Université de Montpellier
Environmental regulation threatened by scal
avoidance must hit `the green'
Masha Chistyakova† * and Philippe Mahenc*
* LAMETA, Montpellier I University, Avenue Raymond Dugrand, Site de Richter, C. S. 79606, 34960
Montpellier Cedex 2
26 june 2013
Abstract
In incomplete markets scal avoidance may be worrisome to the regulator of polluting
emissions. We advance the previous research of pollution taxation in markets with multiple
distortions and a single regulatory instrument by integrating scal avoidance into the
environment characterized by pollution externalities, imperfectly competitive market, and
asymmetric information to study optimal regulation. In our model an authority induced by
environmentally conscious consumers imposes pro-green policy on a polluting monopolist,
who resorts to scal avoidance. We show that higher levels of under-compliance cause
optimal environmental regulation to inict a more stringent policy on `the clean' than on
the conventional good, and hence to unambiguously hit `the green'. We conclude vis-à-vis
that in the setting with high levels of scal avoidance the Pigovian tax rule seizes to be a
reference that optimally internalizes pollution externality.
Keywords: Asymmetric Information, Emission Taxation, Environmental Quality, Fiscal Avoidance, Regulation
JEL Code: D43, D82, H23, L12, Q28
The authors are members of the LabEx Entrepreneurship, Montpellier, France. This
"Laboratory of Excellence" is part of a French government fund recognizing and promoting
performing research initiatives in human and natural sciences.
†
[email protected], [email protected]
Introduction
Environmental regulation in incomplete markets is bounded by monopoly
power, information asymmetry and other distortions. In times of global economic crisis, environmental concern sinks further behind government's top
priorities. Under these circumstances the limited regulatory power, granted
to the environmental authority, gives raise to a potential eciency loss due
to the vigorous resistance of polluting industries to environmental regulation.
Here, we emphasize the distortionary impact of tax avoidance on environmental regulation. We distinguish for willful corporate noncompliance between
legal an illegal forms. The latter term in the economic literature is referred
1
to as tax evasion .
In this paper, we restrict attention to legal willful tax
noncompliance in corporate behavior and we use the term tax avoidance"
2
to set apart from illegal conduct. In the present analysis, tax avoidance is
tantamount to under-reporting of actual prots by multinationals. The literature in environmental economics has thus far overlooked this problem.
Our goal is to show that tax avoidance has serious implications for the the
eciency of environmental regulation, because it creates welfare loss which
is more harmful to the green, especially, in eco-friendly economies.
Fiscal non-compliance is common for rms and individuals.
The jour-
ney around the world of Gérard Depardieu, searching for a preferred tax
regime in Belgium, Russia and recently Algeria, has drawn a caricature of a
private attempt to bypass severe taxation. This raises the question of how
the drain of scal revenues impacts the state regulation and his strategic
action. While an average individual is less likely to improve his nance in
such a way, the practice of scal avoidance in the corporate world is much
more common due to a certain exibility of legislation to choose an optimal
1 See
Andreoni et al. (1998); Slemrod (2007) for comprehensive surveys on tax evasion.
term is used in the spirit of Slemrod and Yitzhaki (2002) as strategic manipulation
of corporate prot with the goal to reduce the total amount of paid taxes, rearranged in
such a way that resulting tax treatment diers from that intended by legislation.
2 The
2
among distinct international tax regimes, driven by a substantial global tax
competition for capital. Multinationals may escape taxes by cross-boarder
investments, locating operation in low-tax rate countries, shifting income,
exploiting international dierences in tax rule. In contrast to non-systematic
individual tax avoidance, the corporate under-compliance is expected and to
some extent traceable. While an anticipation of corporate under-compliance
may strumble on questions of inequality, income distribution etc., hampering the justication of such a strategic behavior of a benevolent party, a
dividend paid on foreign capital can be interpreted as a constraining parameter on planner's jurisdiction without touching on inequality issues. Indeed,
for French Total, Lafarge, German BASF and Russian GazProm the share
of foreign capital in the shareholders structure varies from 30% up to 70%
suggesting a proportional share of prot not entering inland tax base.
As initially recognized by Baron (1985), one important restriction on the
environmental regulator's power is its limited jurisdiction over the polluters,
3
especially if this is a state regulatory agency . Because some of the earned
prot escapes the regulation, signicantly reducing government's tax revenues, the anticipation of scal avoidance undermines the regulator's ability
to transfer emission's tax yields to consumers in whole. Imperfect tax transfer aects welfare in a way that inuences the content and stringency of
environmental taxation. Indeed, if the purpose of environmental taxation is
to force individuals to consider the full set of consequences from pollution
emission, the tax must also internalize the externality associated with the
trouble redistributing tax.
In this paper, by using a stylized partial equilibrium model, we investigate the deadweight loss eect of environmental taxation due to the regulator's limited jurisdiction in an economy where consumers have green prefer-
3 Bower
(1981) claims that a large share of the producer surplus escapes the jurisdiction
of the state regulatory agency. Boyer and Laont (1999); Laont (1994); Lewis (1996);
Spulber (1988) all consider that the environmental regulator's authority is limited by the
cost of transferring the emission tax from the polluter to the polluted.
3
ences. A perfectly green regulator seeks to minimize environmental damage
by emission tax imposed on a monopolist , whose environmental performance
is exogenously set. We consider limited jurisdiction (scal non-compliance)
solely as a black box, which the social planner anticipates; and this particular
strategic behavior of the regulator creates a distortion of an imperfect tax
transfer.
