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The Political Economy of Environmental Tax Design*
Matthieu Glachant, CERNA, Ecole des Mines de Paris
This version: October 2001
Correspondence to: Matthieu Glachant, CERNA, Ecole des Mines de Paris, 60,
boulevard St Michel, 75006 Paris, France, tel: +33 1 40 51 9229. E-mail:
[email protected]
*
I would like to thank Luca de Benedictis and Margaret Armstrong for helpful discussions and comments.
Part of the paper was written while I was Jean Monnet Fellow at the European University Institute.
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Abstract
If regulation remains by far the dominant approach in actual environmental
policy, environmental taxes are no longer a theoretical curiosity. However, existing
taxes' design differ significantly with the theoretical solution envisaged in the
textbooks. In particular, earmarking prevails and actual taxes are usually combined
with regulation. Furthermore tax rates are generally too low to significantly influence
polluters' behavior.
The paper develops a political economy model to explain these design issues. It
focuses on three parameters: tax rate, earmarking pattern and whether the tax is
combined with a regulation. These parameters are jointly selected through a voting
procedure influenced by a green lobby and an industrial lobby making campaign
contributions. One key assumption is the existence of a status quo policy entailing an
emission standard.
Results suggest that an earmarked tax which rate is lower than the regulatory
shadow price emerges in political equilibrium when the status quo regulation is
imperfectly enforced and if the green lobby is sufficiently weak. This is so because
earmarking finance abatement subsidies which reduces regulatory compliance cost. In
this configuration, a tax is thus introduced to promote regulatory compliance. By
contrast, a non-earmarked tax with rate above the regulation shadow price only
emerges when the green lobby is very powerful.
Key-words: Environmental tax; political economy, earmarking, tax design
JEL classification: D72; D78; H23; Q28
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1. Introduction
For years, economists advocate for a widespread use of environmental taxes for
meeting environmental policy targets. The main arguments are that they help to save
pollution abatement costs and provide higher incentives to innovate in abatement
technology than the traditional Command and Control approach based on direct
regulation. If regulation remains by far the dominant approach in actual environmental
policy, environmental taxes are no longer a theoretical curiosity. In 1995, more than
300 environmental taxes were in place in OECD countries (OECD, 1995) and covered
the quasi-complete range of environmental concerns: water or air pollution, noise,
waste, land use etc.
However, existing taxes and charges differ significantly with the theoretical
solution envisaged in the textbooks. In practice, pollution charges are not Pigovian
taxes set at a level where the marginal environmental damage is equal to the marginal
abatement cost. Paraphrasing the title of a famous paper by Hahn (1991), the patients
do not exactly follow the doctor's orders.
Several studies suggest how “real” taxes work (Hahn, 1989, OECD, 1995, EEA,
1997). Three main features are worth mentioning. First of all, tax revenues are
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generally earmarked to finance pollution abatement projects through grants and
subsidized loans in the domain they were collected.1 Hence environmental tax
revenues are "recycled" in pollution abatement subsidies.
Secondly actual taxes usually coexist with regulations. There is a simple
historical explanation for that: when taxes are introduced, they do not substitute but are
combined with the pre-existing regulatory system. Thirdly, tax rates are said to be too
low. This means that rates are below the level of the Pigovian tax (at which marginal
damage is equal to marginal abatement cost). But they are usually even too low to have
a significant incentive effect on polluters' behavior as well. Their main role is thus one
of fund raising.2 This latter feature is probably the most welfare damaging feature of
real tax schemes. If a tax is not capable of influencing the polluters’ behavior, it is a
precondition for the instrument to bring social benefits in terms of abatement cost
savings or innovation incentives that is not being met.
This policy context justifies the relevancy of a political economy analysis
explaining the actual characteristics of environmental taxes. This is what the paper is
attempting to do. It aims to analyze in a political economy framework environmental
tax design issues: why is earmarking prevalent? Why are charge rates low and how the
combination of the taxes with regulatory constraints affect the different charge
parameters? The analysis deals with the three different design parameters: tax rate,
earmarking pattern and whether the tax is combined with a regulation. We propose a
model where these parameters are jointly selected through a voting procedure
influenced by a green lobby and an industrial lobby making campaign contributions.
The political part of the model is directly derived from a simple formulation combining
probabilistic voting and lobbying recently suggested by Persson and Tabellini (2000, p
58) which were adapting a previous formulation by Baron (1994).
As to the "non-political" part of the model, two assumptions are central. Firstly,
we assume the possibility that the status quo is not the absence of any environmental
1
Earmarking remains prevalent even though it has been recently less favoured with the current so-called
Ecological tax Reforms going on in several EU countries. The general principle of this reform is to use
environmental tax revenues to cut labor taxes thus allowing for a "double dividend" in terms of
employment and environment.
2
The universal validity of this claim may be a bit more fragile than the others. To formally establish that
taxes does not influence polluters’ behaviours require econometric studies. As a matter of fact, surveys by
the European Environmental Agency (1997) and OECD (1997) recently argued that econometric
evaluations of environmental tax effectiveness were in fact very scarce. However, based on qualitative
evidence, it is quite universally made (Hahn, 1989, OECD, 1995, Pearson, 1995...).
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policy. Instead we assume that a regulation has been set through the same voting
procedure in the past and is still in force. This captures the fact that a regulation
frequently pre-exists when an emission charge is introduced: the setting up of a new
environmental tax is then a matter of policy change. This strongly affects the political
equilibrium since any policy change proposal is assessed by the agents against the
status quo. The second central assumption of the model is that the regulation is
imperfectly enforced. Again this is in line with what happens in reality: due to limited
administrative resources, full compliance with regulation is unlikely to be observed. As
we will see, this assumption crucially influences tax design in our model: imperfect
enforcement confers a role of regulatory enforcement incentive to the tax only when
revenues are earmarked. This is the key factor that leads political equilibrium to
include an earmarking provision in our analysis.
The paper is organized as follows. A second section reviews the literature which
has already quite extensively worked on some aspects of tax design and discusses the
relevancy of our own contribution in this context. A third section introduces the model.
In section 4., we characterize the status quo policy. Section 5. enters into the core of
the analysis. It focuses on a situation of perfect enforcement of the regulation, so that
the pollution abatement level in status quo corresponds to the level prescribed by the
emission standard. Our analysis predicts that policy changes only occur under very
restrictive conditions in this configuration. More specifically, the green lobby needs to
be much more influential than the industrial lobby to be able to foster its best policy
option: a non earmarked tax. The preference of the greens for non earmarking being
basically determined by the fact that they receive a share of the tax revenue. In that
configuration the tax rate is high (more specifically higher than the regulation shadow
price).
