THE SENT OF AVOIDANCE:The impact of endogenous fiscal

avoidance on environmental taxation

Masha Chistyakova∗, Philippe Mahenc†

LAMETA, Montpellier I UniversityAvenue Raymond Dugrand, Site de Richter, 34960 Montpellier

May 25, 2014

Abstract

A sound environmental regulation depends on the regulator’s abilityto redistribute revenues from environmental taxation to the public. Thecapacity of a firm to resort to tax optimization may undermine the trans-fer. To address this issue, we examine how endogenizing fiscal avoidancemay affect optimal environmental taxation. We find that the optimal reg-ulation serves simultaneously to internalize environmental damage, offsetmonopoly distortion, fine-tune the tax base and correct for the negativeexternality of tax avoidance. The threat of avoidance constraints the reg-ulator from interference. He keeps the tax at zero until the environmentaldamage outweighs the loss from imperfect transfer. Thereafter he antic-ipates an almost full avoidance, sets a tax strictly higher than otherwiseand lets consumers carry the full burden of environmental policy.

Keywords: Emission Taxation, Environmental Quality, Fiscal Avoid-ance, Regulation, Monopoly

JEL Code: D43, D82, H23, L12, Q28

∗Corresponding author: chistyakova@lameta.univ-montp1.fr†The authors are members of the LabEx Entrepreneurship, Montpellier, France. This

“Laboratory of Excellence” is part of a French government fund recognizing and promotingperforming research initiatives in human and natural sciences.

1

1 Introduction

Tax noncompliance has perversive effects on economy. The distinction betweentax avoidance and tax evasion implies that while the evasion involves taking riskfor an illegal activity, the avoidance doesn’t have legal consequences and thusrequires a different analytical approach. Here we develop a model to explorethe effect of tax avoidance on environmental regulation. To our knowledge, theavoidance framework hasn’t been yet formalized. Following Sandmo (2005),we imply by fiscal avoidance legal activities that use holes in the legal rule tooptimize fiscal obligation. Avoidance is "a matter of creative compliance" (?))that may take form of relocating profits to shell companies, manipulating ofcorporate profit to reduce the amount of paid taxes, rearranged in such a waythat resulting tax treatment differs from that intended by legislation etc.Although the impact of avoidance on environmental taxation has been largely

overseen, the examples are numerous when a large corporation susceptible ofnoncompliance exert an activity associated with negative externalities.Boges Limited is running a recently built Boguchany Hydro-power plant

in Far Eastern Krasnoyarsk region, Russia. The firm is registered in Nicosia,Cyprus (Baranova (2013)). Although the exploitation of the power plant is asso-ciated with environmental pollution and degradation of local ecosystem (Jagusand Rzetala (2013)), Boges Ltd. pays zero taxes.The distinction of our analysis is that we abstract from the assumptions of

zero tax elasticity and of a constant tax base. Our model unifies two standsof the literature: of tax compliance and of regulation of pollution. The extentof corporate noncompliance is estimated to average at 17%, whereas figuresfluctuate between 14 and 29%, depending on the firm size (Slemrod (2007)).The strength of our approach is that we use a single regulatory instrument

to internalize pollution, raise revenues and correct monopoly underproduction.The distinction between tax on profit and tax on polluting emissions is redun-dant in our setting because profit tax may escape regulation by avoiding taxes,while emission tax can be escaped by relocating a polluting activity to anothercountry, which is seen usually as politically undesirable and thus as a crediblethreat.We seek to understand how endogenizing fiscal avoidance would affect the

level of the optimal taxation. How the anticipation of the outflow of tax yieldsalter the environmental policy. Is Pareto improvement still feasible? How thetax burden is divided between the consumers and a polluting monopolist?The remainder of the articles is organized as follows. In Section 2 we set up

the formal model. In Section 3 we introduce endogenous avoidance. The resultsare presented in Section 4. Section 5 concludes.

1.1 Literature overview

The formal model of limited jurisdiction was proposed by Baron (1985), whichimplies that the regulator may be limited to impose his power only to a part ofhis jurisdiction. The same notion was developed by Laffont and Tirole (1991),

2

Boyer and Laffont (1999) that states that each unit of fiscal revenue has a socialcost known as a shadow price of public funds. As government transfers are notfully effi cient, they impose an organizational cost.We depart from the Pigouvian principal that requires, in the framework of a

pure competition, to equalize the private marginal cost of a polluting producerto the social marginal cost, i.e. internalizing the environmental damage intothe polluter’s cost, what the rent-seeking polluter would have neglected in theprivate optimization.Incited by critique of the reciprocity of externalities and the evaluation of

costs, Baumol (1972) restates the major principal of Pigou for a purely com-petitive market, emphasizing that the optimal price for externality-generatingproduct is equal the level of its entire social marginal cost.Further,Buchanan (1969) demonstrates that in an imperfectly competitive

market the Pigouvian principal seizes to ensure the optimality. On the exampleof a monopolistic firm the author shows that the optimal environmental tax mustbe set below Pigouvian level to offset the underproduction induced by monopolypower. The idea is further extended by Barnett (1980) who shows that theextent of the price decrease below Pigouvian level (below social marginal cost)in a monopoly depends on the price elasticity of the pollution emitting product,whereas the extent of the price fall increases with a less elastic demand.Another strand of optimal regulation of an imperfect market is marked by

