“OPERATING UNCERTAINTY USING REAL OPTIONS”

to be held on 8 - 9 July 2009

on the island of San Servolo in the Bay of Venice, Italy

Anti-Pollution Protest and Investment in Pollution Abatement Facilities

Walailuck Chavanasporn, Kannika Thampanishvong

and Wen-Kai Wang

Venice Summer Institute 10th

6 - 11 July 2009

CESifo, the International Platform of the Ifo Institute of Economic Research and the Center for Economic Studies of Ludwig-Maximilians University

Anti-Pollution Protest and Investment in

Pollution Abatement Facilities

BY WALAILUCK CHAVANASPORN, KANNIKA THAMPANISHVONG�,

WEN-KAI WANG

School of Economics and Finance, University of St Andrews

Abstract

In this paper, we study the �rm�s response to the protests by resi-

dents who are adversely a¤ected by the pollution resulted from the �rm�s

production by making a decision on the optimal time to invest in the pol-

lution abatement facilities. This paper emphasises that if the �rm bases

its investment decision on the neoclassical rule of investment, i.e. the net

present value (NPV) rule, this could lead to a misleading decision because

such rule does not take into account the irreversible nature of this type of

investment, the uncertainty over future outcomes, and the possibility of

delaying an investment to acquire more information. By using the Real

Options approach to investment, this paper shows how the interaction

between uncertainty and irreversibility a¤ects the optimal timing for the

�rm to invest in the pollution abatement facilities.

JEL Classi�cation: Q53, H23, C61, G11

Key Words: Real Options Theory, pollution, protest, irreversible

investment, uncertainty, abatement

�Corresponding Author: Kannika Thampanishvong, School of Economics and Finance,University of St Andrews, 1 The Scores, Castlecli¤e, St Andrews, Fife, United KingdomKY16 9AL, E-mail: kt30@st-andrews.ac.uk, Tel: +44 (0) 1334 462424, Fax: +44 (0) 1334462444

1

I. INTRODUCTION

This paper is devoted to consider the speci�c problem faced by many �rms,

particularly in the developing countries, whose operations generate various forms

of pollution � for examples, water, noise, soil and air � into the local ecosys-

tem. These pollutions, the by-products of the industrial production process, are

hazardous not only because the local environment is ruined but also the lives

of residents are in danger. How would the residents respond to this threat im-

posed on them by the �rms? The common modes through which the residents

express their dissatisfactions to the �rms vary but the common ones include

anti-pollution protests, roads and/or factory blockage, and backlash. For con-

venience, we collectively refer to these common modes of rebellious collective

actions as the �anti-pollution protest�.

To show how relevant is the anti-pollution protest to the operation of �rms in

practice, in what follows, we give some examples of the anti-pollution protests

that took place in the fast developing countries like China and India during

the past few years. The purpose of these illustrations is to show how the anti-

pollution protests could help ensure that the concerns of the residents in that

particular locality be addressed. The �rst illustration corresponds to an event

taking place in the northern part of India in 2006. On October 4, 2006, there

were over a thousand villagers from the village of Mehdiganj in the north Indian

state of Uttar Pradesh protested at the headquarters of the Coca-Cola Company

in Gurgaon. The aim of the protest was to raise awareness of the company on

the issue of pollution �the polluted groundwater and soil as a consequence of

the Coca-Cola�s bottling plant�s operations �and demand the immediate actions

by the company to clean up its act in India or to leave India (India Resource

Centre, 2006). The second illustration refers to the event that took place in

China in 2005. According to the report by AsiaNews (2005), 60,000 Chinese

in Huaxi Village, Zhejiang Province protested in April 2005 against high, local

levels of pollution emitted by 13 chemical plants located in that particular area.

The residents were angry with the chemical plants because these plants have

2

polluted the water and ground around the village, making agriculture in that

neighbourhood virtually impossible and forcing the farmers to seek other jobs.

These illustrations clearly give us some reassurance how relevant and impor-

tant is pollution generated from the manufacturing activities to the well-being

of the residents living near the production sites. Given that the protesters are

very serious about bringing about some changes to the actions of the �rm con-

cerned and that protests pose a serious threat to the operations of the �rm,

what would be the responses of the �rm to such situation?

