters in shaping optimal tariffs.
A Numerical Example
In table 1 we present the results of numerical simulation of the above dynamic
game using various combinations of elasticities of demand and supply and weights on
consumer and producer surpluses. Besides presenting the optimal tariffs and
contributions, we also present the consumer and producer surpluses before and after
tariffs12. In table 1 below, the first case involves high slopes (low elasticities ) for
demand and supply curves. For this case, notice that as the weight on consumer surplus
increases from .1 to .3, tariff falls. This is obvious as consumer surplus is significantly
higher than the producer surplus (given the choice of this parameter set) and a relatively
small increase in weights on consumer surplus leads to an increase in its weighted value.
Contributions do not necessarily increase with an increase in weight on the producer
surplus. In fact, the highest contributions are when a=.l, b=.2 and the producer is
obliged to contribute more to maintain a tariff level of 5.3, as the government increases
its weights on the consumer surplus. However, as weights on consumer surplus increase
12 The simulations were performed in GAMS. In all of the above cases the tariff and contribution levels
stabilized right from the first time period, hence only the first period results are presented. Fixed
Parameters: r = .1, a = 10,0 = .1,d = 1, y = 1,0' = .15, pw = 1. Figures in brackets after the tariff
in the first column depict the price at which the residual demand for imports is zero.
to .3, contributions fall to zero as the producer is no more able to compensate the
government for the loss of higher consumer surplus concomitant with higher tariffs.
In the next case, when both the slopes of demand and supply curves are low,
tariffs fall significantly compared to the first case. Note that the increase in consumer
surplus far outweighs the increase in producer surplus from this change in slopes.
Contributions are zero all throughout as the producer is unable to influence the
governments welfare function due to its own meager surpluses. Change in tariffs in this
case is solely dictated by the change in weights on the consumer surplus. The third case,
depicts a situation where slope of demand curve is relatively higher. Note that compared
to the previous cases, tariffs are significantly lower. However, this is solely because of a
reduction in the price at which the residual demand becomes zero. That is, the
government in fact, raises tariffs to its maximum possible level. Note that this policy
would also lead to a zero hazard rate, thus stabilizing the risks of invasion. Risk of
invasion plays a role in affecting tariffs in the previous cases too, through its affect on
the postinvasion value function. It is interesting to note that since there are no revenues
in the postinvasion scenario, the postinvasion value function is heavily influenced by
the weight on the consumer surplus. However, the postinvasion value is never
significant enough to enforce a higher tariff thus causing corner solution as in this case.
Further, it was found that as the damages to the rest of the economy from invasion
increased significantly, even the previous cases showed corner solutions, forcing tariffs at
their maximum possible levels. This is because if the damages significantly outweigh the
gains in the postinvasion scenario, higher tariffs can help mitigate the risks of falling in
that state.
Finally, in the last case, when the slope of the supply curve is much higher than
that of the demand curve, tariffs reach their maximum levels. This happens despite the
fact that the consumer surplus is significantly larger than the producer surplus. The
relative differences in the slopes of the demand and supply curves push the point of zero
residual demand higher, enabling higher tariffs, and therefore increasing residual demand
of imported goods (thus increasing revenues) and producer surplus. Their combined
effect outweighs the loss in consumer surplus when assigned lower weights.
Though it is possible to get a different set of results from a combination of a
different set of parameters that assign higher producer surplus than consumer surplus, the
direction movement of tariffs should be fairly intuitive by now. The example highlights
the role of weights and elasticities on the optimal selection of tariffs. While the weights
highlight the significance that the government assigns to this particular industry and also
the rest of the economy (through weights on its own revenues), the slopes of the supply
and demand curves determine the role the lobby group can play in affecting tariffs. A
higher producer surplus also means a higher ability to contribute. Interestingly, the
influence of government weights can be counter balanced by the influence of slopes of
demand and supply as they both directly and indirectly affect government welfare. The
significance of risk of invasion too is dependent upon these weights and slopes as they
affected the welfare in the postinvasion scenario.
While the above simulation analysis is based upon the scenario of no tariffs after
invasion, several other possibilities exist. In the next sections we explore such
possibilities.