Lee (1975), in his article he showed that with different degrees of market powerbetween polluters a uniform pollution tax achieves the lease cost abatement.A different development takes the work of Baron (1985) exploring the regu-

lation of pollution under incomplete information. We mainly built on his model,describing in the same manner the social welfare function where the regulatorassigns unequal weights on the producer and consumer surpluses. The dis-tinction of our work is that we abstract from information asymmetry, supposeenvironmentally conscious consumers (who to some extent internalize environ-mental damage by their disutility of pollution) and allow for endogenous fiscalavoidance.The standard literature on noncompliance analyzes tax evasion in the context

of contractual relationship between the principal and the agent, shareholdersand the manager, determining the incentive to evade (Chen and Chu (2005)).The contract is incomplete to motivate a risk-averse agent to participate inrisky activity of tax evasion to boost profits. The compensation scheme of thecontract. Crocker and Slemrod (2005) explore the optimal penalty: penaltieson managers are more effi cient than on shareholder.

2 The model

A monopolist produces a polluting good in quantity q that generates the amount(1− e) q of polluting emissions, where e ∈ [0, 1] is a parameter for pollutionabatement (for instance, 1 − e is the release of pollutants such as NOx, CO,SO2, per unit of output). If abatement is maximal, emissions are thus zero. If

3

no abatement is undertaken, emissions are equal to output. The overall marginalcost of producing the good is c(e), with c′(e) > 0, meaning that more resourcesdevoted to abatement raise the overall cost of production. Let d(q, e) denote theenvironmental damage function, which is assumed to be strictly proportional tothe amount of polluting emissions: d(q, e) = δ (1− e) q, where δ > 0 measuresdegradation of the environment per unit of polluting emissions.The total number of consumers is normalized to unity. Each consumer pur-

chases at most one unit of the good, which thus indirectly generates the amount1 − e of polluting emissions via consumption. Consumers receive zero surplusfrom consuming outside goods. The good provides all consumers with the samegross surplus v. Consumers differ in their tastes for the good due to their dislikeof pollution. For a given consumer X, the dislike of pollution is measured by themonetary loss (1−e)X, which, besides psychic discomfort, may represent healthcare expenditure and all the adaptation costs to the polluted environment. Theparameter X is uniformly distributed along a segment of unit length. Hence,consumers distinct from 0 partly internalize the polluting externality, and if Xhappens to be equal to δ, the externality is fully internalized for the purchasedunit of the good. Another interpretation is that taste heterogeneity reflectsvarious degrees of social environmental conscience among consumers. If, forinstance, the good is fossil energy, consumers may differ in the aversion to thenegative impact on global warming, and if it is nuclear energy, they may differin their dislike of the potential risks imposed on future generations by nuclearrepositories.Consumer X derives a surplus v − (1 − e)X − p from purchasing the good

at price p. This generates a demand function characterized by D(p, e) = v−p1−e .

Unregulated behavior of the monopolist.– The monopoly profit is πe(p) =(p− c(e))D(p, e) and the first-order condition is given by:

(p− c(e))∂D(p, e)

∂p+D(p, e) = 0 (1)

One can easily check that second-order conditions are satisfied. Let εe(p) =

−∂D(p,e)∂pp

D(p,e) = 11−e

pD(p,e) denote the price elasticity of demand for the good.

We further denote by p̂e the price set by the monopolist. First-order conditionscan be rewritten in the usual way to show that the Lerner index is equal to theinverse of the price elasticity of demand, which implies that market power is adecreasing function of the price elasticity of demand:

p̂e − c(e)p̂e

=1

ε(p̂e)(2)

where ε(p̂e) = p̂ev−p̂e . Substituting this expression in the right-hand side of

(2), we obtain p̂e − c(e) = v − p̂e. Under full information, the monopolist earnsthe profit π̂e with the price p̂e, namely:

p̂e =v + c(e)

2and π̂e =

(v − c(e))24(1− e) (3)

4

Socially optimal allocation of the good.– The welfare standard is the conven-tional one of gross benefits to consumers less production and pollution costs.The welfare function is

W (X) =

X∫0

[v − c(e)− (1− e)x]dx− δ(1− e)X (4)

= [v − c(e)− δ(1− e)X − (1− e)X2

2

The expression δ(1−e)X is the actual environmental damage, while (1−e)X2

2represents the monetary equivalent of consumer dislike of pollution.The optimality condition of (4) is

∂W

∂X= [v − c(e)− (1− e)X]− δ(1− e) (5)

where the term in the square brackets stands for net social value of the goodless privately perceived environmental damage, and the second term, δ(1 − e),represents an objective, scientifically determined environmental damage associ-ated with the production.At the socially optimal solution, the marginal consumer X∗ solves equation

v − (1 − e)X∗ = c(e) + δ(1 − e) so that the marginal social value of the good(v−(1−e)X∗) must exactly offset the total social marginal cost (c(e)+δ(1−e))Thus from the social standpoint, the market size should be:

X∗ =v − c(e)

1− e − δ (6)

We will restrict the parameters of the model to satisfy the following assump-tion in order to ensure that the good is socially desirable:

δ ≤ v − c(e)1− e (7)

First-best regulation.– The first-best outcome implies an unconstrained andfull authority of the regulator on the entire jurisdiction. The regulator is en-dowed with the power to both establish a unit price pe for the output producedwith abatement e and to specify a tax τe on each unit of the polluting emissions.Production and sale of one unit of the polluting good generate τe (1− e)D (pe, e)in revenues for the regulator. Assuming that all tax proceedings are transferredto consumers, the regulator’s problem is to find a policy (p∗e, τ

∗e) that maximizes∫ D(·)

0

[v − pe − δ (1− e)− (1− e)x] dx+ τe (1− e)D (pe, e) + πe (pe, τe) (8)

subject to the individual rationality constraint : πe (pe, τe) = (pe − c(e) −τe (1− e))D (pe, e) ≥ 0.

