ENV TERM PAPER

ENVIRONMENTAL REGULATION IN
THE PRESENCE OF ASYMMETRIC
INFORMATION/ UNCERTAINITY
SUBMITTED TO : MEETA K MEHRA
BY:
KRITIKA GUPTA(34198)
SANCHI VAHAL(10303)

INTRODUCTION
The term ‘political economy’ has a long and deep rich history. In its
earliest manifestations, the two terms, i.e., Economics and Political
Economy were basically used in the same context. However, over a
period of time as economics came to denote the discipline, political
economy has assumed different shades of meaning. It is now, in fact, a
rather elusive term that typically refers to the study of the collective or
political processes through which public economic decisions are made.
‘Information economics’ is a branch of economics that helps us to
analyse the role that information plays in an economic relationship. When
there is imperfect information, learning about the incomplete aspect
becomes a matter of concern and thus needs to be critically analysed. The
problem of informational asymmetry arises when parties that engage in a
contract, do not have access to the same set of information available to
them. It is thus referred to as a situation of “imperfect knowledge”. When
two (or more) individuals are about to agree on a trade, and one of them
happens to have some information that the other(s) do not have, this
situation is referred to as ‘adverse selection’.
There are a number of distinct approaches to understanding this problem.
The traditional neoclassical and normative approach sees regulatory
measures as one means for correcting locative distortions in a market
system. In the following paper our focus is on the impact of asymmetric
information on Environmental Economics. We analyze the informational
asymmetry problem using a ‘principal agent’ paradigm. In this setup,
one of the parties, mostly the agent, has more information regarding
certain personal characteristics, not known to the Principal. This
additional information will be revealed only if it is in the interest of the
agent of doing so. The principle, to begin with, thus has an informational
disadvantage. This is of particular interest since informational
asymmetry distorts the actual outcomes of a plausible process of political
decision making. Recognizing the fact that the prevalence of
informational asymmetry can lead to too large inefficiencies, substantial
work has been done on designing a mechanism to alleviate the problem.
For our purpose in this paper , focus lies on the fact that where
principal (regulator) on one hand ,aims to regulate the level of pollution
in the society and thereby maximizing the social welfare and agent (
firms) on the other hand have no incentive to do so and are more
interested in maximizing their personal benefits. Problem of pollution
control can be complicated by asymmetric information as the polluter has
superior knowledge about the cost of abatement. Given this, it will not
only influence the optimum, but will also influence the appropriate

mechanism of regulating pollution quantities or prices. Given this limited
information, regulator is then left to device policies which may induce
firm to reveal his knowledge correctly and use it to maximize social
interest.
Environmental measures come about largely as a result of the real or
perceived social damages that are borne across the social spectrum from
polluting activities and impose significant cost on the sources of polluting
activities. Environmental economist has played an important role in
designing efficient and effective policy measures for protecting the
environment. However, when we turn to actual policy, we find that
existing measures or institutions are not working well in terms of these
guidelines. To assess the role of different policy measures, one can look
in a historical way at various policy decisions through qualitative case
studies. Such studies abound in the literature; provide valuable insights
into the political economy of particular environmental programs. In the
early days of the environmental movement in the 1960s and early 1970s,
command-and-control approaches to regulation were widely used. Under
these approaches, environmental agencies set standards with little regard
to their economic implications and then issued directives to polluters,
limiting their levels of waste emissions and often specifying the control
technology. The economic prescriptions for the setting of standards by
balancing benefits and costs at the margin and for the use of incentive-
based policy instruments to achieve these standards were largely ignored.
But now things have changed. The resulting dissatisfaction has stimulated
search for alternatives. The most promising approach to understanding
the actual form of environmental measures to be one that tries to
understand how interest groups interact in a specified political setting
with environmental policies as the outcome. People with similar
economic interests organize themselves into lobbying groups that
coordinate their lobbying activities. A change in economic policy
generally gives rise to conflicts of interest among different groups of
people. Through political contributions, the lobbying groups influence
the government's policymaking. There is a wide array of empirical work
in this context. In certain theoretical political-support models it has been
seen that, policy decisions depend significantly on financial contributions
from interest groups. There is wide range of theoretical literature to
support this view in studies of environmental policies. This general
approach has its roots in some early pieces that sought to explain why
existing environmental policies had taken an inefficient form rather than
the kinds of measures suggested by economic analysis.
Though the recent theoretical work on the political economy of
environmental policy is impressive and promising, it is subject to certain