Scenario II: Bargaining Continues after invasion
While elimination of tariffs in the postinvasion scenario is one possibility,
another possibility is that the government retains the tariff structure purely for revenue
purposes. Now, in the postinvasion scenario, the government maximizes its objective
function with respect to tariffs:
(p 8')2 (a pt)2 t t Pt _
(37) a +b (ab) (p ) ( )( ) +
28 2/7 P
where 0'is the new intercept of the supply curve for the producers assuming that an
invasion causes their fixed cost of operation to go up. C' is the contribution in the post
invasion scenario. Taking the first order condition of (37) with respect to tariffs we get:
a (2b + a 1)
(pW" ') + (a p")
(38) Z"* = 2 2,8
(1 b) b 1 1
+ (1 a b)( +)
23 2,/7 
Note that, since the postinvasion scenario does not involve any further threats of
invasion, there is no state variable involved there. As a consequence r* would be the
optimal tariff in each period following an invasion. For the sake of simplicity, we ignore
damages (d) to the rest of the economy from an invasion. Value function in the post
invasion scenario can be derived as the sum of discounted profits in the long run from the
time of invasion t:
(39)
V {a (pW+ ')2 (a w )2 ){ w *) w )tt t
V= a +b +(lab) () +C' er
where the contributions are a function of the tariffs as before:
(40)
C 1
C'
(P' + ')2 (wP" )2 b(a p' r)2
2a b) + (2a + b 1) )2
2S 2S 26
apWr p+r 0' b(ap')2
a b)r{ +2
P 9 23
The current value Hamiltonian for maximization of profits in the pre and postinvasion
scenarios is given by:
(41)
(p"+ 8)2 w _" )2 ap"z p"+ B 1 C w
a 0 (pW+b )+(1ab)( l)(P )+C+
28 2p L P j }
ae(P +(PW +b 80')2 C (a *)2 _b ) wp pW )+ r/+8 )
a +b 2 +(1ab) (P )( .) +C
r 28 2)6 +P
where
(42
( a(pw + Z* _')2 (a P  )2 +(l.b)r p )(P+ T* 0')+ C
152 2,8 8[ Pt y 85 }
is the instantaneous benefits (say, IBpost) in the postinvasion scenario13. Similarly,
(43
(p + r )2 ( p r)2 _ ) _ pw 
a +(P +) b(P) +(1ab) (pw)(pW+ O ) +C
23 2/ P
is the instantaneous benefits (say, IBpre) in the preinvasion scenario. Note that the
difference in these benefits is caused due to an increase in the fixed costs of production,
0 for the private sector.
Proposition 2:
2.1 For any given tariff level, IBPOST would differ from IBPre by a factor f from a
marginal increase in 0.
2.2 Preinvasion tariff level would always be higher than the postinvasion tariff level.
Proof 2.1: In order to see this, let's look at the impact on IBpost from a marginal change
in 0. This change is derived by taking the partial derivative of IBpre with respect to 0.
Substituting the value of C from above into (43)and differentiating we get:
( (IB pre) a(2(pw 0) + r)
(44) <0
80 23
Then, for small enough changes in 0, IBpost can be written as:
IBpost=IBpre+ (IB pre)f where f represents the marginal change derived above in
equation (44).
13 The instantaneous function IB is the same as the government benefit function GB derived before in the
one shot game, except with a time argument.
Proof 2.2: Substituting (44) into the current value Hamiltonian (cvh), the cvh can be
written as:
(45) cvh= IB PRE() + (IB PRE(* ) (1+ f)Aet e t +
I r
In the above, the second term under brackets is IBpost which is some fraction of the IB
pre, evaluated at r*. From equation (44) we also know that f is a negative term. That
is, small changes in 0 would invariably lower IBpre. The two terms under bracket in
(45) denote a tradeoff between the pre and postinvasion instantaneous values, as
A e "t) denotes the chances of invasion exactly at the instant t, thus yielding
(IB pre) (1+ f)e at the time of invasion in discounted sum of future benefits and
r
e t) denotes the chance of the system surviving until time t, yielding IB pre in each
period until invasion. That is, as long as the system is uninvaded, the government
receives, IBpre(r) in each period and after invasion it receives IBpre( r )(1+f) in each
period. Now, we know that the instantaneous benefit is falling in 0 from (44), thus
suggesting IBpre(O', r* )
of r* in the preinvasion scenario too, its per period profits would be higher than those
in the postinvasion scenario. But we also know from equation (20) that the tariff level in
a one shot game is a function of 0 too and is given by :
a
dz 28
(46) 2
S0 ( (1 a b)( +)
28 2/7 / 3
From concavity condition of the instantaneous benefit function we know that the
denominator would be negative, thus making the partial in (46) negative. So
r(O') < r(O). Now when the instantaneous benefits function is increasing but concave in
tariffs, tariffs in the preinvasion situation would always be higher than that in the post
invasion situation, ceteris paribus. When an infinite horizon as above is concerned, it
would pay to raise preinvasion tariffs even higher as it reduces the chances of invasion.