We build signicantly on two standard models.
Following the seminal
paper of Buchanan (1969), we study the optimal environmental regulation
in an imperfectly competitive market. Our results depart from those, extensively rened by Lee (1975), Barnett (1980), that the second-best optimal
policy undertaken with polluting monopolist requires to scale down the tax
below the Pigovian level in order to mitigate the monopolist's tendency to
underproduce.
We demonstrate that scal avoidance may require the op-
timal environmental regulation to overcome Pigovian level. The impact of
incomplete information on the optimal environmental policy is considered
in the spirit of Baron (1985). With information asymmetry, the distortion
stems from information cost that the monopolist of a superior environmental
quality has to carry in order to credibly dierentiate himself from `the brown'
type to prevent him from mimicking. Similar to the results of Baron (1985),
in our model it is the information cost that ultimately determines the relative
severity of taxation on clean and conventional quality.
We nd that tax avoidance creates a new distortion, and in a sense, the
imperfect tax transfer induces the regulator to hit the green. In order to
balance between the conicting regulatory goals, in either setting the social
planner, plagued by the Depardieu's syndrome of multinationals, has to be
more stringent towards `the green' than `the brown' producer.
The subsequent Section develops the model. The characterization of regulation under the assumption of full information is discussed in Section 2.
In Section 3 the assumption of perfect information is relaxed. Implications
of the present analysis for recent discussions of optimal environmental regu-
4
lation and some possible extensions, are considered in Section ??. Section 4
concludes.
1
The model
A monopolist produces a polluting good in quantity
amount
(1 − e) q
1−e
unit of output).
that generates the
e is an eort to abate the
e ∈ [0, 1] is the abatement level
of polluting emissions, where
pollution and to improve the environment,
(for instance,
q
is the release of pollutants such as NOx , CO, SO2 , per
If abatement is maximal, emissions are thus zero.
If no
abatement is undertaken, emissions are equal to output. The overall marginal
cost of producing the good is
c(e),
with
c0 (e) > 0:
to abatement raise the overall cost of production.
more resources devoted
Let
d(D, e)
denote the
environmental damage function, which is assumed to be strictly proportional
to the amount of polluting emissions:
d(D, e) = δ (1 − e) D(pe ).
The total number of consumers is normalized to unity. Each consumer
purchases at most one unit of the good, which thus indirectly generates the
amount
1−e
of polluting emissions via consumption.
Consumers receive
zero surplus from consuming outside goods. The good provides all consumers
with the same gross surplus
v.
Consumers dier in their tastes for the good
due to their dislike of pollution.
pollution is measured by the pure monetary loss
X
X , the dislike of
(1 − e) X . The parameter
For a given consumer
is uniformly distributed along a segment of unit length. Hence, consumers
0 partly internalize the polluting externality, and if X happens
to δ , the externality is fully internalized for the purchased unit
distinct from
to be equal
of the good. Another interpretation is that taste heterogeneity reects the
degree of social environmental conscience of consumers. If, for instance, the
good is fossil energy, consumers may dier in the aversion to the negative
impact on global warming, and if it is nuclear energy, they may dier in
their dislike of the potential risks imposed on future generations by nuclear
5
repositories.
Due to `greenwashing' (Lyon and Maxwell, 2011), consumers are not accurately informed about the harm caused by the good to the environment.
Hence, in the absence of regulation, environmental quality is an experience
attribute of the good, in the sense that consumers never perfectly observe
the pollution generated by the good they purchase. It is consistent with the
proposition made by Karl and Orwat (1999) that the individual costs of ensuring the environmental characteristics of goods are likely to be prohibitive
for consumers.
Potentially, the good may be either brown (e
= b)
or green (e
= g ),
depending on whether the release of pollutant is high or low, with g > b. Initially, without any regulation, the good is believed to be green with probability
µ◦ ∈ (0, 1).
Unlike consumers, rms perfectly know their environmental
practices, hence the actual damage caused to the environment by the good
c (b) = 0 and denote c (g) = c, c ∈ (0, v).
Without regulation, consumer X derives a surplus v−p−(1−E(e))X from
purchasing the good at price p, where expected environmental qualityE(e) =
µ◦ g + (1 − µ◦ )b. This generates a demand function characterized by
they supply. We normalize
D(p, E(e)) =
v−p
1 − E(e)
We rst state the benchmark result prevailing under full information,
when the environmental quality of the good is perfectly observable to consumers.
We characterize the optimal price set by the monopolist and the
corresponding prot for a given level of abatement.
Given abatement
e,
the monopoly prot is
πe (p) = (p − c(e))D (p, e) and
the rst-order condition is given by:
(p − c(e))
∂D (p, e)
+ D (p, e) = 0,
∂p
6
e = b, g
One can easily check that second-order conditions are satised.
εe (p) =
p
− ∂D(p,e)
∂p
D(p,e)
=
Let
p
1
denote the price elasticity of demand for
1−e D(p,e)
the good.
We further denote by
pbe
the price set by the monopolist.
First-order
conditions can be rewritten in the usual way to show that the Lerner index
is equal to the inverse of the price elasticity of demand, which implies that
market power is a decreasing function of the price elasticity of demand:
1
pbe − c(e)
=
pbe
εe (b
pe )
where
εe (b
pe ) =
(1)
pbe
. Substituting for this expression in the right-hand
v−b
pe
side of (1), we obtain
pbe − c(e) = v − pbe
Under full information, the monopolist earns the prot
pbe ,
with the price
namely:
pbe =
2
π
be
v + c(e)
2
and
π
be =
(v − c(e))2
4(1 − e)
Characterization of regulated behavior under
full information
First, let us briey derive what should be the socially optimal allocation of
the good.