The protests and other forms of rebellious collective actions by the local

residents evidently call for actions by the �rm concerned to minimise the overall

emissions of pollutions into the locality. It is interesting to draw an analogy

between the responses of �rm to the Air Quality Regulations, particularly the

1990 U.S. Clean Air Act1 or U.S. Acid Rain Programme, and the �rms�responses

to the anti-pollution protests. While there have been quite an extensive studies

�both theoretically and empirically �on the former, the formal studies on the

latter has been virtually non-existent.

Air Quality Regulations allow �rms to choose between purchasing the right

or allowances to emit speci�ed quantities of pollution, substituting inputs and

making investment in the equipment that help abate pollutions (Herbelot, 1992)2 .

Since allowances for the sulfur dioxide emissions are fully tradable, the coal-�red

electricity generators may purchase additional allowances in a given year, sell

unused allowances or bank them for future use. Alternatively, the electricity gen-

erators have an option to switch the types of fuels to low sulfur coal or natural

gas, which also help abate emissions of sulfur dioxide. Last but not least, the

U.S. power plants could retro�t their plants for �ue gas desulfurization (Halkos,

1993), a method also known as scrubbing or an installation of the scrubbers,

which are pieces of equipment which help remove sulfur dioxide from exhaust

before it is released into the air. Installation of scrubber, the last approach of

making sure that less sulfur dioxide is produced with each unit of output, clearly

requires the power plants to make an irreversible investment, at a time when

3

future prices cannot be known with certainty (Hunter and Mitchell, 1999; Ins-

ley, 2003; Löfgren et al., 2008; Tuthill, 2008). Since the real options approach

is commonly used to examine the �rm�s decision to invest in a large capital

project with uncertain bene�ts/costs, many papers which study the optimal de-

cisions of the electricity generators in the U.S. in retro�tting their plants with

the scrubbers to reduce pollution have followed this approach. This approach

has indeed been developed rapidly over the past few decades. Some examples

are provided in Dixit and Pindyck (1994), Trigeorgis (1996) and Schwartz and

Trigeorgis (2001).

While complying with the Air Quality Regulations give �rms di¤erent choices

of abating sulfur dioxide emissions, �rms do not have much alternative in re-

sponding to the anti-pollution protest by the residents. From the illustrations we

provide at the beginning of this section, it is evident that, facing with the prob-

lem of anti-pollution protest, �rms have no choice but to undertake abatements,

either by cleaning up or making investment in pollution abatement equipment

and/or facilities.

According to Dixit and Pindyck (1994), agents that base their investment

decision on the cost-bene�t analysis suggested by the neoclassical theory of

investment could lead to a misleading decision since the standard framework

ignores three characteristics that are crucial in determining the optimal decisions

of investors. First, there is uncertainty over the future costs and bene�ts of

investment. It is typically very di¢ cult for the agents to gauge/estimate the

future rewards or costs from the investment. The best the agents could possibly

do is to assess the probabilities of the alternative outcomes that could imply a

larger or a smaller pro�t (or loss). Second, there is irreversibility associated with

the agents�investment, which arises from the costs of investment. The initial

cost of investment incurred by the agents is at least partially sunk. Third, in

most cases, there is some leeway about the timing of the investment. In other

words, it could be feasible for the agents to delay their action and wait for new

information about the future.

4

These features clearly characterise the decision faced by the �rms regarding

the investment in pollution abatement facilities to control emissions of pollu-

tion into the local environment and to respond to the anti-pollution protests

by the residents. The type of pollution abating equipment/facilities we refer

to here shares lots of similarities to the scrubbers in the sense that they are

irreversible investment, are costly to install and maintain. This type of equip-

ment/facilities would help minimise the risk that the �rms will need to deal

with the anti-pollution protests in the future. The perceived bene�t of such

facilities then depend on the �rm�s expectations regarding future outputs and

pro�ts. In making a decision to invest in the abatement facilities, the �rms

need to be convinced that this option would be preferable to simply allowing

the residents to protest and obstruct their production. The irreversible nature

of abatement facilities investment and the uncertainty surrounding the outputs

and pro�ts make this problem deems suitable for an application of the real op-

tions approach. The model we consider in this paper is based on the framework

which is useful for identifying critical aspects of optimal decisions of the �rms

under uncertainty, when investment is irreversible and information is revealed

over time. We hope that this analysis would have some useful implications for

policy implementations to deal with the anti-pollution protest.