limitations. The formal models typically characterize “the” public
decision maker in terms of a single objective function.
OBJECTIVE
In this paper we shall explore the essence of political economy and its
impact on government regulation regarding pollution control levels of the
firm. Even though the aim of the regulator is to maximize social welfare,
the presence of interest groups and given their incentives to lobby the
regulator in their favor in the presence of asymmetry information can
have strong impact on government policies. The issue of interest groups
is a complicated one in the context of environmental policy. The
implementation of such legislation provides another arena in which
divergent interest must be reconciled in the actual enforcement of the
policy. To get a better sense of the results, the analysis of the political
economy of environmental policy must thus encompass institutional
setting in which the interplay of interest group takes place. Substantial
amount of work in this line of analysis has already been done by eminent
scholars ‘Laffont’, ‘Tirole’, ‘Boyer’. We begin by analyzing a particular
model developed by ‘Saptarshi Basu Roy Choudhury’ and ‘Meeta
Keswani Mehra’ (January, 2010, Centre for International Trade and
Development , School of International Studies , Jawaharlal Nehru
University , India ) in their work” Aspects of Incentive-Based Optimal
Pricing and Environmental Regulation with Asymmetric Information “ .
In the particular paper two alternative cases that have been considered
are: one, where the lobby represents environmental interests alone, and
another, where the lobby stands solely for firm’s/ industry’s interests.
Based on this we try and extend this basic Principal Agent model to
common Agency model to analyze how the presence of Agency could
influence the regulatory outcomes. Here, we are analyzing the results
with respect to one interest group only i.e., “Firms”. We are trying to
construct a model in which government through environmental policy
instruments prevent firms from bribing ‘Agency’ to misreport
information i.e., information regarding their type in their favor. This
paper therefore considers the formulation of economic policy to be a
product of the interaction between the government, Agency and Producer
group. Our aim in this paper is to investigate whether the presence of
pressure from Producer group can influence regulatory outcome, and then
to make a comparison with the optimal policies.
We begin with first section covering few general observations of our
Preliminary model discussing various theoretical and empirical
approaches that have been employed to study the regulatory behavior.

This body of work draws heavily on the relationship between government
(Principal) and interest groups (agent) where interest groups attempt to
induce the government to do something at a cost to them. Section 2
describes the common agency model in detail and the notations in this
paper we build a common agency model to characterize the interaction
between the Government, Agency and the Interest Groups. We try to
analyze how ‘Producer groups’ uses their political power to bribe agency
to misreport information to government regarding their type. This section
investigates the various properties of the political-equilibrium policies
and compares them with their optimal levels. The last section presents
our conclusion. We conclude the paper with some reflections on role and
responsibilities of government in designing and implementation of
environmental programmers, encouraging tendency to give more weight
to economic analysis in the design of environmental policy.
BACKGROUND: SOME PRELIMINARIES
The paper analyses the problem of optimal regulation of pricing/ output
and environmental pollution of a single-product polluting monopolistic
firm whose cost parameters are not known to the regulator. Given
Informational Asymmetry, it is plausible to assume that the firm has more
information about its cost function, production capabilities and pollution
abatement opportunities than does the regulator. This paper, considers the
case where firm’s costs could be high or low depending on the efficiency
of technology. Highly efficient technology implies lower cost while less
efficient indicates higher cost. Though, the regulator can observe costs,
he cannot observe the firm’s technology type or the level of abatement
activity. The optimal regulatory contract specifies output (or price) as
well as the allowable pollution level of the monopolistic firm. Further, the
analysis is extended to examine whether and how the optimal regulation
gets altered in the presence of lobbying by interest groups. In this case,
the regulator is influenced by lobbies that try to influence it in return for
more favorable outcomes. Two alternative cases of lobbying are
considered: one, where the interest group reflects environmental interest
alone and, another, where the firm/ industry lobby is influential for the
regulatory process. The environmentalists lobby may prefer a lower level
of regulated output and more stringent environmental regulation, while
the firm lobby would tend to benefit from a lax environmental regulation
and lower output/ higher price.