5

For any given price pe, the regulator chooses the tax τe to make the indi-vidual rationality constraint binding. After substitution into (8), the first-ordercondition for welfare maximization yields

p∗e = c(e) + δ (1− e) (9)

τ∗e = δ (10)

With unconstrained and full authority on the entire jurisdiction, the regu-lator charges the Pigovian tax and sets the price equal to the sum of marginalproduction and environmental costs. Throughout the article, we will considerthat the regulator has not the authority to impose a price on the polluting firmwhich can therefore fully exploit its monopoly power. Building on Buchanan’s(1969) framework, the environmental tax will now be the only device availableto the regulator.

3 Endogenizing fiscal avoidance

As initially recognized by Baron (1985), one important restriction on the envi-ronmental regulator’s power is its limited jurisdiction over the polluters. Thisrestriction will take the form here of fiscal avoidance from the firm’s share-holders. Knowing this phenomenon, the regulator recognizes that part of thecorporate profit escapes its jurisdiction, which makes it diffi cult to fully refundtax proceedings to consumers. Hence, the regulator only takes into considera-tion the complying part of business in the welfare function. To endogenize fiscalavoidance, we let it depend on the level of tax. We suppose that shareholdersare heterogeneous in their ability to escape the tax. Although there is no ex-plicit market for tax optimization services, the banks propose their corporateand private clients services such as wealth management, that contain ‘recom-mendations’ to organize fiscal obligation in the most beneficial way (Gravelle(2013)). Alternatively, an internal department of the firm may specialize on taxissues screening for most favorable tax regime. The heterogeneity implies thata firm with an internal department has marginal costs of tax avoidance lowerthan a firm appealing to bank services.Suppose there is a continuum of shareholders whose cost of fiscal optimiza-

tion is uniformly distributed over the interval [0, 1]. For each unit of profit thata shareholder obtains, he has a specific cost of avoidance. Let a denote theshareholder’s cost of tax avoidance. Once the tax grows positive, some share-holders prefer to bypass the tax. For a zero tax and clearly in the case of asubsidy all the shareholders comply, i.e. to receive subsidy. Ultimately, whenthe tax exceeds the highest bound, everyone bypasses the regulation. To denotethe portion of business that comply we introduce β. Mathematically, we canrepresent this parameter as the ratio of firms conforming to the regulation:

β(τ) = 1− τ(1− e) (11)

Figure (1) illustrates the relation between the value of the tax and the extentof tax compliance. If a shareholder’s cost of avoidance a exceeds the tax, he

6

Avoidance

Compliance

Τ>a

1-e

Τ=a

1-e

Τ<a

1-e

1

1-e

tax Τ, cost of avoidancea

1-e0

1

Tax compliance, ΒHΤL

Figure 1: A positive tax implies an avoidance

complies with the regulation, otherwise he avoids. Note that there is a chainreaction: each marginal tax increase makes avoidance beneficial to marginaltaxpayers who switches to avoidance. Hence the tax base shrinks. This requiresthe regulator to further raise the tax rate to cover the loss in tax base. As thetax achieves 1

1−e no shareholder pays the tax. Therefore, the decision to paythe tax is bounded on the interval

0 < τ <1

1− e (12)

thereafter the perfect avoidance prevail.

3.1 The optimal environmental tax with fiscal avoidance

The regulator is a Stackelberg leader who commits to his policy. The sequenceof the game is the following: in the first stage, the regulator imposes the envi-ronmental tax per unit of emissions on the firm, and at the second stage, thefirm sets the price for the polluting good.Let pe(τ) denote the monopoly price under regulation. Then, for the monopoly

profit, πe(pe(τ)) = (pe(τ)− c(e)− τ(1− e))D(pe(τ), e), where pe(τ) must solvethe first-order condition for profit maximization of the monopolist:

(p− c(e)− τ(1− e))∂D(p, e)

∂p+D(p, e) = 0 (13)

This yields the following equilibrium price

pe(τ) =v + c(e) + τ(1− e)

2(14)

and the corresponding equilibrium profit

πe(pe(τ)) =(v − c(e)− τ(1− e))2

4(1− e) (15)

Rearranging the terms, equation (13) can be rewritten to express the Lernerindex

pe(τ)− c(e)pe(τ)

=τ(1− e)pe(τ)

+1

εe(pe(τ), e)(16)

7

The regulator employs the tax on the polluting good not only to internalizethe environmental externality but also to correct for the externality exerted onthe society by the monopoly behavior; the underlying intuition conforms to theresult of Buchanan (1969). Social welfare is W (τ)∫ D(pe,e)

0

[v − (1− e)x− δ(1− e)− pe (τ) + τ(1− e)]dx+ β (τ)πe(pe (τ) , e)

where the demand for the good is described by D (pe (τ) , e) = v−pe(τ)(1−e) . The

parameter β ∈ [0; 1] denotes the weight assigned to producer surplus, whereβ ≤ 1 because the regulator realizes that not all the shareholders’ profit isdeclared and taxed within the jurisdiction while all the consumers do. Takinginto account that a part of shareholders escape taxation, the regulator scalesdown the firm’s weight in the welfare function. Therefore, β is also a compliancefunction that is defined over three intervals: when tax takes the form of subsidy,there is no avoidance and thus the compliance is full For positive tax, someshareholders avoid tax obligation and finally, for the higher values of the tax,the entire profit in the economy bypasses the regulation.