In this paper, we study how, in the midst of the protest by the residents,

irreversibility and uncertainty interact in a¤ecting the �rm�s timing of invest-

ment in the pollution abatement facility that generates less emissions into the

local environment. We introduce the analytical framework in Section 2. We

show how the �rm�s investment problem can be treated as an optimal stopping

time problem and discuss how the model could be solved. Section 3 is devoted

to present the numerical results of the model, while Section 4 concludes and

discusses some policy implications.

5

II. THE MODEL

The Environment

Consider a �rm which manufactures an output, x (t), where x (t) > 0. We

simplify our analysis by assuming that the production of x (t) requires only

physical capitals, K (t; x (t)). Suppose that the �rm�s production of output at

period t, x (t), follows the stochastic di¤erential equation given by:

dx (t) = (K (t; x (t))� �x (t)) dt+ �x (t) dW (t) , x (0) = x0; (1)

where � > 0 is the rate of depreciation, � is an uncertainty parameter, andW (t)

is a Wiener process which represents an uncertainty which could a¤ect the �rm�s

production. An example of uncertainty could be an unexpected decline in the

amount of foreign direct investment (FDI) from other countries3 , causing the

�rm to lack capital/resources to be used in the production of x (t).

We suppose that the price of the output, x (t), is denoted by pb, where

pb > 0. The relationship between K (t; x (t)) and x (t) can be described by

K (t; x (t)) = �x (t), where � < pb. We assume that, with the use of the exist-

ing facility, the production of x (t) generates some pollutions, which could take

the forms of noise pollution, water pollution, etc. as the by-products and such

pollutions are emitted into the local community. The pollutions resulted from

the �rm�s production are assumed to cause damages �both direct and indirect

� to the residents who are living in the neighbourhood of the �rm. In this

context, the direct damages correspond to damages on the residents�physical

well-being, which could include illness or discomfort, while the indirect damages

are associated with damages on the residents�personal belongings, property or

crops. As discussed in the introduction, in the midst of such situation, the res-

idents could express their dissatisfactions on the �rm�s actions by participating

in various forms of rebellious collective actions including anti-pollution protests,

roads and/or factory blockage, and backlash. By obstructing the factory and

interrupting the operation of the �rm, we assume that the anti-pollution protest

6

by residents imposes some adverse e¤ects on the production of x (t).

Formally, how do we model the impact of the anti-pollution protest by the

residents on the �rm? We capture the impact of protest on the �rm�s production,

x (t), through the state equation. In the midst of the anti-pollution protest, the

production of the �rm follows the following di¤erential equation:

dx (t) =��x (t)� �x (t)� �x2 (t)

�dt+ �x (t) dW (t) , x (0) = x0;

where the term ��x2 (t) captures the impact of protest on the production.

Suppose � = �� �. This di¤erential equation can be rewritten as:

dx (t) = (�� �x (t))x (t) dt+ �x (t) dW (t) , x (0) = x0; (2)

How could the �rm deal with the angry anti-pollution protesters? In prac-

tice, we can observe that �rms can deal with the anti-pollution protesters in a

number of ways. For instance, in the case in which the damages caused by the

by-products from the �rms are not so large and the number of residents who

are a¤ected is relatively small, �rms can choose to make lump-sum payments

to compensate these victims of their actions for the damages they receive. Yet

other �rms might choose to clean up the polluted or contaminated areas to make

the protesters stop protesting; however, this approach only helps the �rms tackle

the problem temporarily. In other words, only the pollution resulted from the

past productions is being cleaned up. The pollution that would be emitted into

the local environment as the by-products of the �rms�current and future rounds

of production would necessitate the �rms to take similar actions in the future.