THE MODEL
We consider a three tier system that includes a firm, an agency and a
regulator. All three are risk neutral. The firm enjoys an informational rent
as it has private knowledge about its technology parameter. In our model,
the regulatory structure, the major work of which is to regulate the firms’
prices and rate of return, is two tiered. One is the agency and other is the
regulator. It is assumed that the agency tries to obtain information about
the type of the firms’ technology by spending time resources and
expertise. The agency gives its report to the regulator. The regulator has
only this source of information about the firm, but the agency has
incentives to hide this information from the regulator. These incentives
are provided by interest groups that bribe the agency to conceal the
information from the regulator. The only thing that a regulator can do is
to punish or reward the agency.
We assume that income to the agency given by any interest group is
costly and the associated shadow price is for interest group i. so a $
received by the agency costs 1+ to the i’th interest group.
FIRM:
The firm is assumed to be monopolistic producing a differentiated private
good with the following cost function
C (β, d, q) = β (K-d) q
Here C is the total cost of the firm, q is the output produced, d is the
level of pollution generated by the firms production activity. For a given
level of d and q, the type of the firm is given by β. A low β is indicative
of high efficiency and thus lower pollution whereas a high value of β is
associated with inefficiency.
It is easy to see that the cost of the firm rises with an increase in β and q
and is decreasing in the level of pollution generated by the production of
d.
It is assumed that β can take only two values, β associated with higher
efficiency and β depicting a lower level of efficiency. It is assumed that
the firm is of type β with probability v and of type β with probability (1-
v). Let Δβ = β - β
The regulator pays the firm a lump sum amount in the form of a transfer
t. thus the rent of the firm is given by
U = t - β (K-d) q
Considering a 0 reservation utility, the participation constraint of the firm
is given by
t - β (K-d) q >= 0

The firm gives the agency a signal σ indicating its type to the agency.
Denote the gross consumer surplus by S(q). Then we can write P(q) =
S’(q) as the inverse demand function.
Elasticity of demand is given by
The firm releases pollutants into the environment. The damage function
for the pollution generated by the firm is given by D (d). Damage from
pollution increases at an increasing rate. An assumption here is that the
damage affects all consumers equally. D` (d)>0, D`` (d)>0.
AGENCY:
The utility of the agency depends on the income received from the
regulator. Consider S* as the reservation income of the agency, then the
utility that the agency receives is given by the function,
Z(S) = S - S* >=0
The agency learns the type of the firms. With probability δ the agency is
able to learn the true type of the firm and with probability (1- δ) the
agency learns nothing. The agency is supposed to report to the congress.
Keeping its own interest in mind the agency can either report the signal it
receives σ or it can report nothing Ø.
REGULATOR:
The aim of the regulator is to maximize social welfare. Social welfare is
the sum of producer surplus, consumer surplus and agency surplus.
The regulator pays a lump sum transfer to the firm and collects the firm’s
revenue. The lump sum transfers are raised through taxes that are
distortionary. The taxpayers incur a disutility arising from these taxes.
This disutility is measured by (1+λ) t.
With respect to the firm the regulator, at the time of setting up the
incentive scheme, knows neither β nor σ. It only knows receives
report from the agency. It knows the cost and the output. The
regulator designs an incentive scheme S for the agency and t for
the firm with the aim of maximizing social welfare.

Let S(q) be the gross consumer surplus. With a downward sloping
invertible demand function we have P(q) = S’(q). The revenue of the firm
can be expressed as R(q) = P(q) q.
Aggregate consumer surplus V(q) is the sum of net consumer surplus and
revenue of the regulator that is generated by an output level q of the firm.
V(q) = [S(q) – R(q) ] + (1+λ) R(q)
=S(q) +λR(q)
=S(q) + λ P(q).q
Where V(0) = 0
V’(q) >0
V’(q) <0
As assumed that pollution affects all consumers equally, and that taxes
are distortionary for a consumer,
The net welfare function for the consumer is given by
Consumer surplus = V(q) – D(d) – (1+λ) t
The regulator pays some income to the agency. We assume that the
regulator needs the agency to regulate the firm and thus must pay at least
the reservation income to the firm.
Welfare function of the regulator is thus given by,
W = V(q) – D(d) – (1+λ) t + U + Z – (1+λ) (S)
Where λ is the shadow cost of raising public funds.
WELFARE OF THE REGULATOR
CONSUMER SURPLUS+ PRODUCER SURPLUS + AGENCY
SURPLUS
W = V(q) – D(d) – (1+λ) t + U + Z – (1+λ) (S)
W = V(q) – D(d) – (1+λ) t + U+Z- (1+λ) (Z(s) +S*)
W = [S(q) +λP (q) q] +U+Z-D(d)-(1+λ){t+S}