In section 6., we consider that the case where regulation is imperfectly enforced.
This changes the status quo position since now there is no pollution abatement initially.
It widens the room for policy change: a tax is systematically introduced in this case but
its design differs according to the relative strength of the green and industrial lobbies.
In particular, when the green lobby is less powerful in relative terms, the political
equilibrium involves the introduction of non-earmarked tax which complements the
imperfectly enforced regulation. Tax rate is predicted to be low, that is under the
regulation shadow cost. The basic reason is that earmarking permit to subsidize
regulatory compliance and thus rises abatement level even at a low rate. When
regulatory enforcement is not perfect, the political equilibrium is thus in line with the
prevalent tax design encountered in reality. Section 7. concludes.
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2. The literature on the political economy of environmental tax design
The formal political economy literature on environmental taxes is now
developing quickly. Most contributions focus on the question of the instrument choice:
they investigate why regulation remains much more widespread than environmental
charges or other economic instruments of pollution control (see Djikstraa, 1999 for a
recent survey). In comparison, the literature on design aspects is more limited. Most
papers focus on earmarking.
By far the most popular line of argument put the emphasis on the influence on
interest groups. Buchanan together with Gordon Tullock provide the basis of these
arguments in a very influential contribution published in 1975. The paper is concerned
with instrument choice (pollution tax versus direct regulation) but it directly applies to
earmarking. It can be summarized as follows. In comparison with a non-earmarked tax,
the distributional pattern of earmarking is reversed: the winners are the polluters (since
they get back through subsidies tax payments) and the losers are the consumers (which
would have benefited from tax revenue otherwise). This distributional pattern
combined with the classical Olson's argument suggesting that the polluters' lobby
gathering a lower number of members with higher unit stakes will be more influential
than the consumer lobby leads to predict earmarking in political equilibrium. This is a
positive argument explaining the prevalence of earmarking but it immediately leads to
an efficiency argument developed for instance in a paper by Hansen (1999). In an
incomplete contract setting, Hansen develops a model where earmarking is seen as a
way to limit the political distortions introduced by polluters' lobbying against nonearmarked taxation.
A second line of arguments about earmarking moves the emphasis on voting
concerns and elections. It is convenient to begin its presentation by reminding the
standard "normative" argument of the theory of public finance against earmarking.
Earmarking is essentially a constraint on the regulator's choice over tax revenue
allocation. Ex ante, this constraint can perfectly be justified from an efficiency point of
view. But ex post, this might not be true because the economic environment evolves
over time: earmarking then prevents welfare improving adjustments. A political
economy argument against this view was made again by Buchanan (1963) and
subsequently extended by Goetz (1965). Their point is that the standard argument no
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longer holds when one adopts a more realistic view of the regulator. In particular,
earmarking can be efficient if budgetary decisions are made through a voting process
as it is the case in actual Parliaments. The rationale is that earmarking modifies the
contents of the budgetary decision. Instead of voting twice and separately over public
expenses and revenues, the constrained budgetary decision consists in selecting the
bundle of public goods to be provided. Put differently, earmarking oblige to jointly
decide over the level of provision of a particular public good (like pollution abatement)
and its cost. It transforms the budgetary decision into a uni-dimensional policy choice.
Consequently, earmarking drives away the efficiency problem associated with strategic
voting over multidimensional policy under majority rule: the median voter theorem
holds and there exists a single voting equilibrium. In a recent contribution, Brett and
Keen (2000) suggest another argument. They develop a voting model where
earmarking is shown as possibly efficient by limiting the negative impacts of electoral
cycles and of political uncertainty associated with.
These contributions focussing on voting properties by Buchanan, Goetz or Brett
& Keen actually do not bring positive but efficiency arguments. More precisely, they
do not explain why earmarking prevails. Rather they arguments claim that earmarking
is efficient in a politically constrained context. If we come back to more positive
analysis of earmarking, Bös has recently offered a very rich analysis by entering more
deeply into the government "black box" (2000). He develops of post-election politics
model where the tax is selected by a Parliament controlling two ministers. One is the
finance minister in charge of collecting tax, the other being the tax spender. A
principal-agent setting is used to model the relationship between the Parliament and
the ministers. Considering the internal structure of the government leads Bös to stress
the importance of uncertainty over the future states of the world. If the Parliament or
the ministers face high uncertainties, the scope for earmarking is reduced. The reason
is that they will prefer to benefit from the non affected tax revenue to face a possible
worsening of the economic situation. In other words, earmarking is a "safety net"
against future negative shocks on the economy (and thus on public spending) in Bös'
framework.
In the end, many arguments are available to explain the prevalence of
earmarking. This is not true as regards other design aspects (tax rate, combination with
regulation). To our knowledge, there is only one paper written by Fredriksson (1997)
which explores the relationship between tax rate, abatement subsidy rate, lobby
membership, and product price. There is no earmarking in his model since the
abatement subsidy is exogenous. The political part of the model is the popular common
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agency model introduced by Bernhein and Whinston (1986) and subsequently applied
to political economy issues by Grossman and Helpmann (1994). Fredriksson's analysis
yields classical results about the influence of lobby membership on the tax parameters
(for instance, the more members in the industrial lobby, the lower the tax rate) or other
exogenous variables (e.g. the product price). One interesting result is that total
pollution may be increasing in the abatement subsidy rate because of political
distortions. This is so because inter alia the abatement subsidy reduces the industry's
marginal cost and hence output increases. This may stimulate lobbying activity of
industry because a higher level of output makes a low pollution tax rate more
important.
In this context, a general analysis of tax design seems relevant. Our approach
will be fairly classical in that we will concentrate on the distributional patterns of
different design and their subsequent impacts on lobbies and voters' behavior in line
with Fredriksson's model for instance, or the historical Buchanan and Tullock's paper.
One difference with Fredriksson's paper is that, to model the political process, we will
not apply the common agency approach popularized by Grossmann and Helpman.
Instead, we will use a model of electoral competition with probabilistic voting and
lobbies making campaign contributions. This is a model of pre-election politics since
politicians commit to electoral platforms involving an environmental tax which is
implemented if he wins the election. By contrast, the Grossmann and Helpman's
approach is a post election model with political decisions being made by elected
politicians already in charge who search for re-election. This methodological
difference is not crucial however since both models bring similar results.
3. The model
We assume an open economy made of one (representative) producer of a good
who is also a polluter, a population of individuals who are voters and may be lobby
members and two politicians competing for a future election.
The polluter and the environmental policy
The producer produces a good and emits a pollutant in the environment. More
specifically the producer’s surplus is:
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 (q) = ° - C(q)
where ° is the profit resulting from the production of the good. It is a scalar
because we assume that the economy is small and open so that a change in the
polluter’s total production cost does not alter the good’s market price.3 C(q) is a
pollution abatement function varying with q, the quantity of pollution abated (q>0).
