Taste for diversity, pollution aversion and optimal choice of environmental quality 

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Discussion on the modelling choice of avoidance function

In the present version, we have chosen to model tax avoidance subsequent to an imposition of environmental taxation as an internal decision of the …rm which is exogenous to our analysis. There is no or little speci…cation for the mechanism that the avoidance decision may take. Indeed, di¤erent avoidance schemes may come to mind: it can be pro…t shifting, relocation of production facilities to jurisdictions with a laxer regulation; it can be green washing, or political lobbying against the regulation among others.
It is common knowledge that taxation in general gives rise to tax optimization and may entail non-compliance. Environmental taxation is certainly no exception. Asymmetric information being an inherent feature of environmental performance, in which quality is unobservable and hardly veri…able, renders the enforcement of environmental policy and its monitoring problematic. In this analysis, we have proposed the simplest way to frame the idea that higher tax rates give taxpayers greater incentives to avoid liability. Therefore we let the …rm be immediately responsive to the level of tax, adjust-ing accordingly her compliance levels. Hence the assumption that …rm’s shareholders are heterogenous in the cost of tax avoidance.
Certainly one may argue that dividends are paid on the after-tax pro…t, and sharehold-ers have little interest in or grasp of how to in‡uence a …rm’s compliance behavior. Yet, a …rm has a complex hierarchy for decision-making and …rm’s management is entrusted to executives who are generously rewarded to maintain high …nancial performance. Hence, we abstract from the mechanism of avoidance decision assuming it comes from a black box.
Ultimately, the incidents of successful global environmental policy are few. The EU emission trading system struggles to maintain a ‘meaningful’ carbon price that would re‡ect its social cost. Yet, it still varies around 7 e per ton6. During the past decade the allowances were in oversupply and nevertheless often allocated freely7. An attempt to introduce an eco-tax in France under the Grenelle law has turned out to be a complete failure. It has cost taxpayers the construction of the infrastructure that has never been in use, plus there are penalties for violation of contract terms to the …rm commissioned for the project.
Thus we believe that a …rm with market power and an international infrastructure such as a multinational can and will …nd ways to reduce its environmental liabilities. The micro foundation of avoidance decision is, however, beyond the scope of this paper and hence is left for a future research.

Asymmetric information

In this section we state the separating conditions and derive the equilibria under infor-mation asymmetry.
When consumers have an incomplete knowledge of the producer’s environmental type, the …rm’s strategy is to choose a price that allows consumers to correctly identify its type/ environmental quality. Denote 0 to indicate consumers’prior belief of high envi-ronmental quality. It embraces all the information about environmental quality publicly available to consumers. Then, the perceived quality, e;b is the expected probability that the product is clean, that is eb e ( 0) = 0e + (1 0) e. Rearranging (2.4) we obtain the demand as a function of the perceived quality: q (p; 0) =( e ( 0)) p (2.7).
Note that (2.7) increases in 0 implying that optimistic expectations of environmental quality raises demand. Since every producer type prefers to be taken for the clean regardless of its true type, the …rm of type e can bene…t from revealing its true type when it distinguishes itself from the dirty type thus reaping the green consumption. The producer’s objective is to maximize pro…t with respect to p given consumers beliefs about environmental quality.
The …rm’s strategy must form perfect Bayesian equilibrium where consumers infer environmental quality by observing the price. Let ( ) : R+ ! [0; 1] denote a posterior belief function that relates the …rm’s price to consumers’ perception of environmental quality. Let (e) and (e) be the equilibrium prices for clean and dirty producers re-spectively. Thus, when a …rm charges price (e), then it is inferred to have quality ( ). Then, ( (e) ; (e) ; (p)) is the equilibrium strategy given the conditions:
1. For e = e; e(e) = max p (p; e; ) .
2. If (e) 6= (e), then ( (e)) = 0 and ( (e)) = 1. If (e) = (e), then ( (e)) = 0.
The …rst condition states that for each type the price strategy must be pro…t-maximizing given consumers’beliefs. The second condition imposes the Bayes rule for belief updat-ing. When the price is informative, consumers correctly identify the producers’ type. When the price is uninformative, prior and posterior beliefs equal; and beliefs updating has no e¤ect.

Environmental taxation

The regulator has an objective to maximize the aggregate social welfare by imposing a tax on the polluting emissions. At the time when the regulation is set, a realization of the production type has not yet taken place, so the regulator commits to a policy in anticipation of a probability 0; that the producer is of the clean type. Hence, the regulator’s objective function is W (t): max 0W (e; t) + (1 0) W (e; t) (2.23).
The probabilistic welfare is similar to that of (Freixas, Guesnerie, and Tirole 1985), in our context, alternatively to consumers’prior optimism about the …rm’s environmental performance,. 0 can represent the percentage of clean markets in the economy as a whole.


Optimal second-best tax with equilibrium selection by intuitive criterion.