Regulator does not pay the firms cost. The regulator only gives a lump
sum transfer to the firm.
W = [(S)q)+λP(q)q]+U+Z-D(d)-(1+λ)[U+β(K-d)q+Z(s)+S*]
W = [S(q) +λP(q) q] – (1+λ) [S* +β (K-d) q]-λU – λZ – D(d)
Some additional assumptions:
All individuals maximize their utility/ welfare
The regulator does not know the firms type.
In case of Full information, the regulator maximizes the sum of net
consumer surplus and producer surplus and incase of asymmetric
information, the regulator maximizes the expected value of the same.
SYMMETRIC INFORMATION CASE
Consider the case of symmetric information where government knows the
firm's true type and can deprive it of its rent. Here, the firm signals its
type and the agency reports the signal it receives
[S(q) +λ P(q) q]- (1+λ) [S+ β (K-d) q]-λ U-λ Z-D(d)
First order conditions with respect to pollution (d) and output (q)
With respect to d:
-D’(d) + (1+λ) β q=0
With respect to q:
S`(q) +λ P(q)+ λ q P`(q)-(1+λ)β(K-d)=0
P (q) +λ P(q) + λ q P`(q) = (1+λ) β (K-d)
(1+λ) P(q) +λ q P`(q) = (1+λ) C
This is called the learners index. It is inversely proportional to the
elasticity of demand. It implies that the regulated price is set between the
competitive price (p=c, λ=o) and the monopoly price as λ is positive and
small.

ASYMMETRIC INFORMATION BETWEEN FIRM AND
AGENCY (σ=Φ)
Consider the case of Asymmetric Information where regulator has no
knowledge about firm’s true type and thus firm has an informational
advantage over regulator. Say (d, q, t) and ( ) denote the efforts,
output levels and transfers for types β and .
W = S(q) +λ P (q) q – (1+λ) [S*+β (K-d) q] – λ U-λ Z-D(d)
Income Compatibility constraint of the efficient type:-
t - β (K-d) q t - β (K-d) q - (1)
Income Compatibility constraint of the inefficient type:-
t - β (K-d) q t - β(K-d)q -(2)
Participation Constraint Of the efficient type:-
U = t - β (K-d) q 0 - (3)
Participation constraint Of the Inefficient type:-
U = t - β (K-d) q 0 - (4)
Using (3), (1) & (2), we get
U t - β (K-d) q t - β (K-d) q
U (β-β) (K-d) q
U Δ β (K-d) q 0
U Φ (d, q) where Φ (d, q) is decreasing and convex
0 -Δβ
H = = -Δβ < 0 & Φ’d (d,q) = -Δβq
-Δβ 0

Thus the function is convex. So Φ is decreasing at a decreasing rate. As
the pollution of the inefficient type increases, rent of the efficient type
decreases. As thus as d increases, the cost of the firm will
decrease and its utility increases.
EXPECTED WELFARE (Before collusion)
EW = v{[s(q)+ λP(q)q]-(1+λ)[s +β(K-d)q]-λU-λZ-D(d)-λΦ(d,q)]}
+ (1-v) {[S(q) +λP(q)q]-(1+λ)[S +β(K-d)q]-λU-λZ-D(d)}
EFFICIENT FIRM CASE:
∂EW/∂q = v[V’(q)-(1+λ)β(K-d)] = 0
V’(q) = (1+λ)β(K-d) [Where V(q) = [S(q)+λP(q)q]]
∂EW/∂d = v{-(1+λ)[-β q]-D’(d)} = 0
D’(d) = (1+λ)(β q)
↔ Same result as under Symmetric information case
INEFFICIENT FIRM CASE:
∂EW/∂q = -vλ Φ’q(q,d) + (1-v)S’(q) + (1-v)λP(q) +(1-v)λqP’(q)-(1-
v)(1+λ)β(K-d) = 0
↔ -v λ Φ’q(q,d)+(1-v)V’(q)-(1-v)(1+λ)β(K-d) = 0
(1-v)V’(q) = (1-v) (1+λ) β(K-d)+vλ(Δβ(K-d))
V’(q) = (1+λ)β(K-d)+(v/1-v) λ(Δβ(K-d))
As V`(q) >0 and V``(q) <0 thus the output of the inefficient is lower than
in the case of full information.
∂EW/∂d = -vλΦ’d(d, q)-(1-v) (1+λ) β q-(1-v) D’(d) =0

