COMMUNITY BLOCKADE AND POLLUTION ABATEMENT Tsung-Hsiu Tsai* Department of Applied Economics, National University of Kaohsiung, 700, Kaohsiung University Road, Nan-Tzu District, 811, Kaohsiung, Taiwan (email: [email protected]
Jin-Li Hu Institute of Business and Management, National Chiao-Tung University, Taiwan
Leonard F.S. Wang Department of Applied Economics, National University of Kaohsiung, Taiwan
Abstract Recently, the role of community on pollution abatement is stressed in several empirical studies. These papers however do not analyze the strategic behavior of the resident group and the polluting firm formally. In this paper, we build a theoretical model to examine the effect of the resident group’s blockade threat on the firm’s pollution abatement and bribery behavior.
confirms the empirical finding: When facing the resident’s group blockade threat, the firm will increase its pollution abatement and bribes payment. Nevertheless, the effect of community pressure on pollution abatement should not be exaggerated. Our analysis indicates that the community often has to pay a great amount of blockade social costs to trade the efficiency of blockade. To improve environmental quality and to reduce the frequency of community blockade, we suggest the regulator enhance its capacity on public enforcement and to rise the ex post liability payment when a pollution accident happens.
community pressure, pollution abatement, factory blockade, social costs,
public enforcement JEL classification: N50, Q25, K42
Financial supports from Taiwan National Scientific Council (NSC-91-2621-Z-390-001 for Tsai and
NSC-87-2415-H-032-013 for Hu) are gratefully acknowledged. The usual disclaimer applies. 1
In the existing environmental economics literature, pollution abatement is mostly considered as the public sector’s job.
The public sector acts as an agent for the
community to monitor and enforce polluting firms in order to maintain environmental quality.
In addition to the role of the public sector, several recent empirical studies
suggest that community pressure also plays a role in enforcing industrial pollution especially in developing countries where the public enforcement is weak or absence (Pargal and Wheeler 1996; Blackman and Bannister 1998; World bank 2003). 1 These studies however do not provide a rigid theoretical analysis to support their argument; neither do they study the strategic behavior of the resident group and the polluting firm.
The purpose of this paper is to provide a theoretical analysis to
examine how, and to what extent, can community pressure push the polluting firm to enhance its pollution abatement. When a pollution accident happens, the resident group usually can apply litigation and negotiation to stop on-going illegal pollution or petition to the public enforcer to enhance regulation (Porter 1988).
Most countries’ environmental acts
contain a clause for civil action to allow the resident group to file a lawsuit to the court.
Most firms comply environmental standard in order to avoid litigation costs
and ex post liability payments.
It has been argued that legal lawsuit can be a
complement to public enforcement (Naysnerski and Tietenberg 1992). Using litigation to protect the environment however depends on a well-defined and effective judiciary system (Pargal et al. 2003; Tsai 1998).
some societies, especially in developing countries, the legal system may not be effective, or it may not be a social culture to resolve environmental conflicts in the
court (TEPA 1993). The other alternative to stop the firm’s on-going illegal pollution for the resident group is to negotiate cooperatively or non-cooperatively with the polluting firm (Coase 1970; Porter 1988).
It is very likely that the resident group uses (or threats to
use) protest and violence to strengthen their bargaining power in negotiation (Pargal and Wheeler 1996).
For example, among the four hundred resident-firm
environmental disputes happened in the 1980s, the resident groups in Taiwan negotiated with the polluting firms.
Based on Yeh (1993), 60% of disputes had used
factory blockade, demonstration and protest, and violence to sop illegal pollution while there is only 1% of them applied the litigation strategy.2
In Thailand, more
than 3000 villagers blockaded the Pak Mun dam project in 1999, and 500 villagers from Prachuab Khirikhan protested in a foreign funded coal fired power station project in 2000 (Quah and Tan 2002).
In Indonesia, several polluting firms installed
abatement equipment and compensated local people due to community complaints (Pargal and Wheeler 1996). These community blockade examples show that the resident group is unsatisfied with the existing regulation.