The unique equilibrium, which survives the intuitive criterion, is separating with the price pair (ps; p (e)), and is such that the clean type sets the least distortionary signaling price while the dirty type sets a full information monopoly price. Then, using (3.30) we obtain the explicit form of the regulator’s objective function: W (t) = 0 2q (ps (e; t)) c q (ps (e; t)) F (e) + (2.24).

Welfare implications

In this section we evaluate the impact of environmental taxation on social welfare.
Separating equilibrium. When weak regulation is required, it partially internal-izes the externality from the polluting production of the dirty product. The clean product also grows more expensive making consumers’and producer’s surpluses shrink. It repre-sents a mere deadweight loss because the reduction of output doesn’t serve to control or limit pollution.
When strong regulation is required, the clean variety signals its quality by downward price distortion. Compared to upward signaling, consumers are better o¤ as they bene…t from the lower price of the clean variety. In terms of surplus, the clean producer is indi¤erent to upward and downward price distortion because in the former case a high price margin compensates for thinner demand and vise versa in the latter case. Compared to socially optimal resource allocation, strong regulation with downward price distortion performs relatively better than the weak because both price and output of the clean product are closer to the competitive level. It is clear however, that the optimality of such a sever environmental policy is conditional on relatively high environmental damage, low consumers’expectations, and a su¢ ciently high di¤erence in marginal costs. Figure (2-4) illustrates a parameter map for which all the conditions are veri…ed. As either constraint is relaxed, the strong tax ceases to be optimal because of its high social cost.
It is noteworthy that for both types of regulation, optimistic expectations about en-vironmental quality lessen the severity of the environmental tax. With upward signaling, there is a deadweight loss from the reduced amounts of trade of the clean variety. With downward signaling, it is rather the exercise of market power by the clean type, which enables the signaling price to approach monopoly level.
Pooling equilibrium. When prices are uninformative, the pollution tax a¤ects the pooling price. The optimal tax corresponds to the Buchanan level, softened by the probability of occurrence of the clean variety. The optimal tax equalizes the product’s expected social value to its expected social cost. For the dirty variety, the tax doesn’t entirely corrects pollution externality. For the clean variety, the tax reduces the amount of trade. In addition, private information about environmental quality remains concealed.
Equilibrium selection by undefeated criterion. As it has been shown for equi-libria selection according to Mailath’s undefeated criterion, environmental taxation may a¤ect a producer’s pricing strategy. Thus, the marginal producer who is ex-ante better of with a separating price strategy, would ex-post ‘migrate’, subsequent to the imposi-tion of weak environmental regulation, to a pooling price strategy. Similarly, to have a downward price signal induced by strong environmental regulation, environmental dam-age must be su¢ ciently close to the dirty variety’s social value and the tax level should more than double the di¤erence in marginal production costs, i.e., t > 2c. The …rst c is necessary to reverse the order of cost e¢ ciency, the second – to induce a signaling strategy. Because even being more cost e¢ cient, the clean type’s pooling pro…t would Pareto dominate its separating pro…t, if it costs almost the same to produce a high or a low environmental quality. Thus, the tax may make the clean type prefer the pooling strategy over the separating strategy.
The ‘equilibrium migration’induced by environmental regulation has a negative e¤ect on welfare because consumers lose the ability to distinguish between environmental types when environmental regulation renders pooling equilibrium Pareto dominant.

Table of contents :

I Tax Avoidance 
1 Free-riding on environmental taxation 
1.1 Introduction
1.2 The model
1.3 Second-best optimal tax
1.4 The two-part tax schedule
1.5 The example of BHPP
1.6 Discussion on the modelling choice of avoidance function
1.7 Conclusion
1.8 Appendix
1.8.1 La¤er curve
1.8.2 Proof of Lemma 2
1.8.3 First-order condition for welfare maximization
1.8.4 Proof of Lemma 4
II Environmental regulation under asymmetric information 
2 Environmental regulation with price signaling 
2.1 Introduction
2.2 The model
2.3 Asymmetric information
2.3.1 Separating equilibrium
2.3.2 Pooling equilibrium
2.4 Environmental regulation
2.4.1 Environmental taxation
2.5 Welfare implications
2.6 Conclusion & discussion
2.7 Appendix
2.7.1 Derivation of signalling price
2.7.2 Consumers entirely internalize the pollution externality
2.7.3 The choice of optimal pricing
2.7.4 Proof of Corollary 16: @t @ < 0
III Di¤erentiation in environmental quality 
3 Taste for diversity, pollution aversion and optimal choice of environmental quality 
Résumé du chapitre 3
3.1 Introduction
3.2 The model
3.3 Short-term choice of EQ
3.4 Social choice of environmental quality
3.5 Long-term private choice of environmental quality
3.6 Producers’organization with environmental awareness
3.7 Conclusion
3.8 Appendix
3.8.1 The sequence of the game
Conclusion Générale
General Conclusion


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