(1-v)D’(d) = (1-v)(1+λ)β q - v λ Φ’d(d,q)
D’(d) = (1+λ) β q - (v/1-v) λ Φ’d(d, q) > 0
↔ D’(d) > than that under Full Information
So, Pollution by Inefficient type is higher than that under Full
Information.
RESULT: in asymmetric information equilibrium the optimal level of
pollution for the inefficient firm type is higher than that under efficient
type. The inefficient firm also produces smaller output than efficient fir
i.e. d< and q q.
COLLUSION BETWEEN FIRM AND AGENCY
In this section we allow the firm to collude with the agency. More
precisely, the firm can give a transfer to the agency (so that the agency's
income equivalent becomes S + at cost (1+ λf) , where λf >= 0 denotes
the shadow cost of transfers for the firm.
Let the income of the agency be S1 , 1 ,SO, When report ‘r’ is β , β and
Ø respectively.
Regulator will have to pay

(1 + λf ) (S1 - So ) φ ( 3 3 )

(1 + λf ) (S1 - S *) φ ( 3 3 )

S1 = S + φ ( 3 3 ) / (1 + λf ) ………………………………… A
Consider four states of nature
Type Signal
β β
β Ø
β Ø
β β

Let denote the probability of ith state.
The variables are indexed in the following way
 Index final outcomes by a hat
 The actual transfers between the regulator and the firm and the
regulator and the agency are and in state i respectively.
Let the firms transfer to agency i then we have,
i = Si + i ………………………………...……………-I
i = ti - (1 + λf ) i .. ……………………………………………-II
i 0 ......................................................................-III
i = i - β (K- ) …………………………………………….-
IV
i = i - S* …………………………………………….-V
We claim that for all i
i S* ……………………………………………-VI
Ui 0 …………………………………………….-VII
In state 2, given that the firm is of type β, firm has an incentive to mimic
the behavior of β. This is because only the firm knows its own type,
hence
2 3 + φ ( 3 3 ) ……………………………..-VIII
(1 + λf ) ( 1 - 2 ) 2 - 1 ………………………..........-IX
Expected welfare function is thus written as
EW:
= xi ([ S(qi ) + λ P(qi )qi ] – D(di ) – (1 + λ) (ti +Si) + i + i )
= xi ([ S(qi ) + λP(qi )qi ] – D(di ) – (1 + λ) [ I +(1 + λf ) i + i - i -
using I & II
= xi ([ S(qi ) + λP(qi )qi ] – D(di ) – (1 + λ) [ i + βi ( K - di) qi + (1 + λf
) i + i + S* - i ] + i + i ) - using IV and V
= xi ([ S(qi ) + λP(qi )qi ] – D(di ) – (1 + λ)[ S + λf i + βi ( K - di) qi ] -
λ i - λ( i - S* ) ) - X

If v is the probability that the firm’s type is β and δ be the probability that
the agency learns the true type
Thus we can write expected welfare as
= v δ ([ S(q1) + λP(q1 )q1 ] - D(d1 ) – (1 + λ)[ S + λf 1 + β1 ( K – d1) q1 ]
- λ 1 - λ( 1 - S* ) )
+ v(1- δ) ([ S(q2) + λP(q2 )q2 ] - D(d2 ) – (1 + λ)[ S + λf 2 + β2 ( K – d2)
q2 ] - λ 2 - λ( 2 - S* ) )
+ (1-v)(1- δ) ([ S(q3) + λP(q3 )q3 ] - D(d3 ) – (1 + λ)[ S + λf 3 + β3 ( K
– d3) q3 ] - λ 3 - λ( 3 - S* ) )
+ (1-v) δ ([ S(q4) + λP(q4 )q4 ] - D(d4 ) – (1 + λ)[ S + λf 4 + β4 ( K –
d4) q4 ] - λ 4 - λ( 4 - S* ) )
- XI
= v δ ([ S(q1) + λP(q1 )q1 ] - D(d1 ) – (1 + λ)[ S + λf 1 + β1 ( K – d1) q1 ]
- λ 1 - {λ/(1 + λf )}( φ ( 3 3 ) - 1 ))
+ v(1- δ) ([ S(q2) + λP(q2 )q2 ] - D(d2 ) – (1 + λ)[ S + λf 2 + β2 ( K – d2)
q2 ] – λ φ ( 3 3 ) - λ( 2 - S* ) )
+ (1-v)(1- δ) ([ S(q3) + λP(q3 )q3 ] - D(d3 ) – (1 + λ)[ S + λf 3 + β3 ( K
– d3) q3 ] - λ 3 - λ( 3 - S* ) )
+ (1-v) δ ([ S(q4) + λP(q4 )q4 ] - D(d4 ) – (1 + λ)[ S + λf 4 + β4 ( K –
d4) q4 ] - λ 4 - λ( 4 - S* ) )
- XII
The solutions must satisfy:
for all i
3 = 4 = 0
i = S* for i = 2, 3, 4
= 0 (proved in appendix)
We prove these by maximizing the expected welfare function XII subject
to III and VI-IX.