Public enforcers may respond by raising environmental
standards and enhancing monitoring efforts, however many local residents still complain that environmental enforcement is incomplete. 3
Eventually, in some
Survey the literature. The mass media name the non-litigation strategies of the resident group as `self-remedy’ which is to
remedy sufferings with the victim’s own efforts (Terao, 2002). 3
In Taiwan, industrial pollution is still the number one reason of environmental complaints during
the past decade and the frequencies of civilian petition to the Taiwan EPA against public nuisance have no significant decrease. There were 92,558 cases in 1989 and 110,827 cases in 2002. Another example, in China, the environmental authorities received over 130,000 complaints per year during 1
countries, the resident group and the polluting firms have gradually established a “blockade-and-bribery” culture.
When facing the resident group’s blockade, the
polluting firm is used to pay bribery (or compensation) to the resident group. Without blockade threats, the firm will not pay “candies” to the resident group. Many blockade events in Asia ended with a huge monetary transfer from the firm to the resident group.
In some extreme cases, to ensure certain public NIMBY
facilities operate, the government even provides grants to the local government to ‘bribe’ the nearby villages for the acceptance of the facility (Quah and Tan 2002). In a society with blockade-and-bribery social culture, whether community pressure can help to improve environmental quality becomes an interesting question. On the one hand, it is possible that the firm invests more on pollution abatement in order to avoid the resident group’s blockade.
On the other hand, the firm may be
more efficient to pay the resident group with money rather than to have costly environmental abatement.
From theoretical point of view, it is not so sure that
environmental quality can be improved under community pressure as empirical evidences suggested.
Moreover, if community blockade is effective, are there social
costs associated with it?
What should the public enforcers do to reduce the social
costs of blockade? In this paper, we clarify the role of community pressure in environmental management.
We investigate the effect of the resident group’s strategic behavior on
the firm’s pollution abatement behavior and compensation (or bribe payment) behavior.
By comparing the firm’s response under blockade threat and under no
blockade threat, we explore the trade-off between blockade efficiency and its
1991-93, mostly related to air, water and noise in the urban/industrial centers of east China (Dasgupta and Wheeler 1996). 1
associated social costs.
We then take a further step to investigate the regulator’s
optimal environmental policy in respond to community pressure. This paper is organized as follows.
In section 2, we define a game to represent
the resident group’s strategic behavior in blockade and the firm's response in pollution abatement.
In section 3, we build a benchmark model to represent the
situation when the resident group is not allowed to use the blockade threat.
benchmark model is used to compare with the model in section 4 where the resident group is allowed to blockade.
The comparison of these two models in section 5 will
be used to calculate the social costs of blockade, and to derive the optimal public enforcement policy.
In section 6, we extend the blockade model to examine the
effects of exogenous variables on the firm’s decisions.
Section 7 concludes this
Define The Game
We consider a community with one firm and a group of community residents.
firm emits pollution that imposes a negative externality on the community.
public sector sets an environmental standard to regulate the firm’s polluting behavior. The firm invests on pollution abatement depending on the standard. public sector cannot fully observe the firm’s pollution abatement effort.
Assume the When the
firm’s abatement effort is not sufficient to meet the standard, pollution accidents can happen any time.
The firm then may face the resident group’s blockade threat to
stop illegal pollution. Assume the firm and the resident group negotiate non-cooperatively with each
other, we establish a two-player game to elaborate both groups’ interactions.4 two players are the resident group (R) and the firm (F).
The game takes two stages.
At stage 1, the firm decides the level of pollution abatement (a) and the amount of monetary transfer (b) to the resident group hoping to reduce the scale of blockade threat from them.
Given the firm’s pollution abatement effort, the nature decides the
probability of pollution accident.
If the firm’s investment on pollution abatement is
sufficient to prevent any pollution accident to happen, the resident group will not blockade at all.