The welfare standard is the conventional one of gross benets
to consumers less production and pollution costs. With no regulation, the
welfare function is
7
Z
X
[v − c(e) − (1 − e) x] dx − δ (1 − e) X
W (X) =
(2)
0
= [v − c(e) − δ (1 − e)] X − (1 − e)
The expression
δ (1 − e) X
X2
2
is the environmental damage,
2
(1 − e) X2
rep-
resents disutility of pollution, private perception of environmental damage,
i.e., the aggregate monetary losses experienced by consumers due to their
aversion to pollution.
The optimality condition of (2) is
∂W
= [v − c(e) − (1 − e)X] − δ(1 − e),
∂X
where on the right hand side the term in the rst brackets stands for net
social value of the good less privately perceived environmental damage, and
the second term,
δ(1 − e),
represents an objective (scientically determined)
environmental damage, associated with the production.
At the socially optimal solution, the marginal consumer
X?
solves equa-
v − (1 − e) X ? = c(e) + δ (1 − e): so that the marginal social value of
?
the good (v − (1 − e) X ) must exactly oset the total social marginal production cost (c(e) + δ (1 − e)). Thus from the social standpoint, the market
tion
size should be:
X? =
v − c(e)
− δ.
1−e
(3)
We will restrict the parameters of the model to satisfy the following assumption in order to ensure that the presence of the good on the market is
socially desirable, independent of its environmental quality.
δ ≤ min
v
v−c
,
1−b 1−g
(4)
To see how the market size depends on the consumers' aversion to pollu-
8
tion, we derive
X?
with respect to
e,
which gives:
0
∂X ?
(v − c(e)) − c (1 − e)
=
.
∂e
(1 − e)2
The expression is positive if
0
v−c(e)
1−e
marginal increment in abatement
c
>c,
0
and negative otherwise. Note, that
is equal to c. This means that the socially
optimal market share will increase along with a rise in consumers' environmental consciousness as long as the social valuation of higher environmental
quality is greater than the cost of quality provision. On the contrary, if the
valuation of environmental quality is lower than the cost of its provision,
the market would shrink as a result of a higher demand for environmental
quality.
 Accordingly, this condition requires to distinguish two cases:
 ∂X ? < 0,
∂e
 ∂X ? ≥ 0,
0
v−c(e)
<c
1−e
0
where
c ≤ v−c(e)
∂e
1−e
In the rst interval the market share would shrink and in the second -
where
δ≤
expand as a result of a higher environmental awareness.
In our model we capture limited jurisdiction (scal avoidance, as discussed
in Introduction) by parameter
β
4 , satisfying
0 ≤ β ≤ 1.
We borrow from
Baron and Myerson (1982); Freixas et al. (1985), the approach to reduce
relative social weight of the rm in the regulator's optimization problem as
a consequence of his strategic anticipation of legal willful non-compliance.
In the presence of regulation, there are two instruments at the authority's disposition: the governor may either tax pollution per emission unit,
or propose to the monopolist a menu of price-transfer combination.
Un-
der complete information, it is straightforward that the two instruments are
identical. The social planner's program is to maximize the ex-ante weighted
social welfare
W:
4β
> 1 can be considered as lobby for the monopoly. β attached to the consumer surplus
would have a scent of Leviathan tax (see Wirl and Dockner (1995)), when government
budget is appreciated for its own value, granting political strength and negotiation power.
9
Z
D(pe ,e)
[v − pe − (1 − e)x − δ(1 − e) + τe (1 − e)]dx + βπe (pe , e) =
W (τe ) =
0
[v − (1 − β)pe − βc(e) + (1 − β)(1 − e)τ − δ(1 − e)]D(pe , e) − (1 − e)
D2 (pe , e)
2
In the following we analyze comparative statics of optimal environmental
policy by successively relaxing the assumptions of unlimited jurisdiction, of
price-setting power, and of perfect information.
2.1
First-best regulation: powerful and omniscient regulator
To see a benchmark, we rst consider the regulator who has complete information about environmental quality of the rm is endowed by unconstrained
power of regulation., but also the regulator gives equal weights to consumers'
surplus and prot. In addition, the regulator is allowed to use as many policy
instruments as there are distortions in the economy, namely, the polluting
externality and the rm market power. His optimization problem is to nd
a regulatory policy
Z
(pe , τe )
that maximizes social welfare
D(·)
[v − pe − δ (1 − e) − (1 − e) x] dx + τe (1 − e) D (pe , e) + πe (pe , τe )
(5)
0
subject to the individual rationality constraint :
πe (pe , τe ) = (pe − c(e) −
τe (1 − e))D (pe , e) ≥ 0.
For any given price pe , it is desirable from the viewpoint of the regulator to
choose the tax τe so as to make the individual rationality constraint binding.
Hence,
τe =
pe − c(e)
1−e
10
Recall that
D (pe , e) =
v−pe
.
1−e
Substituting
τe
into (5), we dierentiate
social welfare to get the following rst-order condition
δ−
pe − c(e)
=0
1−e
Lemma 2.1.1. The regulator endowed with an unconstrained authority would
set
5
p∗e = c(e) + δ (1 − e)
τe∗ = δ
The resulting combination sets the unit price equal to social marginal
costs composed of production expenses and environmental damage per unit
of output and the tax rate equal to the Pigovian level. A transfer that ensures
the binding condition on individual rationality constraint, withdrawing the
entire monopolist rent.