Proof:
A) maximizing the expected welfare function subject to III and using
Kuhn tucker theorem we get i =0 for all i.
(Proved in appendix)
B) i = S* for i = 2, 3, 4
Given assumption VI we have the following constraints,
1 -S*>=0
2 -S*>=0
3 -S*>=0
4 -S*>=0
Maximizing the expected welfare function (XII) with respect to these
four constraints and using Kuhn tucker conditions we get i = S* for i =
2, 3, 4.
C) 3 = 4 = 0
i = i - φ ( , )
i= ti - (1 + λf ) φ ( , )
As proved for all i,
i= ti - φ ( , )
i= = ti - φ ( , )
Hence, using VII
-XIII
Maximizing expected welfare equation XII subject to XIII and using
Kuhn tucker theorem we get 3 = 4 = 0.
= 0
Maximizing XII with respect to is equivalent to maximizing

-λ -λ
As solution satisfy
For all i
i = S* for i = 2, 3, 4 -XIV
3 = 4 = 0 -XV
= 0 (proved in appendix)
 The equations VIII and IX hold with equality
 We have shown 1 = 0
 VII and IX together imply (1 + λf )( 1 – S ) = φ ( d, q) - 1
Now the expression for expected welfare becomes
EW:
=v δ ([ S(q1) + λP(q1 )q1 ] - D(d1 ) – (1 + λ)[ S + β1 ( K – d1) q1 ] -
{λ/(1 + λf ) }( φ ( 3 3 ))
+ v(1- δ) ([ S(q2) + λP(q2 )q2 ] - D(d2 ) – (1 + λ)[ S + β2 ( K – d2) q2 ] -
λφ ( 3 3 ) )
+ (1-v)(1- δ) ([ S(q3) + λP(q3 )q3 ] - D(d3 ) – (1 + λ)[ S + β3 ( K – d3) q3
])
+(1-v) δ ([ S(q4) + λP(q4 )q4 ] - D(d4 ) – (1 + λ)[ S + β4 ( K – d4) q4 )
- XVI
From above we deduce the following Propositions:
1) Collusion reduces social welfare.
2) Pollution of the inefficient type firm is higher. The firm is given a low
powered incentive scheme.

3) Output of the inefficient type under asymmetric information is lowered
to (d, q)
4) The efficient type enjoys a lower rent than in the absence of collusion
φ (d, q) < φ (d, q)
5) Pollution increases with λf.
Proof:
1)
∂ EW/ ∂ λf = δ
φ –
=>
λ
λ δ φ
2)
∂ EW/ ∂ d3 = - λ / (1 + λf ). v δ φ’d3 ( 3 3 ) - v(1- δ) λ φ’d3 ( 3
, 3 ) -(1-v) (1-δ) D’(d3) + (1-v)(1- δ) [(1 + λ) (β3 q3 )] =0
Let δ
= (v) (1- δ
= (1-v) (1- δ
= (1-v) δ
x3 (1 + λ) (β3 q3 ) - λ / (1 + λf ). x1 φ’d3 ( 3 3 ) – x2 λ φ’d3 ( 3 3 ) =
x3 D’(d3 )
D’(d3) = (1 + λ) (β3 q3 ) – [{λ / (1 + λf ). x1 / x3 } + x2 /x3 . λ}] φ’d3
( 3 3 )
D’(d3) = (1 + λ) (β3 q3 ) – λ [{x2 /x3 } + { x1 / x3(1 + λf )}]φ’d3 ( 3 3
)
Result: given that φ is convex, and hence φ’d3 ( 3 3 ) <0 thus
pollution under asymmetric information in case of collusion for an
inefficient type firm is higher than under without collusion.