Since cleaning up is usually quite costly, the �rms need to seriously take this into

account when they makes a decision on this matter. Alternatively, some �rms

can try to get around the problem in a very short-sighted way; for instance, if

contamination in the water is the source of the problem that triggers the resi-

dents in Village X to go to protest, these �rms might instead try to divert the

drainage of wastes and chemicals to other villages, such as Village Y or Village

7

Z that are close-by. By doing so, these particular �rms do not directly tackle

the problem as, in the near future, the residents in Village Y or Village Z who

get a¤ected by the �rms�actions might initiate similar kinds of anti-pollution

protests, demanding the �rms to take some serious actions to solve the problem.

With these di¤erent ways of addressing the problem in mind, in this paper,

we restrict our attention to a (sunk) investment by the �rm in the pollution

abatement facilities, which generate less emissions into the local environment

as, from our opinion, this is the way the �rm can address the problem at its

root. Suppose the sunk cost incurred by the �rm from investing in the pollution

abatement facilities is given by I, where I = I1x+ I0, I1 > 0 and I0 > 0. Since

investing in the pollution abatement facilities involve sunk costs, the �rm faces

an irreversible investment problem.

Before the �rm decides to adopt the pollution abatement facilities, the �rm

faces the following problem:

max�E

8<:�Z0

e�rtpbx (t) dt+ e�r� (Va (x (�))� I (x (�)))

9=; ; (3)

subject to equation (2), where r denotes the discount rate, � is the time that the

�rm invests in the pollution abatement facilities, I (x (�)) is the cost incurred by

the �rm from investing in pollution abatement facilities and Va (x (�)) is �rm�s

value function after it invested in the pollution abatement facilities.

What happen after the �rm makes an investment in the pollution abatement

facilities? After the �rm invests in the pollution abatement facilities, we assume

that the residents stop protesting as the level of pollution emitted by the �rm

into the local environment substantially declines to the level that is no longer

hazardous to the residents. As a consequence, protest no longer has any adverse

impact on the �rm�s production, i.e. � = 0. In this sense, an investment in the

pollution abatement facilities is bene�cial for the �rm. However, the �rm needs

to face the cost of C (t; x (t)) in maintaining the new facilities. Since it is not

rational for the �rm to bear the entire burden of an increase in costs by itself,

8

the �rm should have an incentive to pass on this additional cost to the �nal

consumers who purchase the �rm�s products by raising the retail price; thus,

the new price of the �rm�s products after the pollution abatement facilities are

put in place is given by pa, where pa > pb. After investing in the pollution

abatement facilities, the present value of the �rm�s pro�ts is given by:

E

8<:1Z�

e�rt (pax (t)� C (t; x (t))) dt

9=; ; (4)

and the �rm�s production of output, x (t), now follows the following stochastic

di¤erential equation:

dx (t) = �x (t) dt+ �x (t) dW (t) : (5)

We assume that C (t; x (t)) is linear in x (t), or formally, C (t; x (t)) = Cx (t),

where 0 < C < pa. Since equation (1) has a Markovian structure, it follows

that the optimal stopping time problem takes the form of:

� = inft�0fx (t) = x�g ; (6)

where x� is the output threshold. The problem of �nding the optimal time for

this particular �rm to invest in the pollution abatement facilities is essentially

equivalent to �nding the output threshold, x�. It is important to note that equa-

tion (2) follows a Geometric Mean Reverting (GMR) process and each moment

has been derived in Ewald and Yand (2007). The dynamic of equation (2) is

tied to the mean reversion level �� and �, a parameter which captures how fast

the economy reacts to the disturbance from �� . Equation (5), however, follows

a Geometric Brownian Motion (GBM). It is commonly known that the GBM

process is unbounded. The following are some properties of the GMR and GBM

processes. Both of these processes are non-negative; moreover, they have the

property that, once they reach 0, they remain there. Interpreting such property

in the context of our analysis would be the situation in which the �rm enters

9

into a bankruptcy.

Solving the Model

We begin by solving system (4) subject to (5), which characterises a situation

after the pollution abatement facilities have already been adopted by the �rm.

To solve the model, we apply the Hamilton-Jacobi-Bellman (HJB) equations.

The HJB equation for the system for this system (4) subject to (5) is given by:

rVa (x) = (pa � C)x+�2x2

2V 00a (x) + �xV

0a (x) ; (7)

where Va (x) is the value function for the �rm after it invested in the pollution

abatement facilities.