Next let us look at a case when invasion leads to an alteration in the shape of the
supply curve, altering its marginal costs, however, leaving the fixed cots intact as before.
Under such a situation following proposition is made:
Proposition 3:
3.1 When there is a change in the slope of the cost curve for private producers following
an invasion, IBpost differs from IBpre by a factor g.
3.2 Preinvasion tariff would always be higher than the postinvasion tariff when g is
b
negative and a > 1 
2
3.3 Preinvasion tariff could be lower or higher than the postinvasion tariff when
b
a > 1  and g is positive.
2
Proof 3.1: Following similar marginal derivation of the instantaneous function with
respect to 3 we derive the value ofg to be:
(47)
g= (1b)(+ p 0) (2a+b1)(p" 0) +2(r+p 0)(1ab)}
432
Contrary to the case of a fixed costs change before, g could be negative or positive.
Proofs 3.2: The current value Hamiltonian can now be rewritten as:
(48) cvh= IBPRE(r)+(IB PRE(*) (1+ g)Aet te M + 1l
[ r
Taking the partial of tariffs with respect to the slope of the supply curve we get:
(49)
{ u}(1 b) + b 1 + ( O) a (2b+a1)( p) l 1b 2a
a (p" 8)2 *> +(1ab)(+ I(p" 8) + (a p")' ZS' 3
o2 J2 28 2,8 p 28 2,8 2
0( (1 b) b (1 1)
+ (ab)(l+l)
S28 2/3 /P
From equation (20) we know that the terms under second and third brackets in the
numerator must be negative for any positive tariff level. Therefore the sign of equation
(49) would be determined by terms under the fourth bracket in the numerator as:
( r b b
(50) < 0 if a > and indeterminate if a <1 
98 2 2
Now, when g is negative, proposition 3.2 follows from similar logic as in propositions 2.2
Proof 3.3 : When g is positive, and negative as before, the results could go either
ad
b
way. When a > 1 *(3') < *(3), i.e., tariffs in the postinvasion scenario would be
lower. However, if the fall in instantaneous profits from a fall in tariffs in the post
lower. However, if the fall in instantaneous profits from a fall in tariffs in the post
invasion scenario is more than compensated by the rise in instantaneous benefits from a
positive g, preinvasion tariffs would be lower than the postinvasion tariffs, as lower
tariffs increase the risks of invasion and make it possible to reap higher postinvasion
rewards. When the magnitude of positive g does not compensate for the fall in IB from
lower tariffs, tariffs in the preinvasion scenario would be higher. This situation is
depicted in figure 4 below.
INSERT FIGURE 4 BELOW
Point Y leads to unambiguously lower instantaneous benefits from an increase in
3, whereas point X and Z lead to a lower and higher benefits respectively.
INSERT FIGURE 4 HERE
Finally, when both the fixed and variable costs change due to invasion, instantaneous
benefit functions may intersect, thus making any unambiguous results difficult to predict.
In the end, let us also look at a situation where government readjusts its priorities
with respect to the lobby group by changing the weights on the producer surplus in the
postinvasion scenario. This may happen for several reasons. For one, a seriously
damaging pest invasion may change the way rest of the country views the role played by
the government in combating it. That is, the government may increase the weights on
either the consumer or producer surpluses, as it may add to its vote prospects from people
outside the affected industry. This might be inferred as a further subjective weighing of
the monetary rewards to the government from consumer and producer surpluses accruing
from this particular industry. The government, on the other hand, may readjust the
weights downwards after invasion, if the prospects from other lobby groups become
relatively more bright. Under this situation the following proposition can be made.