An allmighty regulator would oset the monopoly
power, completely internalize environmental impact.
revenues raised from
τ /T
We assume that the
are transferred to consumers, and thus used, for
instance, to decrease negative eect of other distortionary taxes, or to nance
xed costs of public utilities, thereby raising the social welfare.
2.2
Second-best optimal tax of type I: omniscient but one-armed regulator
with no scal avoidance
Second-best condition implies that the authority is no longer in power to
impose a price on the monopolist, i.e. the benevolent regulator sets a tax
τ
on each unit of polluting emissions to maximize welfare given the monopoly
behavior.
The variable
τ
will take negative values if it turns out to be a
subsidy.
5 Alternatively,
the rst best regulation may be represented by a combination of a xed
price enforced upon the monopolist and a transfer, denoted by T . To see this, note that
Te = τ (1 − e)D(pe )
11
The sequence of the game is the following: the regulator is a Stackelberg
leader who commits to his policy: in the rst stage he imposes environmental regulation on each unit of pollutant emission. At the second stage the
producer optimally sets the price taking the tax level into account.
Let
pe (τ )
denote the monopoly price under regulation.
monopoly prot,
Then, for the
πe (pe (τ )) = (pe (τ ) − c(e) − τ (1 − e))D (pe (τ ) , e), pe (τ )
must solve the rst-order condition for prot maximization of the monopolist:
(p − c(e) − τ (1 − e))
∂D (p, e)
+ D (p, e) = 0.
∂p
(8)
This yields the following equilibrium price
pe (τ ) =
v + c(e) + τ (1 − e)
,
2
(9)
and the corresponding equilibrium prot
πe (pe (τ )) =
(v − c(e) − τ (1 − e))2
4(1 − e)
Rearranging the terms, equation (8) can be rewritten to express the
Lerner index
τ (1 − e)
1
pe (τ ) − c(e)
=
+
.
pe (τ )
pe (τ )
ε(pe (τ ),e)
The regulator employs the tax on the polluting good not only to internalize the environmental externality but also to correct for the externality
exerted on the society by the monopoly behavior. Social welfare is
W (τ ) = [v − c(e) − δ (1 − e)] D (pe (τ ) , e) − (1 − e)
D (pe (τ ) , e)2
2
The following proposition provides an explicit solution for the second-best
optimal tax.
12
Proposition 2.2.1. The welfare maximizing environmental tax is:
τeI = 2δ −
v − c(e)
1−e
(10)
Given the assumption (4), it is straightforward that
τeI < δ .
Thus, the
Pigovian tax rule requiring to charge a tax equal to marginal damage cannot
be applied here due to the monopolist's behavior.
The second-best tax of
type I should be optimally set below the marginal damage.
Note that substituting (3) into (10), we get
∂τeI (X ? )
increase in environmental consciousness,
∂e
τeI = δ − X ? .
?
= − ∂X
, raises
∂e
A marginal
the optimal
regulation if the cost of quality provision is higher than the private valuation
of increment in environmental quality (see (2)). Thus, with unlimited jurisdiction the optimal tax decreases with abatement eort as long as the cost
of quality provision is below its net social value. Here the regulator is more
stringent on the polluting producer.
Rearranging (10), we get
X ? = δ − τeI , representing the detrimental eect
on monopolistic behavior on social welfare, as an increase in tax reduces the
output.
Hence, if pollution is not too costly to abate and/or the good is
highly valued by consumers (for characteristics other than environmental),
an increase in pollution abatement may require a subsidy for the monopolist,
as initially showed by Buchanan (1969). Since we can interpret
of consumer environmental concern, a rise in
e
e as an index
would mean that consumers
are more willing to pay for the good. But this raises the monopoly power,
thereby worsening the monopoly distortion. It follows that regulation is more
lenient to correct for the monopolist's tendency to underproduce.
There are two implications in place:
Corollary 2.2.2.
•
∂τeI
∂e
>0
if
0
c <
v−c(e)
, the optimal regulation is less
1−e
stringent as long as environmental consciousness grows.
• τeI < 0 if 2δ <
v−c(e)
, the optimal regulation is a subsidy if the net social
1−e
value of a good twice exceeds the marginal environmental damage per
13
unit of output.
The proof is straightforward.
These parameter combinations call for a subsidy for a polluting monopolist to encourage (conventionally low) emissions when a good is of a high net
social value relative to a low negative environmental impact. This constellation prevails when the good is either highly appreciated by consumers (high
values of
v)
and/or is inexpensive to produce (low
tal damage is insignicant (low
δ ).
c(e)),
or the environmen-
A subsidy would reduce production cost
for the monopolist, resulting in a lower price, an increased output; hence
lowering welfare loss induced by monopolistic behavior at the cost of higher
emission.
2.3
Second-best optimal tax of type II: one-armed omniscient regulator
with limited power on jurisdiction
In this section we introduce limited jurisdiction, captured by
β ∈ [0, 1].The
the interval
β,
dened on
environmental authority maximizes social welfare
according to the rule:
Z
D(pe ,e)
[v − (1 − e)x − δ(1 − e) − pe + τe (1 − e)]dx + βπe (pe , e)
W (τe ) =
0
The sequence of the game is the same as in the previous subsection.
We proceed by backward induction.