C(q) is assumed twicely differentiable, continuous and convex because of decreasing
returns to pollution abatement. In the absence of environmental policy, the polluter
discharges a quantity of pollution, Q. We also maintain throughout that ° > C(q), q
(pollution abatement cannot lead the producer to bankruptcy).
The producer possibly faces a regulation imposing a quantitative constraint on
its polluting emission. More specifically, we assume an emission standard prescribing
the polluter to abate a minimal quantity of pollution R.
We explicitly model the enforcement of the emission standard. This is done in a
very simple way. The non-compliant polluter bears an expected lump sum fine F
(which is the product of the fine with a probability of inspection). In this context, he
decides whether to comply by considering R the difference between the sanction and
the cost of compliance
R = F - C(R)
In section 4., we consider the case where  is positive, that is the polluter
complies. Section 5. deals with the opposite case.
The polluter also faces an emission tax to be paid on each unit of pollution
discharged at a flat rate t. The polluter's tax payment generates a revenue  (q, t) = (q
– Q)t which can be used in two different ways. This is represented by an index
variable  which takes the value 1 and 0 if revenues are "recycled" to finance pollution
abatement (= earmarking), or redistributed to the whole population respectively.
When earmarking prevails ( = 1), charge revenues are used to finance an
abatement cost subsidy. This subsidy is granted to the polluter if he decides to abate
beyond Q, its initial level of pollution. The subsidy is equal to a fixed proportion s of
its abatement cost with s  [0, 1]. Hence total subsidy is s.C(q). The fact that the
subsidy is based on abatement cost (and not on the quantity of pollution abated for
3
This assumption greatly simplifies the analysis driving away general equilibrium aspects. It is made in
other contributions where consequences on the labour, or good markets are not the core of the analysis
(see for instance Fredriksson, 1997).
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instance) is in line with the reality where revenues are distributed to polluters through
investment grants and soft loans in order to reduce net abatement costs.
In our setting, s is endogenous since it is given by the earmarking constraint:
sC(q) =  (Q-q)t
(1)
In the absence of earmarking ( = 1), tax revenues are totally distributed as a
lump sum subsidy to the population.4 Hence the total revenue redistributed to the
population is (1 - )(Q-q)t
To sum up, the polluter faces a policy vector denoted h = (t, , R).
The population
The economy is populated with heterogeneous citizens of three distinct types, J
= G, C, I representing the greens, the consumers and the industrialists, respectively.
The size of the population is normalized to one. The population share of group J is J,
with J =1. The three groups have very different stakes vis-à-vis the polluter’s
activity.
Only the individuals of the green group G derive utility from pollution
abatement. In the case where tax revenues are not earmarked (  = 0), they also receive
a fraction of the revenues generated by the tax. As individuals share identical
additively separable preferences, we immediately consider the total utility of the group
UG = B(q) + G(1-)  (q, t)
(2)
where B(q) represents the environmental benefit of pollution abatement. We
have B>0, B’>0 and B(0) = 0. When deriving the political equilibrium, the individual
utility is more convenient to use. It will be denoted uG = UG/G
Consumers of group C are neither affected by pollution damages nor by the cut
in producer’s profit due to pollution abatement. But they derive an utility U° from the
consumption good produced by the polluter. U° is again a scalar in line with the
assumption that the economy is small and open. In the case tax revenue are not
4
We assume that there is no shadow cost for providing public funds. This assumption is justified by the
willingness to avoid any efficiency advantages to one of two instruments (tax versus regulation). This
allows for concentrating the analysis on the political factors. Assuming a shadow cost would have de facto
given a cost advantage to the regulation.
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earmarked, they receive a fraction of the revenue. Hence, the group total utility and the
individual utility are respectively:
UC = U° + C(1 - ) (q, t)
uC = UC/C
(3)
The industrialists from group I own the polluter and are thus negatively affected
by compliance costs and tax payments. Just as the other groups, they receive a fraction
of tax revenues when there is no earmarking. Conversely, when revenues are
earmarked, the producer receives the totality of the revenue in the form of cost
subsidies. The industrialist group’s total utility is thus given by:
UI = ° - C(q) - (1 - I)(1-)  (q, t)
(4)
And the individual industrialist utility remains denoted uI = UI /I
The political process
How is the environmental policy vector selected? We consider a probabilistic
voting model where two candidates P =A, B maximize their probability to win the
elections pP. They are elected by the individuals from the population on the basis of
electoral platforms. Some voters are organized in lobbies so that they can make
campaign contributions that influence the results of the elections.
More precisely, at the initial stage of the political game, each candidate P
commits to an electoral platform consisting of a particular policy vector hP. Individuals
are assumed to vote sincerely considering the platform and two variables  and iJ.  is
a random variable measuring the average (relative) popularity of candidate B over
candidate A in the population as a whole. It is the probabilistic element of the voting
process:  is unknown to the candidates when they commit to platforms. iJ represents
the ideological biases of the individual i from group J in favor of the candidate B (or in
favor of the party of candidate B). Hence, a voter from the group J behaves as follows:
If uJ(hA) > uJ(hB) + iJ + , he votes for the candidate A
If uJ(hB) < uJ(hB) + iJ + , he votes for the candidate B
If uJ(hA) = uJ(hB) + iJ + , he decides randomly
iJ is common knowledge and is uniformly distributed over the interval
[-1/2, 1/2]. Lobby groups are able to influence the popularity shock  through
campaign contributions. This leads to a new important assumption:
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Only groups G and I are organized in lobbies. This hypothesis introduces the
political distortion that will make the political equilibrium deviating from the
utilitarian optimum. This is justified on the ground that they are the two groups with
special interests in the environmental policy to be adopted. In comparison the
consumers are only concerned by the general interest aspect of the policy: the
redistribution of the charge revenues. The indicator variable OJ indicates whether the
group J is organized or not. It takes a value of one if it is true, zero otherwise. Hence
OG = OI = 1 and OC = 0.
Organized groups have the capacity to contribute to the campaign of either of
the two candidates. Let JP the contribution per member of the group J to the candidate
P. Hence the total contributions collected by candidate P can be expressed as
P =  OJ JJP
These contributions are used by the candidates to increase their popularity. More
specifically we assume that  has two components:
 =  + g(A – B)
g is a parameter measuring the effectiveness of campaign spending and  is a
random variable uniformly distributed over the interval [-1/2, 1/2].