Only when the pollution abatement level is not enough and the
probability for pollution accident is greater than zero, the resident group decides whether to blockade the firm at stage 2. If they decide to blockade the firm, the scale of their blockade density (d) will depend on the firm’s take-it-or-leave-it offers on monetary transfer and pollution abatement. The game tree is illustrated in Figure 1.
[Figure 1 here]
Since the resident group’s strategic behavior on blockade only happens when the firm causes a pollution accident, we define the probability of pollution accident as the following.
Given the government’s regulated emission standard ( e ), the firm
decides a pollution abatement effort (a).
The firm’s pollution emission (s) depends
on its abatement effort: More efforts in pollution abatement will reduce the firm’s emission level, i.e., s ′( a ) < 0 .
To meet the public sector’s emission standard, the
firm needs to invest a unit of pollution abatement, i.e., s ( a ) = e .
If the firm’s
Since the players act non-cooperatively, the Coasian bargaining solution does not apply here. 1
abatement effort is less than a , its emission level will be higher than the regulation standard.
Denote e(a) as the firm’s overcharged emission, i.e., e( a ) = s( a ) − e .
Assume e(a) is a convex decreasing function with e′( a ) < 0 and e′′( a ) > 0 .
probability of an environmental accident is denoted by θ(e(a)). Assume θ(e(a)) is an increasing concave function with θ a′ ( e( a )) < 0 , θ a′′( e( a )) > 0 , and θ(e(a)) is converging to 1 as e(a ) → ∞ .
Notice that the probability of an environmental
accident is zero whenever the firm obeys the pollution standard e , i.e., when e( a ) ≤ 0 , θ ( e( a )) = 0 .
With the above assumption, we graph e(a) and θ(e(a)) in
(Figure 2 )
The Model Without Blockade
We fist consider the situation that the resident group is not allowed to use the blockade threat to stop the firm’s illegal pollution.
This is a benchmark model in
which we want to compare it with the one that allows the resident group to blockade. In this model, the resident group cannot blockade the firm even when they know the probability of environmental accident is greater than zero. the firm’s illegal pollution by filing a lawsuit to the court.
They can only deter
Assume the court can
fully observe the firm’s probability of pollution accident and the legal cost is zero. The resident group’s expected total reimbursement from the court is the product of the probability of pollution accident θ(e(a)) and unit ex post liability (L).
situation, the firm does not have to bribe the resident group, however, it still needs to invest on pollution abatement to lower the total reimbursement to the resident group.
Without blockade, the resident group’s decision on the scale of blockade density d=0, even when the probability of pollution accident θ ( e( a )) > 0 .
group’s expected utility is as follows: ~ U ( d = 0) = θ ( e( a )) ⋅ L − h ⋅ e( a ) .
The first component represents the expected ex post reimbursement received from the firm authorized by the court θ ( e( a )) ⋅ L ; it depends on the magnitude of the firm’s abatement effort (a) and the unit ex post liability L.
The second component of the
resident group’s expected utility is the negative externality caused by the firm’s emission; the parameter h represents the unit harm caused by the firm’s overcharged emission.
Overall, the resident group’s expected utility depends on the firm’s
decision on pollution abatement. Without community blockade threat, the firm does not have to pay a monetary transfer to the resident group, b=0.
The firm only has to decide the level of
pollution abatement based on the following profit-maximization problem. Max π~( a ) = π 0 − φ ⋅ a − f ⋅ e( a ) − θ ( e( a )) ⋅ L , a
where π 0 represents the firm’s net revenue; φ represents the unit cost of the firm’s pollution abatement; f represents the unit fine paid to the government due to the overcharged emission; the last term is the total amount of ex post liability payment paid to the resident group. The firm’s optimal abatement level is determined when the marginal cost of abatement (denoting as MCANB) equals to the marginal benefit of abatement (denoting as MBANB). MBANB = − f ⋅ e′( a ) − θ a′ ( e( a )) ⋅ L = φ = MCANB The marginal cost of abatement is φ.