β (τ) =

1 if τ ≤ 0,

1− τ(1− e) if 0 ≤ τ ≤ 1(1−e) ,

0 if 1(1−e) ≤ τ ≤

v−c(e)1−e

(17)

Using D (pe (τ) , e) = v−c(e)−τ(1−e)2(1−e) and πe(pe (τ) , e) = (1− e)D (pe (τ) , e)

2,we have

W (τ) = (1− e)[(

1

2+ β (τ)

)D (pe (τ) , e)

2+ (τ − δ)D (pe (τ) , e)

](18)

The first order condition of is

(τ − δ)(1− e)∂D(pe (τ) , e)

∂pe (τ)

dpe (τ)

dτ− dpe (τ)

dτD(pe (τ) , e) + (1− β(τ)) (19)

(1− e)D(pe(τ), e) +dβ(τ)

dτ[pe (τ)− c(e)− τ(1− e)]D(pe (τ) , e) = 0

Using ε (pe (τ) , e) = −∂D(pe(τ),e)∂pe(τ)pe(τ)

D(pe(τ),e), the expression reduces to

τ−δ+pe (τ)

(1− e)ε−(1−β(τ))pe (τ)dpe(τ)dτ ε

−dβdτ

(pe (τ)−c(e)−τ(1−e)) pe (τ)

(1− e)dpe(τ)dτ ε= 0

(20)Substituting 1−e

2 for dpe(τ)dτ

τ = δ +pe (τ)

ε

[−1

1− e +2 (1− β (τ))

1− e +2dβ

dτ

pe (τ)− c(e)− τ(1− e)(1− e)2

](21)

8

The tax consists of four components to correct four effects: to internalizeenvironmental damage and monopoly power, to fine tune the tax base and torise levies. Indeed, the first term in (21) is the damage rate, δ, so as originallyintended, environmental tax seeks to internalize the environmental damage atthe Pigovian level. The second term measures the extent of monopoly power.The overall distortions in tax are inversely related to the price elasticity ofdemand. Thus, the deviation from the Pigovian level is higher on marketswhere consumers are less sensitive to price changes.The optimal environmental tax departs from Pigovian level because of the

distortionary impact of monopoly pricing and fiscal avoidance. Within thebrackets the first term measures monopoly distortion. It must be negative asthe monopoly output at optimum is set below the socially optimal level. To mit-igate the monopoly distortion, the optimal tax must be set below Pigovian level(Buchanan (1969)). The remaining two terms represent tax avoidance. Whenthe regulator considers raising the tax, he has to take into account two effectsassociated with the failure in transferring tax revenue to consumers. When theregulator engages in the environmental policy, he commits himself to redistrib-ute the tax to consumers. Fiscal avoidance undermines this ability leading toa disturbance in tax transfer/ creating transfer imperfection. Hence, the firsteffect is the negative externality imposed by whose escaping the regulation onthe rest of the society. By not levying the tax from the all shareholders, theregulator lacks suffi cient resources for the redistributive transfer. To overcomethis externality, the regulator raises the tax up to the amount 2(1−β(τ))

1−e , whichcorresponds to the shortfall in tax yields caused by avoidance. The second ef-fect is the forgone revenue due to the reduction of the tax base. Every marginaltax increment makes fiscal avoidance attractive for a marginal shareholder forwhom τ → a

1−e . Every lost tax payer worsens the disturbance in transferringtax, thereby creating a welfare loss. The regulator scales down the tax by anamount that exactly offsets this welfare loss, i. e. 2dβdτ

pe(τ)−c(e)−τ(1−e)(1−e)2 .

Using (14) in (21) gives

τ = δ +v − c(e)− τ(1− e)

2

[−1

1− e +2 (1− β (τ))

1− e +dβ

dτ

v − c(e)− τ(1− e)(1− e)2

](22)

For each level of avoidance the optimal environmental regulation is conformto (22).

Lemma 1 The welfare maximizing tax schedule is

τe =

2δ − v−c(e)

1−e if τ ≤ 0,4(v−c(e))−1+

√4(v−c(e))2−20(v−c(e))+1+24δ(1−e)

6(1−e) if 0 < τ ≤ 1(1−e)

2δ3 + v−c(e)

3(1−e) if1

(1−e) < τ < v−c(e)1−e

(23)

When β = 1, the transfer between the firm and consumers doesn’t disturbwelfare. Consequently, the two last terms in (22) are both zero. The propositionprovides an explicit measure of optimal tax. Given the assumption (7), it is

9

straightforward that τe < δ if τ < 0. The Pigovian rule that requires to chargea tax equal to marginal damage cannot be applied here because of monopolisticbehavior. As established by Buchanan (1969).in the presence of market power,the tax should be optimally set below the marginal damage. Henceforth werefer to this tax level as a Buchanan tax, which serves the main reference forthe analysis.As β = 0, every shareholder bypass regulation. The transfer entails a loss in

welfare of producer surplus. It is easy to see that τe > δ when τ > 11−e . The

failure in tax transfer is at its height, the consumers bear the whole burden offiscal avoidance.