At the second stage the monopolist's
program is to maximize his prot:
max [pe − c(e) − τ (1 − e)] D(pe , e)
pe
By the rst order condition we have that
+ D = 0.
(pe − c(e) − τ (1 − e)) ∂D
∂p
Using the price elasticity of demand, the monopolist's prot margin is:
14
pe − c(e) − τ (1 − e) =
pe
ε(pe ,e)
The regulator's program at the rst stage, in anticipation of monopolistic
behavior captured by the Lerner's rule, is to maximize social welfare
max [v − (1 − β)p − βc(e) + (1 − β)(1 − e)τ − δ (1 − e)] D (pe (τ ) , e)
τ
− (1 − e)
D2 (pe (τ ) , e)
2
The following proposition states an implicit solution for
τ.
Proposition 2.3.1. The second-best optimal tax of type II is
τeII = δ −
pe (τ )
2pe (τ )
+ (1 − β)
(1 − e)ε(pe (τ ),e)
(1 − e)ε(pe (τ ),e)
(11)
With limited jurisdiction , the optimal environmental regulation performs
three tasks. First, the tax internalized environmental externality. Second it
corrects for the monopolist's tendency to underproduce. Third, it outweighs
the foregone revenue due to scal avoidance.
Under the circumstances
τ
also strives to correct for imperfect tax transfer, distorted by partial evasion
of monopolist prot.
The third component of (11) precisely reects this
distortion.
The planner's need for the revenues raised from environmental taxation
is inversely related to the jurisdiction size. When
β
is one and the jurisdic-
tion is whole, there is no unbalance between revenues and taxation, no conict in weighing gains and disadvantages between polluting manufacturing
and environmental consciousness, since the burden of pollution and benets
from production are equally shared. Once
β
falls below one, from the social
standpoint it becomes increasingly desirable, as external part of shareholders grows, to discriminate against the producer by levying progressively high
15
environmental tax consistent with consumers' higher valuation of environmental quality.
The explicit form of the environmental tax is given by:
τeII =
2
1 v − c(e)
1 − β v − c(e)
δ−
+2
3 − 2β
3 − 2β 1 − e
3 − 2β 1 − e
or simplied:
τeII =
2δ
2β − 1 v − c(e)
−
3 − 2β 3 − 2β 1 − e
The impact of scal avoidance on the optimal environmental regulation
is given by:
4
v − c(e)
∂τeII
=
(δ
−
)
∂β
(3 − 2β)2
1−e
Note, that
∂τeII /∂β < 0
by the assumption (4).
increase in scal avoidance (decrease of
β)
This means that and
leads to an increase in taxation
severity.
The impact of an increment in environmental awareness on the optimal
environmental regulation is given by:
∂τeII
1 − 2β
=
∂e
3 − 2β
The sign of the expression changes for
v−c(e)
1−e
−c
1−e
0
β = 1/2 and depends of the relation
between relative net social value of the good and the cost increment.
The cross-partial derivative of optimal regulation with respect to scal
avoidance and environmental awareness is given by:
∂ 2 τeII
4
=−
∂β∂e
(3 − 2β)2
v−c(e)
1−e
−c
1−e
0
The cross-derivative is negative as long as relative net social value of the
good exceeds the cost increment of the quality provision.
16
Further, the revenue-raising objective is dependent on the price elasticity
of demand: the ability to collect revenues grows when demand elasticity falls.
Corollary 2.3.2. The optimal environmental regulation becomes more strin-
gent/tightens up as the jurisdiction shrinks. it is possible to divide the interval
on which
β
is dened into tree segments:
•
For
β < 1/2,
the regulation is always a tax which exceeds Pigovial level.
•
For
β = 1/2,
the regulation is a tax exactly at the Pigovial level.
•
For
β > 1/2,
the regulation is either a tax below Pigovial level or a sub-
sidy, depending on the ratio of net social value to polluting emissions.
Proof. See Appendix.
The two latter components of
directions.
τ
eect the optimal regulation in opposite
Ultimately, as the jurisdiction diminishes, the revenue concern
outweighs, from the social standpoint, the distortion induced by monopoly
output. That is when the tax surpasses the Pigovian benchmark. Contrarily,
for a subsidy to take place, the net social value additionally must suciently
outweigh the pollution damage.
Figure 1 illustrates how the regulation changes depending on the jurisdiction magnitude and the ratio of net social value to environmental damage.
The front horizontal axes depicts the parameter
β over the interval [0, 1].
The
depth horizontal axis represents the relative net social value, which range is
low in the front and grows increasingly while moving in depth. There, the
discrepancy between the social value and social damage of the good increases.
The vertical axis is regulation.
Note that the damage parameter
δ
is chosen arbitrary, since only the
relative relation to the net social value matters, which spreads from the
values close to damage parameter up to those greatly exceeding it.
Then,
if the jurisdiction is approaching one, the optimal regulation is a subsidy to
17
Optimal environmental regulation (δ=3)
5
τ
4
Taxation
3
2
4-5
3-4
1
8,5
7,5
6,5
0
Subsidy
0
-1
0,1
0,2
5,5
0,3
0,4
0,5
0,7
0,8
-2
0,9
2-3
1-2
0-1
-1-0
4,5
0,6
v-c(e)
1-e
-2--1
β 3,5
1
-3--2
-3
Net social value
Extent of jurisdiction
Figure 1: Optimal regulation, jurisdiction magnitude & net social value
a polluting monopolist. However, when the values of social desirability and
damage are almost equal (the front right angle), the regulation is stringent
since the product's relative value is low.