The marginal benefit of abatement comes from 1
The first source is from the marginal benefit of abatement on fine,
denoting as MBAFNB; it represents the reduced fine paid to the government due to an increase of abatement effort, MBAFNB = − f ⋅ e′(a ) with
∂MBAFNB > 0. ∂a
second component is the benefit in the reduced total ex post liability payment due to an increase of abatement effort in lowering the probability of environmental accident. Denote it as MBAPNB, MBAPNB = −θ a′ ( e( a )) ⋅ L with
∂MBAPNB > 0. ∂a
Let a~ be the firm’s optimal abatement effort in this model.
~ group’s expected utility is U = θ ( e( a~ )) ⋅ L − h ⋅ ( e( a~ )) , and the firm’s profit function is π~ = π 0 − φ ⋅ a~ − f ⋅ e( a~ ) − θ ( e( a~ )) ⋅ L , respectively.
The Model With Blockade
In this section, we assume the resident group is allowed to use blockade threat to negotiate with the firm when a pollution accident happens.
This subgame is on the
right knot of the game tree in Figure 1. We use backward induction to solve this sequential game.
4.1 The Resident Group’s Utility Maximization Problem Assume the resident group’s objective function is to maximize their utility.
the firm’s take-it-or-leave-it offer on the abatement effort (a) and bribes (b), the resident group decides the scale of blockade (d).
The resident group’s expected
utility is as the following: d ⋅L 1 − 2 ⋅ c ⋅ d 2 − h ⋅ e( a ) . 1+ b
The resident group’s expected utility is composed with several elements.
Max U ( d ) = b + θ ( e( a )) ⋅ d
element is the bribes b that the resident group received from the firm.
element represents the resident group’s total ex post liability payment received from the firm θ ( e( a )) ⋅
d ⋅L . 1+ b
Different from the model without blockade, the total ex
post liability payment in this model is determined more than the exogenous ex post unit liability L and the magnitude of the probability of pollution accident θ ( e( a )) . We assume the resident group’s scale of blockade d, and the probability of the resident group’s embarrassment in receiving bribers, denoting as
1 , will also 1+ b
affect the magnitude of the total ex post liability payment. The concept of the probability of the resident group’s embarrassment in receiving bribes is from Bruno (1997).
He argues that people often has an environmental social norm in mind.
This social norm refers to the resident group’s subjective evaluation of the physic benefit in participating in the blockade to protect the environment.
resident group’s purpose in participating in blockade is for the environment, receiving bribes from the firm will embarrass themselves.
Overall, the firm’s total liability
payment increases with the scale of blockade, and decreases with the bribes. third element of equation (4) cost.
⋅ c ⋅ d 2 represents the resident group’s total blockade
Parameter c represents the unit cost of blockade.
Finally, the last term
h ⋅ e(a ) represents the harm caused by the firm’s overcharged emission. Solving the resident’s group’s utility maximization problem, we obtain the optimal scale of blockade: d * ( a, b, L, c ) =
θ ( e( a )) ⋅ L . c(1 + b)
In this stage, the resident group’s blockade decision decreases with the firm’s
abatement effort and bribes, i.e.,
∂d * ∂d * < 0 and < 0. ∂a ∂b
4.2 The Firm’s Profit Maximization Problem Given the resident group’s decision on the scale of blockade d*, the firm solves the following profit maximization problem by choosing an optimal amount of pollution abatement effort (a) and bribes paid to the resident group (b):
L⋅d* . Max π ( a, b) = π 0 − b − φ ⋅ a − f ⋅ e( a ) − θ ( e( a )) ⋅ a ,b 1+ b Parameters in equation (6) are similar to the model without blockade.
(6) That is, π0, φ ,
and f represent the firm’s net revenue, the unit cost of pollution abatement and the unit fine paid to the government due to the overcharged emission, respectively.
only difference is on the last term in which the firm’s ex post liability payment is not determined by the court but rather by the resident group’s blockade threat.
4.2.1 Optimal Pollution Abatement The first-order necessary condition of optimal abatement to the maximization problem is when the marginal benefit of abatement (denoting as MBA) equals to the marginal cost of abatement (denoting as MCA). MBA = − f ⋅ e′( a ) − θ ′( e( a )) ⋅
d* ⋅ L L ∂d * − θ ( e( a )) ⋅ ⋅ = φ = MCA 1+ b 1 + b ∂a
The marginal benefit of abatement comes from three sources.