Forms of welfare To characterize the forms of welfare we apply (17) to (18).This results in a function defined over three intervals of compliance. Whensubsidy is optimal, the producers’profit has the same weight for β = 1. For apositive tax, a partial avoidance followed by a perfect avoidance prevail, whenwelfare consists solely of consumer surplus and the environmental damage,W (τ)

(1− e)

[3D(pe(τ),e)

2

2 + (τ − δ)D (pe (τ) , e)]if τ ≤ 0,

(1− e)[(

32 − τ(1− e)

)D (pe (τ) , e)

2+ (τ − δ)D (pe (τ) , e)

]if 0 < τ ≤ 1

(1−e)

(1− e)[D(pe(τ),e)

2

2 + (τ − δ)D (pe (τ) , e)]if 1(1−e) < τ < v−c(e)

1−e(24)

Figure (2) displays the four maxima that may prevail in the market. De-pending on the relation between social value of the good and its environmentalimpact, the welfare optimum make call for a subsidy, a zero tax, a partial taxor a full tax.First, note that the welfare function may have several local optima. The

ultimate result of optimization/global maximum depends on the relation be-tween social value and environmental damage. The solution follows in the nextsubsection.Second, note that when τ = 0, a slight increase in τ entails a fall in welfare.

The welfare function is non-differentiable at τ = 0, the slope of the functionturns from positive to negative. This happens because once tax avoidance beginsthe in tax base inflicts a greater loss then the revenues that the tax raises,because the effect of shrinking tax base dominates the tax yields. The tax mustbe fairly high to balance both effects. This explains a upward jump of τ withrespect to δAs it has been noted before, the optimal regulation depends on combinations

of social value and environmental damage. It follows from (24) that withoutavoidance welfare

Wn(τ) = (1− e)[3D (pe (τ) , e)

2/2 + (τ − δ)D (pe (τ) , e)

](25)

reaches a maximum at τn = 2δ − v−c(e)1−e and Wn(τn) = (v−c(e)−δ(1−e))2

2(1−e) . The

10

1

1-e

m

1-e

Τ

Welfare, WHΤLSubsidy

1

1-e

m

1-e

Τ

Welfare, WHΤLZero tax

1

1-e

m

1-e

Τ

Welfare, WHΤLPartial tax

1

1-e

m

1-e

Τ

Welfare, WHΤLMaximal tax

Figure 2: Possible curves of welfare

partial avoidance entails

Wp(τ) = (1− e)[(3/2− τ(1− e))D (pe (τ) , e)

2+ (τ − δ)D (pe (τ) , e)

](26)

with a minimum τ1 =4(v−c(e))−1−

√4(v−c(e))2−20(v−c(e))+1+24δ(1−e)

6(1−e) and a max-

imum at τ2 =4(v−c(e))−1+

√4(v−c(e))2−20(v−c(e))+1+24δ(1−e)

6(1−e) provided that the

discriminant ∆p = 4 (v − c(e))2 − 20 (v − c(e)) + 1 + 24δ(1− e) > 0; otherwise,Wp(τ) is a decreasing function of τ . With perfect avoidance welfare

Wf (τ) = (1− e)[D (pe (τ) , e)

2/2 + (τ − δ)D (pe (τ) , e)

](27)

reaches a maximum at τf = 23δ + v−c(e)

3(1−e) and Wf (τf ) = (v−c(e)−δ(1−e))26(1−e) .

Proposition 2 In Region I, the optimal tax is τe = τn.

In Region I of Figure (3), the environmental damage is so low relative to thesocial value of the good that the regulator is mainly concerned by correcting themonopolist’s tendency to under-produce. For this, the regulator must subsidizethe good, hence tax avoidance is not an issue.

11

Proposition 3 In Region II, the optimal tax is τe = 0.

In Region II of the Figure (3), the environmental issue is suffi ciently seriousfor the regulator to set a positive tax in absence of tax avoidance. However, thetrade-off between the loss of fiscal base and the disturbed tax transfer constrainsthe regulator to withhold the regulation. He calculates that the remaining taxbase would not be enough to offset the disturbance, hence the optimal policy isto set zero tax.

Proposition 4 In Region III, the optimal tax is τe = τ2.

In Region III of Figure (3), the severity of environmental damage requirespositive taxation, thereby inducing shareholders with low costs of tax avoidanceto escape from regulation. Not all of the shareholders avoid taxation, but thosewho do exert a negative externality not only on those who don’t but also onconsumers since they pay the monopoly price augmented by taxation. Theregulator fine tunes the tax base so that the revenue raised from taxation isenough to outweigh this externality as well as the environmental externality.

Proposition 5 In Region IV, the optimal tax is τe = τf .