As to the cost of the contributions for the lobby group J, we assume it exhibits
decreasing returns. This can be interpreted in two ways. If transfers by individuals are
made in cash, different individuals may differ in their willingness to give. If transfers
are made in kind – by working the in campaign- it may reflect the increasing disutility
of effort. In fact we assume for the cost a simple quadratic form:
J/2(JA2 + JB2),
for J = G, I
J is a fixed coefficient which introduces an heterogeneity between lobby groups
as to their ability to collect contributions and thus ultimately as to their ability to
influence the electoral outcome. We assume GI = 1.
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Finally the timing of events is as follows:
(1) The two candidates simultaneously and non-cooperatively announce their electoral
platform which is a policy vector hP.
(2) The lobbies simultaneously give their campaign contributions to the candidates.
(3) The actual value of  is realized and all uncertainty is resolved.
(4) The elections are held and the winner implements its policy platform (policy
platforms are thus binding promises).
4. The status quo policy equilibrium
In our setting, the status quo is not a "no-policy" situation. Instead, a regulation
is in force. It was set in the past following the same voting procedure. This section
characterizes the status quo policy. It will lead us to identify the general properties of
the political equilibrium that will be used throughout the analysis.
The utilitarian optimum
We start the equilibrium analysis considering the utilitarian optimum. This case
is interesting since it provides a benchmark against which "distorted" political
equilibriums are compared. The utilitarian optimum is given by the maximisation of a
welfare function WS* which sums the three groups’ utility, that is WS* = ° + U° +
B(R) - C(R) which leads to the condition for an interior optimum:
Bq(R) = Cq(R)
(5)
We note the optimal status quo regulation RS* = arg max WS*(R).5
The political equilibrium with lobbying
5
It means that we assume that the regulation was set up “myopically”, that is considering that
enforcement would have been perfect since q = R. This is a very classical assumption in positive analysis
of enforcement that reflects the naivete of political agents and voters with respect to the effectiveness of
policy implementation.
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Things become slightly more complicated when political distortions are
introduced. Some of the voters - the greens and the industrialists - are now organized in
lobby groups. We will analyse the problem going backward, starting with the election
stage. The first step of the analysis is to consider the "swing" voter, that is the voter in
each group J whose ideological bias denoted J, makes him indifferent between the
two parties given the candidates' platforms:
J = uJ(hA) - uJ(hB) -  + g(A – B)
(6)
All voters i in group J with iJ < J prefer party A. Hence, given our
assumptions on the distribution of iJ, candidate A's vote share is:
A =   J [J + 1/2]
(7)
J depends on the realized value of  which is known once platforms are
announced. Hence A is a random variable from the perspective of the candidates, and
the electoral outcome is a random event. Substituting (6) into (7) yields candidate A's
probability of winning:
pA = Prob {A > 1/2} =
Prob { J[uJ(hA) - uJ(hB) + g(A – B)] >  .J }
which can be rewritten using our assumption on the distribution of  :
pA = 1/2 +  [ WS*(hA) - W(hB) + g(A – B)]
(8)
where WS* (gP) = JuJ(hP) is the utilitarian social welfare function. The last term
reflects campaign spending’s influence on the vote share. The candidate B wins the
election with a probability pB = 1– pA.
Prior to characterize the optimal platforms announced by the candidates in stage
1, we need to consider the campaign contributions. Each lobby chooses the
contribution that maximizes the expected utility its members derive from the elections
minus the cost of the contributions
Max pAuJ(hA) + (1 - pA)uJ (hB) - J/2(JA2 + JB2)
(9)
15
In view of (8) into (9) the group J's optimal contribution is derived:6
JA = Max [0, g/J ( uJ(hA) - uJ(hB))]
JB = - Min [0, g/J ( uJ(hA) - uJ(hB))]
(10)
Thus the groups only contribute to one candidate whose platform gives the
highest utility, and never to more than one.
We can now consider the choice of the policy platform by the candidates at stage
1. Intuitively, given that both candidates have the same technology to transform
contributions into votes and given that the contribution schedule are symmetric,
candidates will end up with the same electoral platform. More specifically, each
candidate aims to maximise his probability of winning the elections, taking the other's
policy platform as given. Substituting (10) into (8) and simplifying, the candidate A
and candidate B non cooperatively maximize respectively:
 J[ + OJ(g)2/J]uJ(hA)
 J[ + OJ(g)2/J]uJ(hB)
(11)
This characterizes the sub-game perfect Nash equilibrium of the announcement
game. In equilibrium, both candidates announce a policy platform that maximizes a
welfare function weighed by coefficients J[+OJ(g)2/J]. These coefficients give
more weight to groups gathering more individuals and organized in lobby groups. The
political part of the analysis is now completed and we can plug (2), (3) and (4) into
(11) to get the resulting political support function:
US(R) = H° + [+(g)2I] B(R) – [+(g)2G] C(R)
with H° being a constant term equal to U°–[+(g)2G]°. Political support
maximization immediately yields the condition for an interior maximum which defines
the status quo policy RS:
By (9) the first order condition of the lobby J with respect to JA is
pA /JA [UJ(hA) - UJ(hB)] - JJA = 0
and by (8)
pA /JA = g 
Repeating the same steps for JB we get (10)
6
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[1+g2I] Bq(RS) = [1+g2G] Cq(RS)
(12)
As G and I differ, the regulation deviates from the optimal status quo
regulation RS*. Unsurprisingly, if G > I, that is if the industrial lobby is more
efficient in collecting contributions, abatement level is lower (RS>RS*).
5. The political equilibrium when the enforcement is perfect
Having characterised the status quo policy against which current policy change
will be judged, we are ready to enter into the core of the analysis, that is the
characterisation of the three dimensional policy vector h. As a first step, we will
assume that regulation enforcement is perfect (R > 0). Hence, the level of pollution
abatement in the status quo position is q = RS. We will see that an earmarked tax is
unlikely to emerge as a political equilibrium in this configuration.
The polluter's response to the policy mix
The problem is a bit complicated by the fact that the polluter is targeted by three
policy signals: an emission standard, an emission tax and a cost subsidy (if earmarking
prevails). How will he adjust his polluting behavior? Let us firstly identify the response
of the polluter to the sole tax and subsidy scheme. He minimizes the objective
function:
(1-s)C(q) + t(Q-q)
where the first term is the abatement cost minus the cost subsidy while the last term is
equal to the tax payment based on the polluter’s residual pollution. We immediately
get the first order condition:
Cq (q) = t/1-s
(13)
Together with the earmarking condition (1), (13) defines the polluter’s reaction
function to the fiscal scheme, denoted qf(t, ). This function is strictly increasing in
both t and  as demonstrated in Appendix 1.
How then do the tax and cost subsidy interact with the emission standard R? It
crucially depends on the relative level of qf(t, ) and R:
17
 If qf(t, ) > R, (13) is binding and the polluter abates until qf(t, ). In this case, the
standard does not have any influence on the polluter and the environmental outcome is
fully determined by the tax and the subsidy.