3)
∂ EW/ ∂ =0
= v δ [
λ
φ’ q3 ( 3 3 ) ]+ (1-v)(1- δ)[ (S`( + λ P( +λ
P( ] – (1+λ){β(K- + v(1- δ)
(1+λ)φ’ = 0
= [
δ
λ
δ λ φ’ + (1-v) (1- δ)
[S`( δ λ β
= (1-v) (1- δ) V`( = (1-v) (1- δ) (1+λ) K-
δ) λ
δ
] φ’
δ
δ
φ’
Differentiating this with respect to
V``( = (1+ λ) (K-
<0
4)
The rent of the efficient type is inversely proportional to the
pollution level generated by the inefficient firm.
Φ`(d, q) <0
0 -Δβ
H = = -Δβ < 0 & Φ’d (d, q) = -Δβq
-Δβ 0

As the pollution of the inefficient type increases when there is
information asymmetry problem under collusion the rent of the efficient
type is reduced.
Remark: to prevent collusion, the regulator reduces the stakes i.e. the
efficient types rent under asymmetric information. To facilitate this, the
inefficient type under imperfect information case is given less powerful
incentive scheme than the corresponding scheme in the absence of
collusion. By reducing the efficient firms rent, the government reduces its
power to influence the regulatory outcomes than in the symmetric
information case.
CONCLUSION
The paper demonstrates the common agency model to analyze
interactions between the regulator, Agency and the Producer group. The
paper first characterizes the Symmetric Information Case where
government knows the firm’s true type and hence can deprive it of its
rent. This is a benchmark case and to this regulatory outcomes under
asymmetric information (before collusion between firm and agency) and
after collusion (between firm and agency) will be compared to analyze
changes in the Pareto efficient outcomes.
The general insights of the model are:
 In Asymmetric information case between firm and agency (Before
Collusion): For Efficient firm results are consistent as under
Symmetric Information case. However, in case of Inefficient firm
the choice of the optimal pollution and output are distorted upward
and downward respectively as compared to full information case.
 In case of collusion between firm and agency, under asymmetric
information
1. For an inefficient type firm pollution is higher than
under without collusion.
2. The rent of the efficient type is inversely proportional
to the pollution level generated by the inefficient firm.
3. Since collusion is welfare reducing thus it is optimal
 In this paper agency incentives are provided by rewards, they
might alternatively be provided by punishments inflicted when the
agency is caught colluding with interest groups.

APPENDIX
Maximizing the equation XII with respect to
A)
1 0 :
2 0 :
3 0 :
4 0 :
We get
For 1
-v δ (1+λ)
v δ (1+λ)
Thus
Hence using Kuhn tucker condition 1 0
For 2
-v (1- δ ) (1+λ)
v (1- δ ) (1+λ)
Thus
For 3
- (1-v) (1- δ ) (1+λ)
(1-v)(1- δ ) (1+λ)
Thus
For 4
- (1-v) δ (1+λ)
(1-v) δ (1+λ)
Thus
B) Maximizing XII with respect to the following constraints, using
assumption IV

1 -S*>=0 :
2 -S*>=0 :
3 -S*>=0 :
4 -S*>=0 :
We get
-v (1- δ) λ + = 0
v (1- δ) λ =
Hence using Kuhn tucker condition
2 -S*=0
2 = S*
- (1-v) (1- δ) λ + = 0
(1-v) (1- δ) λ =
3 -S*=0
3= S*
- (1-v) δ λ + = 0
(1-v) δ λ =
4 -S*=0
4 = S*
C)
Maximizing XII subject to XIII
:
:
:
:
We get

- (1-v) (1- δ λ + = 0
(1-v)(1- δ λ =
>0
Thus, using Kuhn tucker condition,
- (1-v) (δ λ + = 0
(1-v)( δ λ =
>0
Thus, using Kuhn tucker condition,
Maximizing XII with respect to is equivalent to maximizing
-λ -λ
Subject to =0
We get
- + = 0
=
Thus
Thus using Kuhn tucker theorem,
= 0

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