In Region IV of Figure (3), the environmental damage necessitate a heavytaxation. It is so severe that all shareholders escape it, leaving the whole bur-den of the tax on consumers through the price at which they purchase the good.As the tax base is reduced to zero, the regulator expects no fiscal revenue tocorrect for distortions. The whole correction relies on the monopoly price ma-nipulation through taxation. The regulator sets the tax to raise the monopolyprice up to the level at which consumers’purchase decisions fully internalize theenvironmental externality.

Proposition 6 The optimal tax is τe =

τn in Region I0 in Region IIτ2 in Region IIIτf in Region IV

Proof. for all the proofs see the Appendix

4 Results

Fiscal avoidance doesn’t affect the outcome if subsidy is socially optimal. Itis straightforward that a subsidy does not induce shareholders to manipulateprofits. Consequently, the planner can assign the same weight on consumers andproducer surpluses, the transfer from the firm to consumers is fully realized.But for every restrictive intervention, the regulation always diverges from

the Buchanan benchmark. The threat of avoidance constrains the regulator’sintervention. Each positive increment of a tax reduces the fiscal base making

12

I

II

III

IV

1

4

1

8

5 + 2 6

5

32

1

16

7 + 3 6

1

Social value, v-cHeL

Dam

age,

∆H1

-e

L

bisector

1

2Hv-cHeLL

1

6H5+ -H-3 + 2 Hv - c HeLLL3 L

1

2HHv-cHeLLH 6 -1LL

1

32H24Hv-cHeLL-1L

1

2Hv-cHeL+Hv-cHeLL2L

Maximal tax

Partial Tax

Zero tax

Subsidy

Figure 3: Tax regimes in relation to social value and damage

avoidance beneficial for a marginal shareholder, the regulator must addition-ally increase tax to offset the loss of taxpayers. Furthermore, once committedto environmental policy he must refund the tax to consumers. The shrinkingtax base creates imbalance between tax yields and tax transfer, the tax mustrise to cover the difference. This creates the chain reaction. For this reasonthe regulator is better off keeping the tax at zero and thus preserving his fiscaljurisdiction avoidance neutral. The regulator retains the status quo until envi-ronmental damage grows into a suffi ciently serious problem. When the damagefrom pollution outweighs the loss in tax transfer, the environmental regulationoccurs.At zero-tax environmental regulation is left to the market, the regulator

prefers market solution because an interference entails a costly trade offbetweenthe tax base and a tax rate. At laissez-faire, as the monopoly price takes intoaccount the consumers’disutility of pollution, it suffi ciently corrects the negativeexternality. As long as pollution is moderate and the disutility is internalizedinto production decision, the laissez-faire is an optimal solution.As the social cost of the environmental damage exceeds the loss from the

distorted transfer, the regulator undertakes a heavy taxation. Ultimately, theresulting price is above that of the regulation-free monopoly, which reducesoutput, and enforces the pollution control.Figure (4) illustrates the optimal regulation for each combination of prod-

uct’s social value and its environmental impact. The dashed line depicts theBuchanan tax, the reference of a regulated polluting monopoly in the absence

13

of fiscal avoidance. The bold curves plot the optimal tax regimes after fiscalavoidance has been endogenized.

v-c HeL2

v-cHeL

Tax, Τ

Low ð

v-c HeL2

v-cHeL

Tax, Τ

Intermediate ð

v-c HeL2

v-cHeLDamage, ∆H1-eL

Tax, Τ

Higher damage and higher social value

Subsidy

Buchanan tax

Tax under fiscal avoidance

Figure 4: The path of the optimal environmental tax

The three plots depicts low, intermediate and high levels of social value andenvironmental damage. Notably, the tax is continuous tax takes place only atvery low social values of the product

(v − c (e) < 1

4 and damage δ (1− e) < 532

).

The continuous tax implies that the planner can always successfully leverage be-tween the tax base and the tax rate, effectively covering the loss of the shrinkingtax base by increasing tax pressure on the complying shareholders. It is feasibleonly at low social values because even with no avoidance they generate a feeblewelfare that may be lower than the one with partial avoidance. As social valuerises, the planner cannot always cover the loss in fiscal base by a higher tax,which creates a discontinuity in the tax path.However, the general tendency is that the tax under avoidance must be

more severe than the Buchanan one. The opposite is true only at low social val-ues

(v − c (e) < 1

2 and damage δ (1− e) < 13

). The reason is that the regulator

has to choose the less evil when contemplating the environmental degradationagainst the trouble to collect and redistribute the tax. As social value increases,the trouble from the tax generates a greater social loss, that is why the regula-tor holds back the intervention. The hold-back creates the gap in the tax path.Once environmental damage becomes severe and of greater social loss than thetax, the planner hits the monopolist with a massive tax. The same logic appliesto the tax with perfect avoidance, that is strictly greater than the Buchanan

14

tax.Ultimately, for low and intermediate levels of environmental damage the

regulation under avoidance is milder than otherwise would have been. Theavoidance imposes the planner to tolerate the pollution. Besides, note thatthe zone of partial avoidance in which some shareholders comply is bounded.Starting from a certain social value, v−c(e) > 1, a partial avoidance tax is alwaysdominated by either zero or maximal tax implying the leveraging between thetax base and tax rate cease to suffi ciently contribute to welfare. Once thelevel of pollution requires the application of maximal tax, it crowds out theentire tax base. This means that the regulator first deliberately condone withmoderate pollution but then taxes heavily presuming the perfect avoidance. Themonopoly passes the tax further to consumers through the price and escapesthe regulation. The environmental policy is thus enforced entirely at the costof consumers.