The optimal regulation depends linearly on the relative net social value;
the extent of the jurisdiction determines if the relation is positive, negative
or neutral. Figure 2 shows explicitly that for
cide with the Pigovial rule, i.e.
τ = δ.
β = 1/2,
the regulation coin-
Consequently, if the major part of
production underlies the regulatory jurisdiction, the good's net social value
is negatively related to the optimal regulation, and vise versa.
restriction imposed on
τ
is that the demand has to be positive.
τ < (v − c(e))/(1 − e) must hold. This
represented by a 45-line in Figure 2.
18
The only
For this
condition is always satised and is
Optimal environmental regulation under limited jurisdiction
(δ=3)
10
8
Regulation
6
4
β=0,1
β=0,5
β=1
2
45°
0
3,5
4,5
5,5
6,5
7,5
8,5
-2
-4
Relative net social value
Figure 2: Optimal regulation & net social value
Note that the smaller the jurisdiction is, the lower both the welfare and
the producer's prot are. Clearly, as an increasing part of monopolist's revenues drift outside the jurisdiction, the more the social surplus falls.
And
similarly, the less the regulator concerns about monopoly prot, the more
stringent the regulation and the lower the prot are. Consequently, the `Depardieu' syndrome is unambiguously detrimental to the welfare.
The critical point for the regulation is where
β = 1/2,
because for this
value of jurisdiction magnitude, the monopoly distortion exactly cancels out
the revenue concern. For very limited jurisdiction (β
< 1/2)
the regulation
never takes form of a subsidy. Moreover, as the net social value grows relative
to damage, the regulation tightens. This happens because even though the
social value grows, environmental concern dominates the the social desirabil-
19
ity of the good. Figure 3 claries the interrelations between the jurisdiction
magnitude and the regulation.
Optimal environmental regulation under limited jurisdiction
(δ=3)
6
Regulation (τ)
4
2
RNSV=3.5
RNSV=6.5
RNSV=8.5
0
0
0,2
0,4
0,6
0,8
1
-2
-4
Extent of jurisdiction (β)
Figure 3: Optimal regulation & jurisdiction magnitude
Figure 3 depicts three dierent paths of regulation, which correspond to
the three arbitrary levels of the relative social value of the good: a low one
(poor environmental performance - the doted line in blue), for which social
value almost coincide with environmental damage, a medium (the continuous red line) and a high (the dashed line in green). The range of regulation
is getting larger, as the discrepancy between social value and environmental
damage grows. The greatest dierence in values is depicted by the dotted
line, for which the regulation changes from stringent taxation for low
subsidy for high
β,
β
to
because as social priorities to correct distortions (pollu-
tion, monopoly output and revenue disbalance) change with jurisdiction, and
20
a higher social desirability aects the magnitude of the optimal regulation
to a greater extent. Consequently, for high values of scal evasion (β
< 1/2)
the regulation for higher environmental quality (green curve) is always more
stringent. Hence, the higher environmental quality is, the more demanding
environmental standard is.
3
Regulation with unknown pollution level
3.1
Second-best solution of type III: regulation under asymmetric information threatened by scal evasion
In the section we extend our model by introducing asymmetric information
so that the regulator is unable to observe neither production costs, nor toxic
emissions, no abatement eort. Knowing the distribution of consumer beliefs
µ(p),
the planner aims to induce the monopolist to reveal his proper type by
oering him a menu of contracts. In this preliminary setting the regulator
has a commitment power making the producer a take-it-or-leave-it oer. The
monopolist thus may choose to refuse and exit the market or produce and
sell the output at a xed price and make a xed transfer
Te .
In the case
when the transfer is positive, it represents a lump-sum tax on the producer,
otherwise it is a subsidy.
The regulator is to maximize the welfare given by:
"Z
max
(v − pg − (1 − g)X − δ(1 − g))dX + β(πg − Tg ) + Tg
µ
(pb Tb ),(pg Tg )
#
D(pg ,g)
0
"Z
+(1 − µ)
#
D(pb ,b)
(v − pb − (1 − b)X − δ(1 − b))dX + β(πb − Tb ) + Tb
0
(12)
21
The choice of a corresponding menu should be individually rational, i.e.
it should ensure a nonnegative prot for either type of the enterprise:
(pe − c(e))D(pe , e) − Te ≥ 0
for
e = g, b
(IRe )
While incentive compatibilities (ICg ) and (ICb ) should prevent the monopolist from mimicking the other type and induce a correct self-identication
by choosing an appropriate contract:
(pg − c)D(pg , g) − Tg ≥ (pb − c)D(pb , b) − Tb
(ICg )
pb D(pb , b) − Tb ≥ pg D(pg , g) − Tg
(ICb )
Since the green producer is willing to distinguish himself from the polluting one and has no incentive to mimic the brown rm, the regulator is
capable of capturing the entire monopoly prot from the clean rm.
makes
(IRg )
This
and (ICb ) binding.
Proposition 3.1.1. The second-best
acterized by the contracts
pSB
= δ(1 − g) + c +
g
(pe , Te )SB
6 optimal environmental policy is char-
that is:
1−µ
(1 − β)c
µ
pSB
= δ(1 − b)
b
TgSB = (pg − c)D(pg , g)
(13)
TbSB = pb D(pb , b) − cD(pg , g)
Proof. See Appendix.
Note, that the feasibility of menu prices is subject to positive demand.