Proposition 4: When there is a change in weights on the producer surplus in the post
invasion scenario, the postinvasion instantaneous benefits function would differ from
IBpre by a factor h. Post invasion tariffs may be higher or lower compared to pre
invasion tariff levels.
Proof 4 : By taking the partial derivative of the instantaneous benefits function with
respect to a, the value ofh could be derived as:
(pW 0O)2 r a pW +pW 0)
(51) h= ap
23 2 P 3
Notice that h could be either positive or negative depending upon whether the third term
is lower or higher than the first term in the expression for h above. Further notice that the
second term encompasses the revenue aspect in government's instantaneous benefits
function, where as the first term is the producer surplus. When the slope of the demand
curve is low, (low fp), h could be negative implying a fall in the postinvasion IB from an
increase in government weights on producer surplus. This happens as the revenue lost
from such an increase in weights outweighs the gain in weighted producer surplus to the
government. This may also happen when the slope of the supply curve is high enough.
When the instantaneous benefits function is concave, optimality would require
the preinvasion tariffs to be higher than postinvasion tariffs when h is negative.
However, if the weights assigned to producer surplus in the postinvasion scenario cause
h to be positive, the postinvasion instantaneous benefits would exceed the preinvasion
instantaneous benefits for any given level of tariffs. This would require lowering of
tariffs in the preinvasion scenario below those in the postinvasion scenario so that risks
of invasion are raised. However, ambiguities arise when the joint impact of a change in
weights and in supply function is considered. As before, the cvh can de derived as:
(52) cvh = IBPRE +(IB PRE) (l+h))Ae Mrt e + l
r
In the above analysis we have assumed that the postinvasion weights are exogenously
affected. However, these weights could be endogenously determined too by the
government, when multiple lobby groups are considered.
Conclusion
Though important to invasive species management, the political economy aspect of
public policies aimed at their control has not deserved much attention in the literature so
far. In this paper an effort is made to explore the role of interest groups affected by
invasive species in affecting import tariffs, thus influencing their effectiveness. The
paper borrows from the existing political economy models in the literature to analyze the
role of lobbyists and policy makers, which are often conflicting to a certain extent, in
influencing tariffs on particular imported goods. First, a one period bargaining game is
designed between the lobby group and the government to derive the relation between
tariffs and contributions as a function of key parameters such as the weights on the
consumer and producer surpluses, slopes of demands and supply curves, etc. While the
nature of the demand and supply curves highlight the capacity of market in influencing
public policy, the weights on consumer and producer surpluses highlight the importance
the government assigns to that particular lobby group and industry. All key results are
found to be dependent upon these weights, which signify the role of market size and
lobby power in influencing public policy. It is shown that the contributions are
increasing and convex in tariffs as long as the bargaining constraints are satisfied and
weights are not extremely high. The bargaining constraints themselves are functions of
the weights on consumer and producer surpluses. It is shown that the bargaining
constraints are less binding for the producers as their objective function has fewer
arguments. The government, using the contribution function, plays the role of
Stackelberg leader in deciding the optimal level of tariffs. Tariffs, in a one shot
bargaining game, cannot include the risk of invasion appropriately, as the risk of
invasion is a cumulative process. In order to incorporate the risk of invasion and its
impact on the welfare of the lobby groups and the government, the model is made
dynamic, with and infinite time horizon. This extension is important to incorporate the
cumulative nature of riskevolution with trade. Most risks of invasion accrue over time
and with economic activity. In order to model these characteristics of threats of invasion,
the risk of invasion is modeled as a Poisson process. The postinvasion value function is
solved for different postinvasion scenarios and incorporated into the preinvasion
optimal policy problem. Numerical simulations throw interesting insights into the
decision process affecting tariff allocation and specifically, highlight the complexity in
predicting tariffs when several conflicting interests are involved. The role of risks in
influencing tariffs is made prominent when the postinvasion scenario value function is
affected. This is shown through extension of the model involving different postinvasion
scenarios. Finally, tariff levels in the preinvasion scenario are compared to tariffs in the
postinvasion scenarios for various cases and key results derived.