 If qf(t, ) < R, the regulatory constraint is binding and the polluter abate until R.
This is now the turn of the tax and subsidy scheme to have no impact on polluter’s
behavior.
In the following, this kinked reaction function is denoted q = q* 0 (t, , R) and
depicted in Figure 1. R = q* defines the shadow price of the regulation denoted tR0
and tR1 for  = 0 and 1, respectively.
Figure 1.
enforced
Polluter's response to the policy mix when the regulation is perfectly
Pollution
=1
abatement
=0
R
tR0
tR1
t
The utilitarian optimum
The characterization of the utilitarian optimum is then straightforward. The
optimal policy vector h* = (t*, *, R*) is the solution of the optimisation problem:
18
Max W(h)
subject to
q = q* 0 (h)
sC(q) =  t(Q-q)
W(h) > WS(RS*)
(polluter's reaction function)
(earmarking constraint)
(status quo constraint)
The last inequality constraint imposes the social welfare W(h) to be higher than
the status quo. As the welfare function has the same form as in the status quo (W(h) =
° +U° +B(q) –C(q) = WS(q)), it is immediate that the unique solution is q = RS*. This
leads to a first proposition.
Proposition 1.
In the case of perfect enforcement of the regulation (R > 0), the
utilitarian optimum h* corresponds to the status quo. That is h* (t*, *, R*) =
(0, 0, RS*)
The proposition simply reflects the fact that our assumptions do not confer any
efficiency (dis)advantage to the regulation over the tax. There is thus no efficiency
reason to modify the status quo in this context. Things will change with the
introduction of political distortions.
The political equilibrium
ˆ ) in the political equilibrium, we substitute
To identify the vector hˆ = ( ˆt , ˆ , R
(2), (3), and (4) into (11) and simplify. It gives the political support function:
V(h, q) = H°+ [+(g)2I] B(q) – [+(g)2G] C(q) +
(1-)(g)2[GI-(1-I)G] t(Q-q)
19
The solution is obtained through the maximization of V(h) subject to the
following set of constraints:
q = q* 0 (h)
sC(q) =  t(Q-q)
V (h) > US(RS)
It is immediately clear that  ≠ 1 in the political equilibrium. If  = 1, then U
and V have identical functional forms (V(q) = US(q) q). Hence RS is the
unconstrained optimum of U whereas hˆ is a constrained optimum of that same
function. Hence hˆ cannot yields a higher political support than the status quo.
The fact that an earmarked tax cannot be introduced in equilibrium is a crucial
result: when enforcement is perfect, the prevalent form of tax observed in practice, that
is an earmarked tax combined with regulation is not predicted by our analysis.7
Intuitively, this is so because, the introduction of an earmarked tax does not bring any
gain to the different groups of the population in comparison with the status quo (a
regulation fully enforced so that the pollution abatement level is RS). It does not
generate revenues which could have been distributed to the consumers or to the greens
otherwise whereas the industrialists are indifferent between the status quo regulation
and a tax fully recycled in the industry via cost subsidies.
This changes when tax is no longer earmarked: tax revenues are then
redistributed to the population deviations from RS become possible, if not systematic.
More precisely, if  = 0, we have V(h, q) = U(q) + [GI-(1-I)G](g)2  (q, t) with
the last term being the revenue function  (q, t) = t (Q-q) weighed by a coefficient.
The possibility for deviating from the status quo then crucially depends on the sign of
A = GI-(1-I)G:

7
If A < 0, the last term enters negatively in the political support function V. Hence
V is systematically inferior to the status quo political support U around the status
quo point (that is V (RS)<U(RS)). This cannot be overcome by deviating from RS
since any move diminishes the first term U(q): RS is its maximum. Hence, we have
the status quo in equilibrium.
As we will see, this will no longer be true as soon as we relax the assumption of perfect enforcement of
the regulation.
20

If A > 0, a move away from the status quo becomes possible since the last term,
enters positively in the political welfare function. As a consequence, the status quo
constraint holds in q = RS in this case. As shown in Appendix 2., deviating away
from RS increases political support up to the point where:
[1+g2G] Cq(q)- [1+g2I] Bq(q) = Ag2 Ωq(q)
(14)
The first term of (14) represents the marginal loss in terms of abatement cost and
environmental benefit from deviating from RS whereas the second term reflects the
marginal benefits in terms of additional tax revenue. Equation (14) highlights what
determines the sense of the deviation from the status quo. It depends on how the tax
revenue function evolves with q. As a matter of fact, the relation between revenue and
tax rate is not monotonic. This a classical story usually represented with the so-called
Laffer curve. This curve depicts how revenues evolve with the tax rate. As shown in
figure 2, this curve is upward sloping up to the maximal revenue Ω* for which Ωq*(q)
= 0 (hence t = Cqq(q)(Q-q) ). Then tax revenue decreases since the tax rate is now too
high for the decrease in tax basis to be compensated by rate increase.
Figure 2.
Tax revenue and tax rate: the Laffer curve
t
Cqq(q)(Q-q)
Ω*
Ω (t)
21
Coming back to (14), the inverted U shape of the Laffer curve implies that the
abatement level q in equilibrium is higher than in the status quo when the Laffer curve
is upward sloping around the status quo. By contrast, q is inferior to the status quo
abatement level if the Laffer curve is downward sloping.
What is the underlying intuition? In order to answer, one need firstly to show
that the greens are the politically powerful actors when A is positive. This can be
demonstrated by giving simple comparative statics results about A. Given that GI = 1
and J = 1, we have:
A/I = G + (1-I)/(I)2
A/G = -1 -I -G/(G)2
A/G = I > 0
A/I = 2G - I
We have A/I > 0 and A/G < 0. A positive coefficient A means that the
greens are relatively powerful in comparison with the industrial lobby. This is
reinforced by the fact that A/G > 0. The fact that the sign of A/I is ambiguous is
of no consequence in this case: A/I = 2G - I implies that A/I only becomes
negative when 2G = I. At this level of lobby relative inefficiency of the green lobby,
A is always negative and thus any change in I will never be sufficient for A to become
positive.
We are now ready to explain the intuition behind (14). When A is positive, the
political equilibrium thus reflects the interest of the greens. If tax revenue (and hence
redistribution to the population) is decreasing in the tax rate t around RS, the greens
may find advantageous a reduction in pollution abatement (via a reduction of the tax
rate) since this may be compensated by an additional tax revenue partly redistributed to
them. If revenue is increasing in the tax rate, it is advantageous for the greens to raise
tax rate in two respects: it rises pollution abatement and tax revenue.