5 Conclusion

In the previous sections we have explicitly demonstrated that the solution tothe problem of how to regulate the polluting monopolist capable to resort tofiscal optimization in the market with green consumers exist.The optimal tax consists of four conflicting components which push the

level of the tax in the opposite directions of the Buchanan benchmark. Theenvironmental policy serves four purposes. Firstly, the tax must internalizethe negative externality of pollution; secondly, it has to correct for monopolyunderproduction, which demands to reduce the level of the tax. Thirdly, itcorrects for imperfect transfer increasing the tax severity and finally, it balancesthe tax base lowering the tax.The figure (3) allow to graphically decompose the areas of optimal envi-

ronmental taxation as a function of good’s net social value, v − c(e), and theits environmental impact, δ. The range of optimal regulation spreads from asubsidy to a severe taxation.Note that the tax is capable of offsetting the four distortions (monopoly,

environment, tax base and transfer) is limited. As the tax bypasses a certainthreshold, it induces a full avoidance. Once it is at play the regulator no longeraffect the tax base and tax transfer. With full avoidance he may offset the envi-ronmental externality, while he completely looses the tax base, the tax transferis completely distorted (what is then with the transfer ? what is his value)and the price is distorted upwards from the monopoly level. The production iscurtailed by a passive tax (what are the emissions ?)Tax transfer, budgetTo understand the weakness of environmental regulation and to envisage

possible diffi culties in its implementation, we introduce in the present paperan endogenous avoidance, i.e. the ability of a strategic planner to anticipatethat the decision to escape regulation is endogenous and depends on the level ofthe tax. Accounting for this leads to two new considerations when choosing an

15

optimal environmental policy. Now, the regulator has to contemplate that aug-menting the tax, on the one hand, incites more capital to evade the regulation,which diminishes the tax base. On the other hand, the need for redistributionrequires the planner to tax harder the complying capital in order to fund thetransfer, thus to exerting negative externality of fiscal avoidance.We have shown that depending on the relation between the net social value

of the good and the cost of avoidance, the optimal environmental regulation varybroadly. The severity of regulation differ from a subsidy, to extreme taxationwith perfect avoidance and budgetary imbalance.

Figure 5: Zero taxes in the Annual Report 2012 of Boges Ltd.

Indeed, coming back to our initial example, the annual report shows thatBoges Ltd has paid no ‘current income tax’during the years from 2010 trough2012 (see line 7, figure 5).This may illustrate how a firm capable to bypass the taxation faces a zero

tax, which must embody an optimal solution when environmental damage hasn’tyet overweighted the loss in tax base...Being yet too early to appreciate dam’scontribution to the regional development, primary consequences have alreadybecome apparent. The indigenous population resettlement evoked disputes andcorruption with property, the uncut woods and uncovered peat floated to thesurface, littering the reservoir, fish perishes massively. The construction of thealuminum plant, which is assumed to become the major consumer of the damand one of the main employer in the region, has not yet been accomplished.With a scarce regional demand, the Bodes Ltd exports the kWh to China...

16

Limitations. Within the framework of partial analysis, we deliberatelyabstract away from the government budget constraint. It allows us to focuson the impact of fiscal avoidance and the consequences for the environmentalpolicy.

5.1 Appendix

Proof. to Lemma 1: Welfare with partial avoidance

Wp(τ) = (1− e)[(3/2− τ(1− e))D (pe (τ) , e)

2+ (τ − δ)D (pe (τ) , e)

](28)

has a minimum τ1 =4(v−c(e))−1−

√4(v−c(e))2−20(v−c(e))+1+24δ(1−e)

6(1−e) and a max-

imum at τ2 =4(v−c(e))−1+

√4(v−c(e))2−20(v−c(e))+1+24δ(1−e)

6(1−e) provided that the

discriminant ∆p = 4 (v − c(e))2 − 20 (v − c(e)) + 1 + 24δ(1− e) > 0; otherwise,Wp(τ) is a decreasing function of τ .Proof. to Proposition 2: If δ ≤ v−c(e)

2(1−e) (Region I in fig. (3)), then τn ≤ 0

and Wn(τn) > max {Wp(τ2),Wf (τf )}. The optimal tax is a subsidy τn =

2δ − v−c(e)1−e . Wn(τn) > Wp(τ2) is straightforward. Wn(τn) = Wf (τf ) if δ =

v−c(e)(1+v−c(e))2(1−e) or δ = 24(v−c(e))−1

32 . However, none of these lies within theregion. The welfare maximizing tax corresponds to that of Buchanan.