The solution for equation (7) takes the form of A1x2+A2x+A3. By substi-

tuting the solution into equation (6), we obtain A1 = A3 = 0 and A2 =pa�Cr�� .

It is crucial to note that our analysis is based on the condition that r > �. This

condition requires that the discount rate, r, be su¢ ciently large to guarantee

that the value function, Va (x), exists. If r � �, the value function, Va (x), does

not exist since the integration may be in�nity. The reason is that the �rm�s

instantaneous pro�t function, (pa � C)x, is increasing in x and equation (5)

is unbounded4 . Therefore, it is important that we suppose that the discount

rate is su¢ ciently large to ensure that the value function of the �rm is a �nite

number.

Next, we proceed with an analysis of the situation before the �rm invested

in the pollution abatement facilities. This corresponds to system (3) subject to

(2). The HJB equation for this system is given by:

rVb (x) = pbx+�2x2

2V 00b (x) + (�� �x)xV 0b (x) ; (8)

where Vb (x) is the �rm�s value function before it invested in the pollution abate-

ment facilities.

10

The free boundary conditions are

Vb (x�) = Va (x

�)� (I1x� + I0) ; (9)

and

V 0b (x�) = V 0a (x

�)� I1; (10)

where condition (9) and (10) are called the �value-matching� condition and

the �smooth-pasting� condition, respectively. The value-matching condition

requires that, at the time the �rm invests in the pollution abatement facilities, its

payo¤ needs to be equal to its payo¤ from investing in the pollution abatement

facilities net of the sunk cost it incurs from such investment, I (x�). The smooth-

pasting condition ensures the continuity of the slopes of Vb (x�) at x�.

Moreover, since both instantaneous pro�t functions are 0 at x = 0, we obtain

the third condition:

Vb (0) = 0. (11)

Note that, when pb = 0, according to Dixit and Pindyck (1994), the solution

takes the form of hx�H (x), where h is a constant and � is given by an appro-

priate positive number. H (x) is a solution to the Kummer�s M function. On

the contrary, when pb 6= 0, equation (8) is non-homogeneous and variation of

parameters leads us to the solution of the form: h (x)x�H (x), for some h (x).

It becomes evident that the problem becomes more complicated to solve. How-

ever, we take advantage of condition (11) and apply the shooting method. The

idea underlying this method is as follows. First, we choose x and suppose that it

is the optimal stopping time. We then apply the shooting method together with

the boundary equations (9) and (11) to solve equation (8), and test whether or

not the solution satis�es condition (10). If condition (10) is not satis�ed, we

then give a small " and move x to x+ " and repeat the procedure until we �nd

x�.This completes the description of how the problem of optimal stopping time

could be solved. In Section 3, we present the numerical results.

11

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x

V(x)

r = 0.2 ; α = 0.25 ; δ = 0.1 ; β = 0.3 ; σ = 0.1 ; p b = 0.3 ; p a = 0.6

VbVa

Figure 1: Numerical Result: The �rm�s value functions and the threshold

III. THE NUMERICAL RESULTS

In this section, we present the numerical results of the model discussed

in the previous section. When choosing the values of parameters to be used

in our numerical simulations, we need to ensure that the following condition,

(�� �)� � �2, is satis�ed in order to ensure that the process is non-negative.

Figure 1 plots the value function, V (x), as a function of output, x, using

the following parameter values: r = 0:2, � = 0:25, � = 0:1, � = 0:3, � = 0:1,

C = 0:1, I1 = 2, I0 = 1, pb = 0:3, and pa = 0:6. The thick line in the �gure

represents the �rm�s value function after investing in the pollution abatement

facilities, Va, while the dash line represents the �rm�s value function before it

invested in the pollution abatement facilities. The result shown in the �gure

shows that it is optimal for the �rm to invest in the pollution abatement facilities

at the threshold, x� = 0:2848. If the �rm invests in these particular facilities

before x� is reached, it would not be worth it for the �rm to do so; on the

contrary, if the �rm chooses to delay its investment in these facilities further,

the �rm would forego some bene�ts.