The first is from the
reduced fines paid to the government due to an increase of abatement effort, denoting as MBAF = − f ⋅ e′(a ) .
The second source is from the reduced total ex post liability
payment paid to the resident group due to an increase of abatement effort in lowering 1
MBAP = −θ ′( e( a )) ⋅
d* ⋅ L > 0. 1+ b
The last source of the marginal benefit of abatement
is from the reduced scale of the resident group’s blockade due to an increase of abatement effort, denoting as MBAD, with MBAD = −θ ( e( a )) ⋅
L ∂d * ⋅ >0 . 1 + b ∂a
Overall, the marginal benefit abatement is decreasing with the firm’s pollution abatement, i.e., MBAa′ < 0 and MBAa′′ > 0 .
Figure 3a shows the optimal
abatement effort a*.
4.2.2 The Optimal Amount of Monetary Transfer The first-order necessary condition of optimal bribes to the firm’s profit maximization problem is when the marginal benefit of bribery (MBB) equals to the marginal cost of bribery (MCB).
That is, MBB = θ ( e( a )) ⋅
L⋅d* L ∂d * − θ ⋅ ⋅ = MCB = 1 . ( ( )) e a (1 + b) 2 1 + b ∂b
The marginal benefit of bribery contains two parts.
The first part represents the
benefit in reducing the firm’s total ex post liability payment due to one more dollar of bribery in raising the resident group’s probability of embarrassment, denoting as MBBE, with MBBE = θ ( e( a )) ⋅
L⋅d* > 0. (1 + b) 2
The second part of marginal benefit of
L ∂d * bribery is denoting as MBBD, with MBBD = −θ ( e( a )) ⋅ ⋅ > 0 ; it represents 1 + b ∂b the firm’s reduced total ex post liability payment due to one more dollar of bribe in reducing the resident group’s scale of blockade. bribes b*.
Figure 3b shows the optimal
4.3 Equilibrium Solutions to the Maximization Problem To ensure optimal solutions exist, we have checked that the Hessian matrix is negative semi-definite, and the second order conditions of equation (4) and (5) are negative.
Moreover, to ensure that the bribes are nonnegative, we assume that the
resident group will blockade only when the unit cost of blockade satisfies the condition of c ≤ 2(θ ( e( a )) ⋅ L) 2 .
With this assumption, we prove there exists
solutions for the firm’s optimal pollution abatement and bribery.
[Proof] solving equation (7), we can obtain the optimal bribery is b = 3 2 [θ ( e( a )) ⋅ L]2 − 1 . c
Plug equation (8) into equation (6), we get − φ − f ⋅ e′( a ) −
2 L2θ ( e( a ))θ ′( e( a )) =0. c 2 3 2 (θ ( e( a )) ⋅ L ) 2 c
Since when a → 0 , equation (6)→+∞, and when a → ∞ , equation (6)→ − φ , we then prove there exists solutions for an optimal a. In equilibrium, the resident group’s expected utility (U*) and the firm’s profit function (π*) are as follows. 1 (θ ( e( a * )) ⋅ L) 2 U =b + ⋅ − h ⋅ ( e( a * )) * 2 2 c(1 + b ) *
π * ( a * , b * ) = π 0 − b * − φ ⋅ a * − f ⋅ e( a * ) −
[θ ( e( a * )) ⋅ L]2 . c(1 + b* ) 2
5. Trade-off Between Efficiency and Social Costs In the last two sections, we have shown the players’ payoff functions in blockade and 1
no blockade situations.
In this section, we compare the models.
Our purpose is to
examine the effect of the resident group’s blockade threat on the firm’s investment on pollution abatement, and to calculate the social costs of blockade.
5.1 The optimal abatement and bribery In the model without blockade, the firm does not have to pay any bribery to the ~ resident group, i.e., b = 0 .
