Group Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 04-10
Title: Invasive species management through tariffs : are prevention and protection synonymous?
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Title: Invasive species management through tariffs : are prevention and protection synonymous?
Series Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 04-10
Physical Description: Book
Language: English
Creator: Ranjan, Ram
Publisher: International Agricultural Trade and Policy Center. University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: December 2004
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Bibliographic ID: UF00089795
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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WPTC 04-10

i -ional Agricultural Trade and Policy Center

Ram Ranjan

WPTC 04-10 December 2004




Institute of Food and Agricultural Sciences




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 multi-disciplinary 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 University-wide 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 nation-wide 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.


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 revenue-interests
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 post-invasion 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

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 32611-0240
Email: rranjan(, Phone: (352) 392 1881 Ext. 326, Fax: (352) 392 9898


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,


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 BSE-CJD).

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 interest-groups'

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 import-competing 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. Post-invasion scenarios may completely differ from pre-invasion 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 one-shot 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 pre-invasion 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.


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
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 (1-a-b) 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


(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 a-pR- 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 ++(1-a-b) (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:


a f b +(1-a-b) -p)L) ( ) +C a(P-2 -+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:


Max c
a )2+b +(1-a-b) (p ) ( )( ) +Ci a +b )2
26 28 2P ( 256 2p

\{(p )2 _(p _0)2_

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:


( -2a b) + + (2a + b 1) (p b(a p )2
1 28 28 2,
2(1-a-b) a b)a-p- pW+rz-0 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:


2a (p + ) b(a p r)
aC 1 8 P
dr 2(1- a b) az a-p pw+z- + 1 1
S( -a-b){ (1 a -b)r{-+-}
P 8 P p

02C (1 l-2a- 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.


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:


a 2 I_ )2 t2 t t (p, w_ 2 (a w, 2
S a +b +(l-a-b) (p'-p") ( )-( +C a +b
r pT2 28 2,8 a 28 2fi

(-1 + 2a + b)f + (-2 + 2a + 3b)3

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 non-positive 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


(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.


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 ((1-a-b) 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 +(1-a-b) (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


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 post-invasion 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


(23) p(t) = (q(r(s)))ds


(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

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 :


(a )2 (a +(1-a-b) (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 post-invasion 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 -(1-a -b)d
(28) V 2 2,- er

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:


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( ) -(1-a-b)d
oa-p" -r +p"-O. (1-a-b)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:


2 1-b b 2a+b-1) W2 b
(r+p- 0) { }+(a -r- )2{ -}+(p 0)2( +(a-p)2 +
43 4,8 49 4,
a b _e) +
W a(P ((pW )2 + -(a- p)2 (1 -a-b)d
a- p _r+p" -0 (-a- b) 2+ 2e c t
P 3 2 r
a1( + p r)

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 1-a-b (a-pw) (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 -(1-a-b)d
26 2,
-r7 e-" =f1e

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 post-invasion 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 (1-a-b) ) 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 post-invasion value is positive, an increase in tariffs would still be

warranted as long as the pre-invasion value exceeds the post-invasion value. The optimal

path of tariffs would be decided by the no-arbitrage conditions derived below:


S1-b ) 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 -(1-a -b)d
a b. -)+ z -(P -0 Q- a b)z( b 25 28
a-p'-r r+p- (1-a-r 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:


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 (pW-0')2 + (a- p)2-(1-a-b)d
a-pW-r r+pW-O} (1-a-b)r 2- (p 2/3
P 8 2 r
+rle" +le'A

Rewriting the above we get:


r + {r{


1-b b 2a+b-1 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 1-b (a -p )b 1-a-b (a -pW)
-+--(1 -ab)(+ ) +(p -)(-)- + (
25 2, JP 25 2, 2 P
(p -)2 (apW)2 -(1- a -b)d
22 2 ert

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 1-b b 1 1
(36) -= +--(1-a-b-+
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 +


(p -0).

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 pre-invasion 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 post-invasion value falls due to

reduced risks. Figure below shows the graph of for a low combinations of the

weights on consumer and producer surpluses1.


Steady State

Steady state implies / =0, which would happen when the hazard rate is zero. Solving

ctd +/
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 post-invasion value function. It is interesting to note that since there are no revenues

in the post-invasion scenario, the post-invasion value function is heavily influenced by

the weight on the consumer surplus. However, the post-invasion 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 post-invasion 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 post-invasion 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


Scenario II: Bargaining Continues after invasion

While elimination of tariffs in the post-invasion scenario is one possibility,

another possibility is that the government retains the tariff structure purely for revenue

purposes. Now, in the post-invasion scenario, the government maximizes its objective

function with respect to tariffs:

(p 8')2 (a pt)2 t t Pt _
(37) a +b (-a-b) (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 post-invasion 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:


V {a (pW+ ')2 (a w )2 ){ w *) w )tt t
V= a -+b +(l-a-b) ()- +C' e-r

where the contributions are a function of the tariffs as before:


C 1

(P' + ')2 (wP" )2 b(a- p' r)2
2a -b) + (2a + b 1) )2
2S 2S 2-6
a-pW-r p+r -0' b(a-p')2
a -b)r{ +2
P 9 23

The current value Hamiltonian for maximization of profits in the pre and post-invasion

scenarios is given by:


(p"+ 8)2 w- _" )2 a-p"-z p"+ -B 1 C w
a 0 (pW+b )-+(1-a-b)( 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 +(1-a-b) (P )-( .) +C
r 28 2)6 +P



( 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, IB-post) in the post-invasion scenario13. Similarly,


(p + r -)2 (- p -r)2 -_ ) -_ pw -
a +(P +-) b(-P-) +(1-a-b) (-pw-)-(pW+ O ) +C
23 2/ P

is the instantaneous benefits (say, IB-pre) in the pre-invasion 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, IB-POST would differ from IB-Pre by a factor f from a

marginal increase in 0.

2.2 Pre-invasion tariff level would always be higher than the post-invasion tariff level.

Proof 2.1: In order to see this, let's look at the impact on IB-post from a marginal change

in 0. This change is derived by taking the partial derivative of IB-pre 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, IB-post can be written as:

IB-post=IB-pre+ (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)Ae-t e t +
I r

In the above, the second term under brackets is IB-post 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 IB-pre. The two terms under bracket in

(45) denote a trade-off between the pre and post-invasion 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

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 un-invaded, the government

receives, IB-pre(r) in each period and after invasion it receives IB-pre( r )(1+f) in each

period. Now, we know that the instantaneous benefit is falling in 0 from (44), thus

suggesting IB-pre(O', r* )
of r* in the pre-invasion scenario too, its per period profits would be higher than those

in the post-invasion 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 :

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 pre-invasion 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 pre-invasion 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, IB-post differs from IB-pre by a factor g.

3.2 Pre-invasion tariff would always be higher than the post-invasion tariff when g is

negative and a > 1 -

3.3 Pre-invasion tariff could be lower or higher than the post-invasion tariff when

a > 1 - and g is positive.

Proof 3.1: Following similar marginal derivation of the instantaneous function with

respect to 3 we derive the value ofg to be:


g= (1-b)(+ p -0) -(2a+b-1)(p" -0) +2(r+p -0)(1-a-b)-}

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= IB-PRE(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:


{ u}(1-- b) + b 1 + ( O) a (2b+a-1)(- p) l 1-b- 2a
a- (p" -8)2 *-> +--(1-a-b)(+ I-(p" -8) + (a- p")' ZS' 3
o2 J2 28 2,8 p 28 2,8 2
0( (1 b) b (1 1)
+ --(-a-b)(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

way. When a > 1 *(3') < *(3), i.e., tariffs in the post-invasion 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, pre-invasion tariffs would be lower than the post-invasion tariffs, as lower

tariffs increase the risks of invasion and make it possible to reap higher post-invasion

rewards. When the magnitude of positive g does not compensate for the fall in IB from

lower tariffs, tariffs in the pre-invasion scenario would be higher. This situation is

depicted in 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.


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

post-invasion 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 post-invasion instantaneous benefits function would differ from

IB-pre 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= a-p
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 post-invasion 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 pre-invasion tariffs to be higher than post-invasion tariffs when h is negative.

However, if the weights assigned to producer surplus in the post-invasion scenario cause

h to be positive, the post-invasion instantaneous benefits would exceed the pre-invasion

instantaneous benefits for any given level of tariffs. This would require lowering of

tariffs in the pre-invasion scenario below those in the post-invasion 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 = IB-PRE +(IB -PRE) (l+h))Ae Mrt e + l

In the above analysis we have assumed that the post-invasion weights are exogenously

affected. However, these weights could be endogenously determined too by the

government, when multiple lobby groups are considered.


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 risk-evolution 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 post-invasion value function is

solved for different post-invasion scenarios and incorporated into the pre-invasion

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 post-invasion scenario value function is

affected. This is shown through extension of the model involving different post-invasion

scenarios. Finally, tariff levels in the pre-invasion scenario are compared to tariffs in the

post-invasion 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 pre-invasion tariffs may be lowered if

the weights on consumer and producer surpluses are not the same after invasion. Tariffs

in the pre-invasion 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 post-invasion

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 post-invasion 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-

to-one 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.


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 : 954-977

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: 964-975

3. Clarke, H. R., and W. J. Reed, 1994. Consumption/Pollution Tradeoffs in an

Environmental Vulnerable to Pollution-Related Catastrophic Collapse. Journal of

Economic Dynamics and Control 18 (1994): 991-1010

4. Grossman, G. M., and E. Helpman, 1994. Protection for Sale. American

Economic Review 84(4): 833-50

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





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


4 -----Producer's
Bargaining Constraint

2 G government's
bargaining Constraint

2 4 6 8 10



-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


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



z (

(g+ ve)

r*(a >1-


r (a > 1 )


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