There are several parameters in the model that could a¤ect the �rm�s value

function, V (x), and thus the threshold, x�. In what follows, we examine how Vb,

12

0 0.1 0.2 0.3 0.4 0.5 0.60

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

pa = 0.5 →

pa = 0.55 →

pa = 0.6 →

r = 0.2 ; α = 0.25 ; δ = 0.1 ; β = 0.3 ; σ = 0.1 ; p b = 0.3

x

V(x

)

VbVa

Figure 2: How the �rm�s value function and the threshold are a¤ected by changesin pa

Va and x� are a¤ected by changes in the values of the following parameters: (i)

the price of the �rm�s product after the �rm invested in the pollution abatement

facilities, pa; (ii) the impact of protest on the �rm�s production, �; (iii) the

volatility parameter, �; (iv) the sunk costs from investment in the pollution

abatement facilities, I0 and I1; and (v) the cost of maintaining the pollution

abatement facilities, C.

We begin by examining how changes in the price the �rm charges after it

invested in the pollution abatement facilities, pa, a¤ect its value function and

the threshold. Figure 2 depicts the results of our numerical simulations on V (x)

and x� for three di¤erent values of pa, namely 0.5, 0.55 and 0.6. It is clear from

the �gure that, a higher is pa, a smaller x� would be. The interpretation for

this result is that, if the �rm can increase the price of its product to pass on

the additional cost it incurred from the investment in the pollution abatement

facilities to the consumers, this would shorten the time the �rm has to wait to

have su¢ cient money to cover the large cost of installing the pollution abatement

facilities.

Next, we examine how the �rm�s value function and the threshold change

13

0 0.1 0.2 0.3 0.4 0.50

0.5

1

1.5

2

2.5

3

← β = 0.1

← β = 0.2

← β = 0.3

r = 0.2 ;α = 0.25 ;δ = 0.1 ;σ = 0.1 ; pb = 0.3 ; pa = 0.6

x

V(x

)

VbVa

Figure 3: How the �rm�s value function and the threshold are a¤ected by changesin �

when we allow for a variation in �, which captures the impact of protest on the

�rm�s production. The result of this numerical simulation is shown in Figure

3. In the �gure, we conduct the numerical simulations on V (x) and x� using

three di¤erent values of �, given by 0.1, 0.2 and 0.3. It is evident from the �gure

that, if protest imposes a larger adverse impact on the �rm�s production, the

�rm would try its best to ensure that the protest subsided as quickly as possible

by investing in the pollution abatement facilities. Therefore, a larger is �, a

smaller would be the threshold x�.

In Figure 4, we present the results from our simulations on V (x) and x� with

three di¤erent values of �, which is the volatility parameter. It is clear from the

�gure that x� becomes higher as � increases. Therefore, the �rm needs to wait

longer to invest in the pollution abatement facilities. This result is intuitive

as, the more uncertain is the future cost and bene�t from its investment in the

costly facilities, the �rm should have an incentive to delay its investment.

In what follows, we examine how the changes in the costs associated with the

pollution abatement facilities a¤ect the �rm�s decision to invest in the facilities

and its value function. Figure 5 shows how an increase in the sunk cost, I1,

14

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

← σ = 0.1

← σ = 0.15

← σ = 0.2

r = 0.2 ; α = 0.25 ; δ = 0.1 ; β = 0.3 ; pb = 0.3 ; pa = 0.6

x

V(x

)

VbVa

Figure 4: How the �rm�s value function and the threshold are a¤ected by changesin �

a¤ects V (x) and x�. It is clear from the �gure that a larger sunk cost parameter,

I1,would cause x� to be higher. This indicates that the �rm tends to delay its

investment in the pollution abatement facilities if the sunk cost involved in the

investment in such facilities is high.

In Figure 6, we show how a variation in the value of I0, another sunk cost

parameter a¤ects the threshold and the �rm�s value function. The �gure clearly

shows that an increase in I0 leads to a higher x�. This result is intuitive since

if the �rm realises that the sunk cost it needs to incur from investing in the

pollution abatement facilities is higher, it should have an incentive to delay its

investment even further.