In the model with blockade, the firm will pay b* to the
~ resident group, since b* ≥ 0 , we have b* ≥ b = 0 . As to the firm’s pollution abatement effort, we find it is intuitive that the firm’s pollution abatement level with blockade threat is greater than the pollution abatement without blockade threat, i.e., a * > a~ .
This is because the marginal cost of
abatement in these two models is the same, i.e., MCA=MCANB=φ, however the firm’s marginal benefit of abatement under blockade threat is greater than the marginal benefit of abatement without blockade threat, i.e, MBA>MBANB. (3a) we can get a * > a~ .5
Based on Figure
We then derive proposition 1.
The firm will invest more on pollution abatement when facing
the resident group’s blockade threat than without.
Environmental quality thus is
better off when the firm faces community blockade threat. Proof:
Q a * > a~ and e′( a ) < 0 , we get e( a * ) < e( a~ ) .
The firm’s overcharged
emission under blockade threat is less than the one without threat.
2⋅d* ⋅L MBA − MBANB = − f ⋅ [e ′( a * ) + e ′( a~)] − [θ a′ ( e( a * )) ⋅ ⋅ +θ a′ ( e( a~ )) ⋅ L] > 0 1+ b
Q e′( a ) < 0 and θ a′ ( e( a )) < 0 . 1
This result confirms the findings by Blackman and Bannister (1988), Pargal and Wheeler (1996), Hettige, et.al. (1996), and World Bank (2003) in which they show community pressure plays a role in industrial pollution abatement based on empirical data from Mexico, Indonesia, and China respectively.
5.2 The Social Cost of Blockade Although community blockade can be effective in pushing the firm to invest more on pollution abatement, blockade is not costless to the community.
The concept of
social costs often refers to as the sum of private costs and external costs.
this concept, we define the social costs of blockade as the following.
Define the social cost of blockade as the sum of the firm’s extra
total abatement cost, total monetary bribe paid to the resident group, total blockade cost of the resident group and the reduced damage from the firm’s overcharged emission.
Based on this definition, we calculate the social cost of blockade. ≥ SC = φ ⋅ ( a * − a~ ) + b* + 12 ⋅ c ⋅ d *2 + h ⋅ [e( a * ) − e( a~ )] 0 ≤ From the social point of view, to reduce the amount of social welfare, the regulator should asks the firm to at least invest on a : Min a
SC = φ ⋅ ( a * − a~ ) + b* + 12 ⋅ c ⋅ d *2 + h ⋅ [e( a * ) − e( a~ )]
db* dd * de( a ) + c ⋅d* ⋅ +h⋅ =0 da da da
Max W = π * ( a * , b* ) + U * ( a * , b* ) = π 0 − φ ⋅ a * − f ⋅ e( a * ) − h ⋅ e( a * )
φ = f ⋅ e′( a * ) + h ⋅ e′( a * ) not yet finished!!!!
Comparative Static Analysis of Blockade Model
Without considering the social cost of blockade, we have shown that community blockade is effective on pollution abatement from proposition 1.
This indicates that
in certain circumstances, private enforcement can be an alternative to public enforcement.
In this section, we discuss how the firm’s policy variables in response
to changes in exogenous variables.
Table 1 summarizes the results of comparative
statics analysis.6 Propositions  to  are derived directly from table 1.
Comparative Statics of the Optimal Level of Abatement (a) and Bribery (b) under the Blockade Model
The unit fine imposed by the regulator
The unit of ex post liability
The resident group’s unit blockade cost
PROPOSITION 2: The firm’s optimal abatement effort unambiguously increases with the government’s emission fine; and the optimal bribery unambiguously decreases
Please refer to the appendix for the detail calculation. 1
with the government’s emission fine. Proof:
dMBAF > 0 , ∴MBA increases. df
pollution abatement investment.
The firm thus will invest more
The increase of a lowers the probability of
pollution accident θ ( e( a )) and drags the firm’s marginal benefit of bribery MBB. The firm thus is less willing to pay bribery to the resident group.