Proof. to Proposition 3: If δ ∈

v−c(e)2(1−e) ,

v−c(e)2+v−c(e)

2(1−e) , for v − c(e) ≤ 14

min{24(v−c(e))−132(1−e) , (

√6−1)(v−c(e))2(1−e)

}, otherwise

(Region II), then Wn(0) ≥ max {Wp(τ2),Wf (τf )}. If δ ≥ v−c(e)

2(1−e) , then Wn(τ)

is increasing at τ = 0, which makes it a local maximum. Wp (τ) is decreas-

ing if ∆p ≤ 0 all over the interval[0, 1

1−e

]. If ∆p > 0, Wp (τ) has two

roots, with the second, τ2, a local maximum. The equality Wp (τ) = Wn(0)

holds if δ = 24(v−c(e))−132 . Additionally, τ2 is restricted on 0 < τ2 ≤ 1

1−e ,as the partial avoidance begins with a positive tax and grows to a completeavoidance at 1

1−e . This is equivalent to δ ≤v−c(e)2+v−c(e)

2(1−e) for the values of

v − c (e) ≤ 14 to ensure a positive root. Further, δ ≤ (v−c(e))2−3(v−c(e))+4

2(1−e)must hold to control for τ2 ≤ 1

1−e . Finally, τf may be a local maximum, for

τf ≥ 11−e (i. e., for parameter values such that δ ≥ 3−(v−c(e))

2(1−e) ). Straight-forward calculations show, first, that Wn(0) ≥ Wf (τ2) for all parameter val-ues such that δ ≤ 24(v−c(e))−1

32(1−e) < v−c(e)1−e , and second, that Wn(0) ≥ Wf (τf )

for all parameter values such that δ ≤ (√6−1)(v−c(e))2(1−e) < v−c(e)

1−e . As a result,Wn(0) ≥ max {Wp(τ2),Wf (τf )} for parameter values inside Region II.

17

Proof. to Proposition 4: If δ ∈

(v−c(e)1−e ; v−c(e)+(v−c(e))

2

2(1−e)

], if v − c (e) ∈

(0; 14)(

v−c(e)1−e ; 24(v−c(e))−132(1−e)

], if v − c (e) ∈

[14 ; 5+2

√6

8

)(v−c(e)1−e ;

(v−c(e))(√6−1)

2(1−e)

], if v − c (e) ∈

[5+2√6

8 ;∞) (Region

III), then Wp(τ2) ≥ max {Wf (τf )),Wn(0)}. One can check that, for all parame-ter values inside Region III, the discriminant∆p > 0 because 4(v−c(e))

2−20(v−c(e))+124(1−e) <

24(v−c(e))−132(1−e) , and τ2 exists. As τ2 = 4(v−c(e))−1+

√·

6(1−e) may become negative only

as v − c (e) < 14 , the parameter δ is restricted only for v − c (e) ∈

(0; 14)by

δ > v−c(e)+(v−c(e))22(1−e) to have τ2 > 0. Once δ < (v−c(e))2−3(v−c(e))+4

2(1−e) , we have

τ2 <11−e . The welfare under full and partial avoidance are identical Wf (τf) =

Wp(τ2) if δ =

[ v−c(e)1−e

36(v−c(e))−1±√(1−6(v−c(e)))(1−6(v−c(e)))254(1−e)

As5+√(3−2(v−c(e)))(2(v−c(e))−3)2

6(1−e) ≤

(v−c(e))2−3(v−c(e))+42(1−e) for ∀δ and ∀ (v − c (e)), within the entire region of admis-

sible values of τ2, it holds that Wf (τf ) ≤ Wp(τ2), while δ must lie below5+√(3−2(v−c(e)))(2(v−c(e))−3)2

6(1−e) to ensure that τ2 induces a higher welfare than

τf . Note that τ = 0 can also be a local maximum over v−c(e)2(1−e) < δ < v−c(e)

1−e .Further calculations show that Wn(0) ≤ Wp(τ2) for all parameters satisfying

δ ∈

(

0, v−c(e)1−e

), for v − c (e) ∈

(0; 5−2

√6

2

][20(v−c(e))−4(v−c(e))2−1

24(1−e) ; v−c(e)1−e

)for v − c (e) ∈

(5−2√6

2 ; 14

][24(v−c(e))−132(1−e) ; v−c(e)1−e

)for v − c (e) ∈

(14 ;∞

]Proof. Proposition 5: If δ ∈

[max

{5+√(3−2(v−c(e)))(2(v−c(e))−3)2

6(1−e) ; (√6−1)(v−c(e))2(1−e)

}, v−c(e)1−e

](Region IV), then Wf (τf ) ≥ max {Wp(τ2),Wn(0)}. All δ > max

{5+√(3−2(v−c(e)))(2(v−c(e))−3)2

6(1−e) ; (√6−1)(v−c(e))2(1−e)

}is also greater than 3−(v−c(e))

2(1−e) , for which τf = 11−e and where its definition do-

main begins, implying that τf can be the local maximum. For the same para-meter configuration, one can check that when ∆p ≥ 0, τ2 could be a local max-

imum too, but it must satisfy τ2 < 11−e , amounting to δ <

(v−c(e))2−3(v−c(e))+42(1−e)

which is always below the aforementioned interval. Thus, within the regionwe have Wf (τf ) ≥ Wp(τ2). Further, suppose τ = 0 is a local maximum.

As δ ≥ max

{5+√(3−2(v−c(e)))(2(v−c(e))−3)2

6(1−e) , (√6−1)(v−c(e))2(1−e)

}is more restrictive

than δ ≥ v−c(e)2(1−e) , implying that Wn(τ) is increasing up to zero. Moreover,

δ ≥ (√6−1)(v−c(e))2(1−e) is equivalent to Wf (τf ) ≥ Wn(0). Hence, for all δ inside[

5+√(3−2(v−c(e)))(2(v−c(e))−3)2

6(1−e) , (√6−1)(v−c(e))2(1−e)

]τf is the local maximum.

18

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