Last but not least, we show in Figure 7 how an increase in the maintenance

cost, C, a¤ects V (x) and x�. From the �gure, it is quite obvious that if the

cost of maintaining the pollution abatement facilities is high, the �rms would

have an incentive to wait longer in order to ensure that it has enough money

to invest in the facilities that help abate the pollution. It is important to note

that the �rm�s value function at x�, V (x�), changes slightly compared to the

15

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

I1 = 2 →

I1 = 2.5 →

I1 = 3 →

r = 0.2 ; α = 0.25 ; δ = 0.1 ; β = 0.3 ; σ = 0.1 ; pb = 0.3

x

V(x)

VbVa

Figure 5: How the �rm�s value function and the threshold are a¤ected by changesin I1

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

I0 = 1 →

I0 = 1.5 →

I0 = 2 →

r = 0.2 ; α = 0.25 ; δ = 0.1 ; β = 0.3 ; σ = 0.1 ; pb = 0.3

x

V(x)

VbVa

Figure 6: How the �rm�s value function and the threshold are a¤ected by changesin I0

16

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

C = 0.1 →

C = 0.15 →

C = 0.2 →

r = 0.2 ; α = 0.25 ; δ = 0.1 ; β = 0.3 ; σ = 0.1 ; pb = 0.3

x

V(x)

VbVa

Figure 7: How the �rm�s value function and the threshold are a¤ected by changesin C

changes in the threshold, x�.

IV. CONCLUDING REMARKS

With a relatively less stringent environmental standard or legal control on

pollution in some developing countries, this gives lots of leeway for the �rms in

these countries to continue to use cheap but dirty production facilities, which

generate quite a large amount of pollution into the local environment. In re-

sponse to the damages resulted by the �rms�actions, the anti-pollution protests

have become increasingly common modes through which the residents who are

the victims of pollution express their dissatisfaction. By blocking the factories

or obstructing the workers from performing their usual tasks, the anti-pollution

protest could have a detrimental impact on the �rms�production. In this paper,

we study the optimal timing for the �rms to invest in the expensive pollution

abatement facilities that would help reassure the �rms that the threat of protest

is subsided, taking into account the irreversibility nature of such investment, the

uncertainty and the possibility of delaying the investment.

17

The results from our analysis show that a number of parameters play a

crucial role in determining the optimal timing for the �rms, particularly the sunk

costs the �rms would incur from making such investment and the maintenance

costs for the pollution abatement facilities. Our numerical results clearly show

that, in general, the high costs associated with the investment in the facilities

that help abate pollution could cause the �rms to delay their investment. This

provides a scope for policy intervention by the governments in such countries.

To encourage the �rms in their countries to take a quick step against pol-

lution that results from their actions, the governments could consider o¤ering

some �nancial supports to these �rms so that they could a¤ord such an expen-

sive investment and no longer be able to use this as an excuse for not making an

investment in the pollution abatement facilities. The �nancial supports could

take various forms, such as loans dedicated for the purchase of pollution abate-

ment facilities or subsidies which allow these �rms to buy the expensive facilities

at the lower price. Even though this could essentially imply that a large amount

of taxpayers�money need to be devoted for this purpose, from our opinion, this

is one of the most direct solutions to the problem. However, the governments

need to closely monitor the retail prices of the �rms�products after the new fa-

cilities have been installed. The governments need to make sure that the �rms

that undertake investment in the expensive pollution abatement facilities do not

take too much advantages of their consumers by charging too high retail prices.

Notes

1According to Insley (2003), Title IV of the 1990 Clean Air Act mandated a 10 million ton

(or equivalent to 50 percent) reduction from 1980 levels of acid rain precursor emissions from

electric utilities, particularly the sulfur dioxide (SO2).

2Hunter and Mitchell (1999), Insley (2003) and Löfgren et al. (2008) provide a very good

review of literature in this area.

3For illustration, let us consider the case of the car manufacturing �rms in Thailand, which

heavily rely on the FDI from the Japanese companies such as Toyota, Honda and Mitsubishi. If

the headquarter of Toyota Company has a policy to substantially reduce its direct investment

18

in Thailand because of the political instability, the impact this would cause on the production

of cars in Thailand would be quite sizable.

4The solution for equation (5):

x (t) = x0e

����2

2

�t+�W (t)

and it is well-known that the

1Z0

ef(x)dx does not exist if f (x) is positive.

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