When several conflicting interests such as the lobby group, the government and the
rest of the economy are involved, the impact of tariffs on risk could be compromised by
such conflicting considerations. Further, it is no longer straightforward to predict the
level of tariffs over time. This is especially evident from the comparison of pre and post
invasion tariff levels in the second scenario where preinvasion tariffs may be lowered if
the weights on consumer and producer surpluses are not the same after invasion. Tariffs
in the preinvasion scenario could also be higher or lower depending upon the weights on
producer and consumer surpluses when an invasion leads to a change in the supply
function for the producer.
In the first scenario, when the government does not get revenues in the postinvasion
period, tariffs may be increased to avoid invasion. Tariffs are also increased when high
damages are expected to the rest of the economy in the postinvasion situation. However,
when damages occur only to the interest groups concerned, the net impact on tariffs
would be a function of the weights assigned.
While the above model assumes the case of an open economy, thus leading to a one
toone relation between tariffs and an increase in domestic prices, it is possible that in the
case of a large economy such a relationship would not hold. That is, an increase in tariffs
would lead to a less then full transformation into an increase in domestic prices. Under
such a scenario, the government may have a higher flexibility in its tariff policies as it
can increase tariffs without significantly affecting its revenues, as an increase in tariffs
would not necessarily reduce import demand significantly. However, the net effect,
including the effect on contributions would be subject to the mix of key parameters
analyzed above.
References
1. McAusland, C. and C. Costello, 2004. Avoiding Invasives: Trade Related
Policies for Controlling Unintentional Exotic Species Introductions. Journal of
Environmental Economics and Management 48 : 954977
2. Costello C. and C. McAusland, 2003. Protectionism, Trade, and Measures of
Damage from Exotic Species Introductions. American Journal of Agricultural
Economics, Vol. 85, Issue 4: 964975
3. Clarke, H. R., and W. J. Reed, 1994. Consumption/Pollution Tradeoffs in an
Environmental Vulnerable to PollutionRelated Catastrophic Collapse. Journal of
Economic Dynamics and Control 18 (1994): 9911010
4. Grossman, G. M., and E. Helpman, 1994. Protection for Sale. American
Economic Review 84(4): 83350
Table 1: Results of Numerical Simulation using various Weights and Elasticities
f =1.5, 3 =2.5 a=.1, b=.l a=.1, b=.2 a=.2, b=.l a=.1, b=.3
r (6.3) 5.3 5.3 5.3 2.2
c 4.7 6.4 4.3 0
csb,csa (27,4.6) (27,4.6) (27,4.6) (27,15)
psb, psa (.16,7.7) (.16,7.7) (.16,7.7) (.16,1.9)
/ =.5, =.5
r(5.1) 2.6 2.1 2.7 1.3
c 0 0 0 0
csb,csa (81,41) (81,48) (81,40) (81,59)
psb, psa (.81,12.3) (.81,8.9) (.81,13) (.81,4.9)
/ =1.5, 3=.5
r (2.58) 1.58 1.58 1.58
c 2.9 3.5 2.51
csb,csa (27,18) (27,18) (27,18)
psb, psa (.81,6.1) (.81,6.1) (.81,6.1)
S/=.5, =2.5
r (8.4) 6.2 5.3 6.2 4
c 0 0 0 0
csb,csa (81,8.1) (81,13) (81,8) (81,25)
psb, psa (.2,10) (.2,8) (.2,10) (.2,5)
Figure 1: Contributions as a Function of Tariffs
C
30
20
10
6 8 10
a=10; P=1.5;6=2.5; a=.l;b=.1;
Figure 2: Producer and Government bargaining Constraints as a Function of
Tariffs
4 Producer's
Bargaining Constraint
2 G government's
bargaining Constraint
2 4 6 8 10
2
4
6 Tariffs
a=10; p=1.5; 0=.1;6=2.5; pw=l; a=.l;b=.l
Figure 3: Time Path of Conditional Shadow Price of Cumulative Risk of Invasion
rm
a=10; p=1.5; 0=.1;6=2.5; p'=l;y=l;a=.l;b=.1; r=.1; 0'=.15;d=l; t=10;
1 2 3 4 5
Figure 4: Optimal Tariffs before and after Invasion
Instantaneous
Benefits
X
z (
IBPre
(g+ ve)
r*(a >1
(gve)
b
r (a > 1 )
2
Tariff