To summarize, we have:
Proposition 2.
If regulation enforcement is perfect (R>0), the political
equilibrium crucially depends on the sign of A = GI-(1-I)G:
1)
If A < 0, the equilibrium policy vector corresponds to the status quo.
22
2)
If A > 0, policy change occurs. In particular a non earmarked tax is introduced
which substitutes the regulation. More precisely, the policy vector in equilibrium hˆ is
given by:
ˆt = Cq(q)
ˆ  = 0
ˆ <q
R
[1+g2I] Bq(q) = [1+g2G] Cq(q) - Ag2 Ωq(q)
The tax rate is thus higher than the regulation shadow price.
Moreover when the tax revenue function Ω(q) is upward sloping (that is Ωq(q) =
Cqq(q)(Q-q)-Cq(q) is strictly positive, the pollution abatement level is superior to the
status quo. If the function is downward sloping, abatement is lower.
The room for policy changes thus centrally depends on the coefficient A. In this
regard the room seems narrow. In the special case where the two lobbies are equally
efficient I = G, A is negative and no tax is introduced. As a consequence the green
lobby needs to be much more efficient that the industrialists' lobby to obtain a policy
reform to its interest. In the political economy literature it is usually admitted that this
cannot be true based on the Olson's argument: the green lobbies would be structurally
weaker than industrial pressure groups because the size of individual members' unit
stakes is much smaller and because they gather more individual members. In our
setting, one can be more explicit about why greens need to be so strong in comparison
with the industrialists for their point of view to prevail in the political equilibrium: this
is so because the greens benefits only partly from the tax revenue when it is not
earmarked (they get a share G) while the industrialists lose much more in that case
(they exactly lose a share 1-I).
Welfare evaluation of the political equilibrium
A final stage of the analysis is to wonder whether the introduction of a non
earmarked tax (when A is positive) is increasing the social welfare in comparison with
the status quo.
23
In the case where Ωq(q) is positive, the answer is straightforward. When A>0,
then G < I. Given (5), (12) and (14), it implies:
qˆ > RS > RS*
and thus
W( qˆ ) < W(RS) < W(RS*)
This is a classical argument: the existence of tax revenue to redistribute is an
additional motive for rent seeking. It thus rises the political distortions in comparison
with a policy approach like a regulation entailing no financial transfer among agents.
When the Laffer curve is downward sloping, the result is ambiguous. Simple
manipulations of (14) yields:
Bq (qˆ ) 
1  g 2 ( GI   I G )
Ag 2
ˆ
C
(
q
)

Cqq (qˆ )(Q ˆq )
q
1  g 2 I
1 g 2  I
As 1+g2(GI +IG) < 1+g2I and as the second term is strictly negative,
the comparison with (5) and (12) yields
RS > RS* > qˆ
As qˆ lies below RS*, the impact on welfare is ambiguous. If qˆ is very close to
the optimal level RS*, the introduction is welfare improving since qˆ is much closer to
the efficient level that the status quo level RS. But if the Laffer curve is very steep, qˆ
can fall very far from the efficient level so that W( qˆ )< W(RS). Intuitively, this
ambiguity can be explained in the following way. The greens pursue two objectives:
rising revenue and reducing pollution. When the Laffer curve is downward sloping,
these objectives are contradictory. If well-balanced, this contradiction can mitigate
political distortions so that the introduction of a non earmarked tax is welfare
improving.
5. The regulation is imperfectly enforced
We now consider that the regulation is poorly enforced. More specifically we
assume that R = F - C(R) is strictly negative. Hence, in the absence of tax or subsidy,
24
the polluter’s response is non-compliance. The major consequence is that status quo
now entails no pollution abatement even though the status quo regulation RS remains
the same. The room for policy change is thus larger than in the previous case.
The polluter’s reaction function
In the case the regulatory constraint is not binding (that is if t > tR ), the
polluter’s response remains the same as in the perfect enforcement case since it is fully
determined by the fiscal scheme. But the fact that t < tR alters the picture. When the
regulation was perfectly enforced, the polluter abated until R and the fiscal scheme had
absolutely no impact on the polluter’s behavior. But we will see that the fiscal scheme
may now affect regulatory compliance decision when enforcement is imperfect even
when tax rate is inferior to the regulatory shadow cost. This is demonstrated below to
be true if and only if tax revenues are earmarked ( = 1).
If  = 0
Compliance with the regulation depends on the sign of:
 (t, R, q) = C(q) - C(R) + t (R -q) + F
subject to:
Cq(q) = t
We have a first lemma.
Lemma 1.
When the tax is not earmarked ( = 0), if t < tR0 , then  < 0
Proof.
see appendix 3.
Lemma 1 establishes that non earmarked tax does not have any impact on
regulatory compliance when the tax rate is below the regulation shadow price tR0 .
If  = 1
Compliance occurs if:
 (t, R) = (1-s)[C(q) - C(R)] + t (R-q) + F > 0
subject to the earmarking constraint and Cq(q) = t /(1-s).  (t, R) = 0 determines a
particular value for t denoted tE. This leads to the second useful lemma:
25
Lemma 2. When the tax is earmarked ( = 1), /t is strictly positive. Moreover if
t < tR1, then 0 < tE < tR1
Proof.
See appendix 3.
Lemma 2 is crucial. It establishes that the earmarked tax may promote
compliance at tax rate below the regulation shadow price. More specifically, if tE < t
< tR1, the polluter complies. Hence q = R. If t < tE, the polluter does not comply and
sets his abatement level under the sole influence of the charge and subsidy scheme. We
thus have Cq(q )= t /(1-s).
In the end, the polluter’s behavior is depicted in the figure 2. and summarized by
proposition 3. In the following, we note q = q* 0 (t, , R) the corresponding reaction
function.
Proposition 3.
When the regulation is imperfectly enforced, the polluter sets its level of
pollution abatement q as follows:
If the tax is not earmarked ( = 0), Cq(q) = t. That is the abatement level is only
determined by the tax. The regulation plays no role.
If the tax is earmarked ( = 1), the polluter's reaction function becomes
discontinuous. More specifically:
 When t  [tE, tR1], the environmental outcome is only determined by the
tax and subsidy scheme and the environmental outcome is given by the
polluter’s reaction function qf(t, ). The regulation has thus no impact on the
polluter.
 When t  [tE, tR1], the regulatory constraint is binding and t is
sufficiently high so that >0. The polluter’s best response is to comply with the
regulation and the environmental outcome is R. In this intermediate interval,
the charge and subsidy scheme thus has a role of enforcement incentive in
that it leads to regulatory compliance.