This imposes a restriction on values, which is binding only for the price of
the green good, conditions for which are given by:
6 The
corresponding rst-best solution is discussed in the section 2.1
22

v − δ(1 − g) − c −



1−g

v−c


>δ
1−g
We rewrite the second inequality as
1−µ
(1
µ
v−c
1−g
− β)c
= δ + ,
>0
where
stands for the
dierence between social value and the environmental damage of the good,
simplify and substitute into the rst inequality; we get:
>
1−µ
(1 − β)c
µ
The condition rises the restriction on the value of a green product: it
must be more valuable than weighted (by
1−µ
(1
µ
− β))
private cost of the
good in order to ensure a positive demand for the clean product. In other
words, under asymmetric information, the relative net social of the green
good must be higher than when the environmental quality is observable.
Prices incorporate the marginal damage for both goods. The price of the
brown good is the same as that in the rst-best solution, and so the brown
rm produces the socially ecient amount of the good.
In contrast, the
price of the green good is distorted upward relative to the rst-best solution,
and this distortion would not exist in the absence of scal evasion.
The
regulator forces the green rm to produce an ineciently small amount of
good, in order to make the combination
rm.
(pg , Tg )
less attractive to the brown
The green rm suers relatively less from lost consumers than the
brown rm, therefore the regulator hits the green rm with a reduction in
quantity. In fact, this punishment aims at preventing the brown rm from
misrepresenting its costs.
For the same purpose, the regulator oers the
brown rm a tax lower than that required by the rst-best solution. This is
given by the term
cD(pg , g)
in the expression
Tb
of (13), meaning that some
strictly positive prot is left to the brown rm, which can be interpreted as
a reward for revealing the true costs. Contrarily, a zero prot is left for the
23
`green' monopolist.
The welfare implication of the second-best solution is socially ineciently
high pricing for the green product and an ineciently low transfer from
the brown rm. The regulator here uses prices to correct for the pollution
externality as in the rst-best situation.
In addition, the regulator must
internalize the brown rm's tendency to masquerade as the green rm. The
most ecient way to x the problem is to distort - relative to the rst-best
solution - upward the price intended for the green good, and downward the
tax intended for the brown rm.
3.2
Comparison with unregulated outcome
In this context it is informative to make a comparison with the solutions
obtained in rst-best and laissez-faire situations.
First, we want to investigate for which parameter combinations the secondbest solution is less ecient than the laissez-faire, in other words when
.
> pmon
pSB
e
e
It is easy to show that the condition holds if:
δ<
1−µ
2c
v−c
< 2δ +
(1 − β)
1−e
µ
1−e
Hence, within a region where relative net social value of the good is rather
low, the pricing of second-best solution is socially inferior to an unregulated
outcome. Note that the higher bound of the interval for the green product
depends on
β.
Since the derivative of
negative, this means as
β
2c 1−µ
(1
1−e µ
− β)
with respect to
β
is
falls, i.e. a large-scale scal evasion takes place,
the upper bound increases. Thus the larger the scal evasion is, the greater
the region where regulation is less ecient then market solution.
Now we turn to properties of x transfers.
∂Tb
1 − µ c2
=−
∂β
µ 1−g
24
The xed transfer for conventional product increases when
β
falls. This
means that as scal evasion grows, the monetary transfer from the polluting
monopolist grows
The derivative of a xed transfer for the green rm is given by:
1 − µ (pg − c) − (v − pg )
∂Tg
=
c
∂β
µ
1−g
(pg − c) − (v − pg ). Rearranging we
pg > v+c
, that is when the menu price
2
The sign of the fraction depends on
get that the expression is positive if
for green product is higher than the unregulated monopoly price. In other
words, in the inecient range of regulated prices - if the second-best price for
the green product must be set above the monopoly price - the xed transfer
from the green rm would also increase with scal evasion. Otherwise the
xed transfer would fall with growing scal evasion. This happens because
the transfer is the entire prot.
4
Conclusion
In the present paper we integrate principal approaches that prevail in analysis of environmental regulation.
In particular, based on a highly stylized
model we analyze the impact of scal evasion on the optimal environmental
regulation carried out by a governor whose authority may be limited in different respects as to oset monopolistic pricing or to observe the production
costs or abatement eorts. To create a benchmark, we contrast the results
to those which would prevail in the presence of an omniscient regulator capable of inicting the rst-order solution. This allows to see the systematic
inuence of the threat of scal avoidance on the regulation - the governor
must be more stringent towards the good of a higher environmental quality. We distinguish between two case: complete and incomplete information.
For the former case, the severity of regulation augments with the net social
25
value of the good. This happens because a higher extent of scal avoidance
increases the distortion associated with the imperfect tax transfer, which
requires a toughening of the tax regime.
For the case of imperfect infor-
mation, the intuition for these results is akin to Dupuit (1962)'s statement
that the monopolist hits the poor <...> to frighten the rich or to that of
Mussa and Rosen (1978) that in order to extract surplus from customers
with higher reservation for quality one needs to degrade the quality of the
low-niche product. However, in present case it is the high quality that has
to bear the burden of dierentiation. When both green and brown products
are authorized on the market, to distinguish between environmental qualities
the regulator undertakes a policy that is more severe to the green rm than
what would require the Pigovian recommendation but laxer to brown rm,
there is a tax rebate relative to the rst-best level. The policy towards the
green rm has to be, under certain circumstances, so severe that the green
product is evicted from the market altogether.