The increase of the government’s fine indicates that the firm’s overcharged emission is more expensive. pollution abatement effort.
It is not surprisingly that the firm will increase its
As to the bribery, it can be treated as a “punishment” to
the firm for its overcharged emission. bribery is paid to the private sector.
Instead of paying it to the public sector, the In this sense,
db* < 0 indicates that the firm df
will pay fewer bribes to the resident group if it has to pay higher fine to the government. substitute.
Fine (public enforcement) and bribery (private enforcement) are This result differs from Naysnerski and Tietenberg (1992) in which they
conclude private enforcement is a complement to public enforcement.
The firm’s optimal pollution abatement effort unambiguously
increases with the ex post liability payment; however, the optimal bribery may increase or decrease with the ex post liability payment.
dMBAD dMBAP dMBA > 0 and >0, ∴ > 0 , the firm increases dL dL dL
pollution abatement effort a.
The marginal benefit of bribery due to an increase of
ex post liability L is however not straightforward. 1
On the one hand, the firm’s
increase of a lowers the probability of pollution accident θ ( e( a )) and drags down the marginal benefit of bribery MBB; on the other hand, the increase of ex post liability L rises up the level of MBB.
Overall, the firm can decrease or increase its
optimal bribery in respond to the change of ex post liability L.
PROPOSITION 4: The firm’s optimal pollution abatement effort decreases unambiguously with the resident group’s blockade cost; however, the bribery payment may increase or decrease with the resident group’s blockade cost. Proof:
dd * dMBAP dMBAD dMBA 0
~ [π~, U ]
Game Tree of the Model
Figure 2a: Abatement and Overcharged Pollution Emission
Figure 2b: Overcharged Pollution Abatement and the Probability of Pollution Accident
a* Figure 3a: Optimal Pollution Abatement Effort
MCB=1 MBB b* Figure 3b: Optimal Bribery
Appendix: Comparative Statics Analysis on the Blockade 1
Model Denote the first order conditions as
π a = φ + f ⋅ e′( a ) + π b = −1 +
1 1 ∂d * ⋅ θ ′( a ) ⋅ m ⋅ d * + ⋅ θ (a ) ⋅ m ⋅ =0 ∂a 1+ b 1+ b
1 1 ∂d * * ⋅ θ ( a ) ⋅ m ⋅ d − ⋅ θ ( a ) ⋅ m ⋅ =0 (1 + b) 2 1+ b ∂b
Since this is a maximization problem, the Hessian matrix is negative semifedinite, the second order condition π aa ≤ 0 , π bb ≤ 0 and
π aa π ab ≥ 0 . Moreover, we have π ba π bb
π ab = π ba < 0 .
(A1) Comparative static analysis on L Totally differentiate equation π a and π b , we obtain π aa π ba
π ab da π af π ⋅ = − aL ⋅ dL − π bb db π bL π bf
π ⋅ df − ac ⋅ dc π bc
π aL > 0 , π bL > 0 Apply the Cramer’s rule,
π da 1 = − ⋅ (π aL ⋅ π bb − π ab ⋅ π bL ) > 0 , where A= aa π ba dL A
π ab ≥0 π bb
< db 1 = − ⋅ (π aa ⋅ π bL − π aL ⋅ π ba ) 0 > dL A
(A2) Comparative static analysis on f Because π af = e′( a ) < 0 and π bf = 0 , apply the Cramer’s rule, we have 1 da = − ⋅ (π af ⋅ π bb − π ab ⋅ π bf ) = 0 , Q π bb = π bf = 0 . df A 1 db = − ⋅ (π aa ⋅ π bf − π af ⋅ π ba ) < 0 . df A
(A3) Comparative static analysis on c
π ac < 0 π bc < 0 Apply the Cramer’s rule, da 1 = − ⋅ (π ac ⋅ π bb − π ab ⋅ π bc ) < 0 , dc A < 1 db = − ⋅ (π aa ⋅ π bc − π ac ⋅ π ba ) 0 > dc A