26
Figure 3: The polluter’s response to the policy mix when enforcement is imperfect
Pollution
abatement
=1
=0
R
t
R
R
t 1
t
R
t 0
Characterization of the political equilibrium
As usual, both candidates converge to announce a policy vector which is the
solution of the optimization problem:
Max U(h) = Max H° + [+(g)2I] B(q)
– [+(g)2G] C(q) + (1-)(g)2A Ω(q, t)
subject to
q = q* 0 (h)
s C(q) =  t(Q-q)
U(h) > 0
(15)
In comparison with the perfect enforcement case, the sole differences lie in the
status quo constraint and in the polluter's reaction function. Again we start by solving
separately two optimization problems for each value of . Then, we will compare the
27
two solutions in order to identify the equilibrium which brings the highest political
support.
If  = 0
The solution is straightforward since the problem becomes:
subject to
Max H° + [+(g)2I] B(q) – [+(g)2G] C(q)] + (g)2A (q, t)
Cq(q) = t
U(h) > 0
The condition for an interior maximum is thus identical to (14):
[1+g2I] Bq(q) = [1+g2G] Cq(q) - g2A q(q)
(15)
If  = 1
The maximization problem is:
H° + [+(g)2I] B(q) – [+(g)2G] C(q)
subject to
q = q* 0 (h)
s C(q) =  t(Q-q)
U(h) > 0
As only the variable q enters in the political support function, the earmarking
constraint is not binding and the solution is given by:
[1+g2I] Bq(q) = [1+g2G] Cq(q)
(16)
(16) is identical to the condition defining the status quo regulation (12) ; hence q = R S
and tE < t < tR1.
28
A view on (15), (16), and the considerations already developed to demonstrate
proposition 2. then yields the following proposition which is together with proposition
2. the central result of the paper:
Proposition 4.
1)
If A < 0, the equilibrium policy vector h˜ is an earmarked tax which
complements the regulation. More specifically h˜ is given by:
tE < ˜t < tR1
˜ = 1
R˜ = RS
In this case, the tax rate is thus lower than the regulation shadow price.
2)
If A > 0, the equilibrium policy vector h˜ is a non-earmarked tax combined with
a regulation given by:
˜t = Cq( q˜ )
˜ = 0
R˜ < q˜
[1+g2I] Bq( q˜ ) = [1+g2G] Cq( q˜ ) - g2A q( q˜ )
In this latter case, the abatement level will be higher (lower) than the status quo
level RS if the Laffer curve is upward (downward) sloping. The tax rate is higher than
the regulation shadow price.
Proposition 4. and proposition 2. (the perfect enforcement case) only differs
when A is negative. In this case (when the green lobby is not very powerful), the
analysis predicts the generic form of environmental tax encountered in reality, that is
an earmarked tax combined with the regulation and which tax rate remains below the
shadow price of the regulation. This leads the policy mix to the pollution abatement
level that will be obtained under a fully enforced regulation. The intuition is that when
29
enforcement is imperfect, the greens are in favor of a non earmarked tax since it
permits to improve regulatory compliance and thus abatement level. Nevertheless,
since A is negative, they are not sufficiently strong to push abatement above the status
quo regulation. As a result, the tax rate remains below the regulation shadow price.
In the previous section, looking carefully at coefficient A, we have argued
intuitively how small was the room for the introduction of a non earmarked tax.
Conversely, the same reasoning applies here to claim that the room for the introduction
of an earmarked is very large. In particular, a non earmarked tax is introduced when
the two lobbies are equally powerful (G = I ).
Welfare evaluation of the political equilibrium
We need only to consider the case where A<0 since the other case has already
been analyzed in the previous section. Does the introduction of an earmarked tax
improve welfare in comparison with the status quo? As in the status quo, q = 0, the
answer is immediately positive.
6.
Discussion of the results
To summarize, the model predicts three possible policy outcomes:
The introduction of a non-earmarked tax in combination with a regulation at a tax
rate above the regulation shadow price
This happens when coefficient A = GI-(1-I)G is positive. This coefficient
basically reflects the relative green lobby's strength in comparison with the industrial
lobby: I and G are the share in the whole population of pro-industrial and green
voters, respectively whereas I and G reflects the ability of the industrial and green
lobbies to collect campaign contributions.
The intuition of the result is the following. When A is positive, the greens are
politically very influential and are able to foster their first best policy option: a non
earmarked tax. The greens benefit from non earmarking since they get a share of the
tax revenues redistributed to the whole population.
30
The benefit in terms of redistribution of tax revenues also explain why tax rate
is above the regulation shadow price: it allows for maximizing tax revenue for a given
level of pollution abatement.
The status quo, that is no tax is introduced
This happens when the status quo regulation is perfectly enforcement and when
A is negative (that is the relative green lobby's strength in comparison with the
industrial lobby is below a certain threshold). The threshold is quite high. For instance,
in the particular case where the two lobbies face identical contribution cost functions
(I = G), A is negative whatever the share of green and pro-industrial voters in the
population.
In this case, the greens are simply not sufficiently influential to impose the
industrialists a non earmarked tax, also because the status quo position is relatively
satisfying for the greens: the enforcement being perfect, the polluter abates at the level
of the status quo emission standard
The introduction of an earmarked tax in combination with the status quo regulation
at a tax rate below the regulation shadow price
This happens when the greens are not very influential (A is negative) and when
the status quo regulation is imperfectly enforced, so that the status quo abatement level
is zero. In this configuration, the loss for the greens in the status quo position is
sufficiently large (no pollution abatement) to compensate their relative weakness vis-àvis the pro-industrialists. They are thus able to obtain a policy change.
Why then an earmarked tax? This design presents an advantage for both sides.
In the industrialist view, earmarking obviously implies that the polluter gets back his
tax payment in the form of cost subsidy. The gain for the greens is more subtle: cost
subsidies financed by the tax allow for reducing the cost of compliance with the status
quo regulation. Earmarking thus helps to rise the incentive for the polluter to comply
with the regulation and subsequently leads to additional pollution abatement. This
peculiar impact of the tax on regulatory compliance exists even when the tax rate is
below the regulation shadow price. To sum up, a tax is simply introduced to promote
compliance with the status quo regulation.
These predictions seem in line with what is observed in reality. In actual
environmental policies, the status quo prevails (the use of regulation). Furthermore,
31
when taxes are introduced, we have already mentioned that earmarking prevails and
that tax rates are generally below the incentive level, that is the regulation shadow
price. Our analysis suggests that this is explained by the willingness to promote
compliance with existing regulation.
Another factual evidence supporting our analysis is the particular case of taxes
envisaged to cope with energy efficiency and GHG emissions in the frame of climate
change policies. It is well-known that, in this realm, taxes face severe political
difficulties which frequently prevent their introduction. But one apparent paradox is
that when the political forces allows for their introduction (like in Germany, the United
Kingdom, Belgium or many Scandinavian countries), this is a non earmarked design
which is selected . Why the less politically damaging earmarking option is not chosen?