We analyze a short-term model with xed level of emission and technology. The mechanism to achieve the optimal environmental quality is to
impose a polluting rm to reduce its output.
The regulator uses one sole
instrument - the price-tax combination - to counteract multiple distortions.
5
Appendix
Proof of Proposition 2.3.1 and Corollary 2.3.2.
Proof. To show the negative relation between regulation severity and the extent of jurisdiction we rst substitute
ε(pe ,e) = −(∂D(pe , e)/∂pe )/(D(pe , e)/pe )
and using (9), we get:
0
τ∗ =
1 v − c(e)
1 − β v − c(e)
2
δ−
+2
3 − 2β
3 − 2β 1 − e
3 − 2β 1 − e
26
(14)
Next, we derive
0
τ∗
with respect to
β,
which yields:
0
2(δ − v−c(e)
)
∂τ ∗
1−e
=
∂β
(3 − 2β)2
(15)
The fraction (15) is negative, since the numerator is negative by assumption: marginal environmental damage
of the good
v − c(e),
δ(1 − e)
is less than net social value
while the denominator is quadratic and thus always
positive.
Note that
β = 1/2
is the threshold for intervention to be a subsidy.
Rearranging (14), we have:
0
τ∗ =
2β − 1 v − c(e)
2δ
−
3 − 2β 3 − 2β 1 − e
For the regulation to be a subsidy, it suces that
Provided
β ∈ [0; 1], β
must be greater than
1/2
(16)
β>
1
2
+
δ(1−e)
holds.
v−c(e)
and the ratio
(δ(1 −
e))/(v − c(e)) must not exceed 1/2, which means that the net social values of
the good v − c(e) should be suciently high relative to marginal environmental damage per unit of output δ(1 − e) (or the damage should be suciently
low relative to its value).
For (16) to exceed the Pigovial level,
always holds for
0
τ∗
has to be greater to
δ
which
β < 1/2.
Proof of Proposition 3.1.1.
Proof. Since
(IRg )
and (ICb ) are binding, from (IRe ) we get:
Tg = [pg − c] D(pg , g)
(17)
Substituting (17) into (ICb ), we have:
Tb = pb D(pb , b) − cD(pg , g)
27
(18)
Plugging (17) and (18) into (12), the regulator's optimization problem
simplies to:
1−g 2
D (pg , g)
(19)
max µ (v − δ(1 − g) − c)D(pg , g) −
pg pb
2
1−b 2
+(1 − µ) (v − δ(1 − g))D(pb , b) −
D (pb , b) − (1 − β)cD(pg , g)
2
The rst order conditions of (19) are satised when:
pb = δ(1 − b)
pg = δ(1 − g) + c +
5.1
Put
1−µ
(1 − β)c
µ
Leviathan approach
β
on the consumer surplus to derive the outcome for Leviathan
government.
References
Andreoni, J., Erard, B., and Feinstein, J. (1998). Tax compliance. Journal
of Economic Literature, 36(2):818860.
Barnett, A. H. (1980). The pigouvian tax rule under monopoly. The
American Economic Review, 70(5):10371041.
Baron, D. P. (1985). Regulation of prices and pollution under incomplete
information. Journal of Public Economics, 28(2):211231.
28
Baron, D. P. and Myerson, R. B. (1982). Regulating a monopolist with
unknown costs. Econometrica, 50(4):911930.
Bower, R. S. (1981). Impact of regulation on economic behavior:
Discussion. The Journal of Finance, 36(2):397399.
Boyer, M. and Laont, J.-J. (1999). Toward a political theory of the
emergence of environmental incentive regulation. The RAND Journal of
Economics, pages 137157.
Buchanan, J. M. (1969). External diseconomies, corrective taxes, and
market structure. The American Economic Review, 59(1):174177.
Dupuit, J. (1962). On tolls and transport charges. International Economic
Papers, 11:7.
Freixas, X., Guesnerie, R., and Tirole, J. (1985). Planning under
incomplete information and the ratchet eect. The Review of Economic
Studies, 52(2):173191.
Karl, H. and Orwat, C. (1999). Economic aspects of environmental
labelling. In The International Yearbook of Environmental and Resource
Economics 1999/2000. Edward Elgar Publishing, Inc.
Laont, J.-J. (1994). The new economics of regulation ten years after.
Econometrica, 62(3):507537.
Lee, D. R. (1975). Eciency of pollution taxation and market structure.
Journal of Environmental Economics and Management, 2(1):6972.
Lewis, T. R. (1996). Protecting the environment when costs and benets
are privately known. The Rand Journal of Economics, pages 819847.
Lyon, T. P. and Maxwell, J. W. (2011). Greenwash: Corporate
environmental disclosure under threat of audit. Journal of Economics &
Management Strategy, 20(1):341.
Mussa, M. and Rosen, S. (1978). Monopoly and product quality. Journal of
Economic Theory, 18(2):301317.
Slemrod, J. (2007). Cheating ourselves: The economics of tax evasion. The
Journal of Economic Perspectives, 21(1):2548.
29
Slemrod, J. and Yitzhaki, S. (2002). Tax avoidance, evasion, and
administration. Handbook of public economics, 3:14231470.
Spulber, D. F. (1988). Optimal environmental regulation under asymmetric
information. Journal of Public Economics, 35(2):163181.
Wirl, F. and Dockner, E. (1995). Leviathan governments and carbon taxes:
Costs and potential benets. European Economic Review,
39(6):12151236.
30