Our analysis suggests one explanation. In the case of GHG emissions and energy
efficiency, there is no regulation in force. We are thus in a situation where there is no
necessity of promoting regulatory compliance.
To conclude, it worth mentioning that a non earmarked tax at a rate above the
regulation is the more efficient policy solution among the three possible political
outcomes according to the "normative" environmental economics point of view. This
solution avoids the drawbacks frequently attached to earmarking (lack of flexibility,
the risk for competition distortion on international markets, etc.). It leads the tax to
determine the abatement level across polluters with all the advantages attached in
terms of incentives to innovate and pollution abatement cost savings. Finally, it
confines regulation in a role of "safety net" ensuring everywhere a minimal level of
pollution abatement which can be very useful to avoid "hot spots", that is accumulation
of pollution in certain locations. Our analysis is rather pessimistic as regards the
possibility to implement this efficient solution.
References
Bernheim, B.D, Whinston M.D. (1986) "Menu auctions, resource allocation, and
economic influence", Quarterly Journal of Economics, 101, pp 1-31
Brett C., Keen M. (2000) “Political uncertainty and the earmarking of environmental
taxes”, Journal of Public Economics, 75(3), pp 315-40
32
Baron D. (1994) "Electoral competition with informed and uniformed voters",
American Political Science Review, 88, pp 33-47
Buchanan J.M. (1963) "The economics of earmarked taxes" Journal of Political
Economy, 71(5), pp 457-69
Buchanan J.M., Tullock, G. (1976) "Polluters' profits and political response: direct
control versus taxes", American Economic Review, 65(1), pp. 139-47
Djikstraa B. (1999) The Political Economy of Environmental Policy, chapter 2, pp 931, Edward Elgar Publisher
European Environmental Agency (1997) Environmental Taxes. Implementation and
Environmental Issues, Environmental Issues Series No. 1, Copenhagen, 63 p
Fredriksson P. G. (1997) "The political economy of pollution taxes in a small open
economy", Journal of Environmental Economics and Management, 33(1), pp 44-58
Goetz C.J. (1965) "Earmarked taxes and majority rule budgetary processes", American
Economic Review, 58(1), pp 128-36
Grossman G.M., Helpman E. (1994) "Protection for sale", American Economic
Review, 84(4), pp 833-50
Hahn R.W. (1989) A Primer on Environmental Policy Design, Fundamentals of Pure
and Applied Economics, Harwood Academic Publishers.
Hahn R.W. (1991) "Economic prescriptions for environmental problems: how the
patient followed the doctor's orders", Journal of Economic Perspectives, 3(2), pp 95114
Hansen L.G. (1999) "Is there a weak double dividend? Some implications of regulatory
capture and revenue rules for environmental taxes", working paper, AKF, Institute for
Local Government Studies, Denmark
Persson T., Tabellini G. (2000) Political Economics: Explaining Economic Policy,
MIT Press, 533 p.
OECD (1995) Ecotaxes in OECD Countries, Paris, OECD
33
Appendix 1
We will show that
Cq (q) = t /(1-s)
(A.1)
s C(q) =  t(Q-q)
(A.2)
implies that q is strictly increasing in t.
It is straightforward if  = 0. It implies that Cq(q) = t and thus that t/q > 0 since
Cq>0. When  = 1, combining (A.1) and (A.2) yields
t
Hence
Cq (q)C(q)
C(q)  (Q  q)Cq (q)
if C(q) + (Q - q)Cq(q)  0,
2
2
2
2
t C(q) C' (q)  (Q  q).C(q)Cq (q)  Cqq (q)C(q)

?
?2
q
C(q)  (Q q)Cq (q)
(A.3)
(A.4)
that is strictly positive because Q>q, and that C, Cq and Cqq are strictly
positive for any q. If C(q) + (Q - q)Cq(q) = 0, q is necessarily equal to 0.
Appendix 2
The problem is to study the marginal properties of  (q, t) = t (Q-q) with
q = q* 0 (t, R). The analytical problem lies in the fact that q* 0 is kinked in q = R. In
order to solve it, one can separately treat the two cases q > R and q < R.
If q > R, then t = Cq(q). The tax revenue function can thus be written
 (q, t) = Cq(q)(Q-q) and  (q, t)/q = Cqq(q)(Q-q) – Cq(q). Depending on how much
“convex” is the cost function,  /q will be either positive or negative. This is the
classical story depicted by the Laffer curve. But it is clear that if  /q (RS) 0,
deviating upward or downward from RS is increasing political support. The equilibrium
thus involves a policy vector hˆ given by:
34
ˆ  = 0
ˆt = Cq(q)
[+(g)2/G] Bq(q) = [+(g)2/I] Cq(q) + A(g)2 Ωq(q)
ˆ<q
R
The latter condition yields an infinity of equilibrium because. However a very simple
ˆ = 0. As the regulation plays no role in the
refinement of the equilibrium suggest that R
ˆ = 0, q and ˆt remain unchanged, the regulation is useless. Assuming nonsense if R
zero administrative costs, it is worthwhile not to keep the regulation in place. Thus
ˆ = 0.
R
If q = R, then t < tR0 . The partial derivative of  with respect to t is /t = Q - R
which is strictly positive; hence the tax rate maximising revenue is given by the corner
solution t = tR0 . It follows that  (q, t) can be rewritten  (q, t) = Cq(q)(Q-q) as
q = R. It is the same function as in the first case. It thus leads to the same equilibrium.
Appendix 3
Proof of lemma 1.
It is easy to show that t (t, R)<0. Indeed, we have  (t, R) = C(q*)-C(R) + Cq(q*)[Rq*] + F. The partial derivative of this expression with respect to q* is
q*(q*, R)/q* = -q*Cqq(q*) which is strictly negative. This implies that t(t, R) <0
since q* strictly increases in t. When t = 0,  (t, R) = F – C(R) which is strictly
negative by assumption. It follows that  (t, R) > 0,  t > 0 and R > 0
Proof of lemma 2
We have
subject to
and
 (t, R) = (1-s)[C(q*)-C(R)] + t(R-q*) + F
s C(q) = t(Q-q)
q = q* 0 (t, 1, R)
When t = tR1, R = q*(t) and hence  = F>0. Moreover, when t = 0, s = 0 and  = FC(R) which is strictly negative. Moreover, t is strictly positive. In effect, plugging (1)
in  yields  (t, R) = C(q*) - C(R) + F which is strictly increasing in t. Hence 0 < tE <
tR1.