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Environmental Policies: Principles and Instruments. 1. Environmental taxes and standards - Optimal pollution level - The Pigouvian tax - Taxes vs. Standards 2. Natural resource management and intertemporal or intergenerational choices

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environmental policies principles and instruments

Environmental Policies: Principles and Instruments

1. Environmental taxes and standards

- Optimal pollution level

- The Pigouvian tax

- Taxes vs. Standards

2. Natural resource management and intertemporal or intergenerational choices

- Next generations and the problem of the discounted value

- Optimal extraction (exploitation) rate

environmental policy and the optimal pollution level
Environmental Policy and the optimal pollution level

Recall that: the optimal allocation of the environmental resources can be restored by assigning exclusive property rights and allowing for free transactions on them (Coase Theorem)

The achievement of this social optimum still being the objective, environmental policies are designed to efficiently pursue this objective any time voluntary negotiations and trade do not occur or become too costly or favour speculative strategic behaviour (free-riding, for instance).

We analyse now some classical environmental policy instruments that aim at restoring optimal use by affecting the voluntary behaviour of agents (mostly, of those who use the environmental goods, the “polluters”): :

Environmental taxes

E. standards

E. payments (or subsidies or incentives)

E. negotiable rights (permissions)

We discuss these instruments in terms of ability to achieve the optimal pollution level (the optimal combination between social benefits and costs) but also in terms of distributional effects (who is going to pay the costs, who is going to receive the benefits)

the optimal pollution level definition
The optimal pollution level: definition

Let’s go back to our simple “model”: the polluter vs. the polluted; the private good (Q) vs. the public good (E). In general terms, starting from zero-pollution we can think about 3 different levels of pollution:


(Pareto irrelevant)


(Pareto relevant: regulation)



Pollution level that does not imply costs (reduction of welfare) ( zero pollution)


environmental policies the pigouvian tax
Environmental policies: the Pigouvian tax

In the case of “polluter vs. polluted”, even when the negotiation a lá Coase does not work, it remains possible to restore the optimal pollution level (QS) through a direct intervention of the “State” (“Government”) that eliminates the Pareto-relevant negative externality

The solution relies on the internalization of the social cost, that is, on making social cost be part of the private (polluter) cost in producing Q. This can be achieved by introducing a tax on production of Q.

A tax on the polluting good (Q) that equalizes private costs and (relevant) social costs is also called Pigouvian tax (A.C. Pigou)

In many applications, environmental (or pollution) taxes behave as Pigouvian taxes.

Let’s see, conceptually, how such tax is expected to work

the pigouvian tax 1
The Pigouvian tax - 1

Pigouvian tax

Bm(Q)t = Bm(Q) - t




the pigouvian tax 2
The Pigouvian tax - 2
  • The tax lowers Bm(Q) by t for any level of Q. Therefore the after-tax benefit of the polluter is: Bm(Q)t = Bm(Q) – t. However, as it also includes the tax revenue, the benefit of the society remains the same:

(Bm(Q)t + t) = Bm(Q) – t + t = Bm(Q)

  • Whenever t is exactly fixed at the value of the social marginal cost in QS, i.e. Cm(QS), we have the optimal Pigouvian tax (t*), as it induces the polluter to spontaneously produce the socially optimal level QS : all the Pareto-relevant negative externality is internalized
    • In fact, such tax should be in principle established as follows: 1) indentify the optimal pollution level QS; 2) compute the respective (social) marginal cost Cm(QS); 3) fix and impose the tax t = Cm(QS)
  • What about the Pareto-irrelevant negative externality?
    • The state obtains a tax revenue(t* x QS) that can be redistributed as compensation payments to those that still bear the Pareto-irrelevant costs.
the pigouvian tax pros
The Pigouvian tax - PROS
  • The idea behind the Pigouvian tax is straightforward and intuitive and it applies the polluter pays principle:
    • It achieves the social optimum (allocation problem) through a spontaneous (market) decision of the polluter
    • The polluter fully pays the cost he/she generates thus eliminating the Pareto-relevant costs while compensating the Pareto-irrelevant one (distributional problem)
  • It looks like an application of the Coase Theorem.
      • The state initially holds the exclusive property rights on the polluted good (E)
      • The state is the representative of all polluted individuals and thus negotiates with the polluter by accepting to sell rights on E (therefore accepting pollution) only at price equal to or higher than Cm(Q)
      • Negotiation will eventually come to an end with the polluted (represented by the state) selling at price t* rights corresponding to QS
      • Transaction implies that the polluter pays the total tax revenue(t* x QS) for these rights
the pigouvian tax cons
The Pigouvian tax - CONS
  • Asymmetric information: once more, to fix the optimal tax we need to know both the value of Cm(Q) and Bm(Q). For the former, we have already discussed the difficulties we may encounter. For the latter, the state may find problems in finding information about Bm(Q) as, under taxes, the polluter will have all the interest to do not reveal it (evidently t* increases as Bm(Q) increases). The tax-imposing institution has to face this problem of incomplete information about the polluter
  • Risk of over-taxation: even if we accept that property rights “naturally” belong to the state and that the polluter pays principle must hold, it remains true that the Pigouvian tax implies that:
  • 1) The tax “takes away” from the polluter more than the Pareto-irrelevant cost (externality). This implies a net redistributional effect against the polluter itself and in favour of the polluted (over-compensation)
  • 2) The tax applies also to the pollution levels still under the assimilation capacity (Q0) thus inducing an unjustified taxation for low levels of Q
environmental standards 1
Environmental standards - 1
  • To achieve a solution (in both allocative and distributional terms) about the use of environmental goods, one often adopted alternative to imposing environmental tax is fixing environmental standards
  • In practice, those standards are technical thresholds that can not be exceeded by the polluters, therefore a sort of maximum admitted cost generated in terms, for instance, of water or air pollution and expressed as maximum admitted concentration of nitrates in water, of PM10 in air etc. Such standards are mostly established on the basis of technical (medical, biological, engineering…) evaluations rather than according to economic considerations.
  • Nonetheless, we are interested in dealing with environmental standards as viable alternative to environmental taxes, therefore according to their economic implications in terms of allocative efficiency and distributional effects. Thus, it is worth recalling that:
    • We are considering pollution in a sort of static representation, that is, assuming a constant technology for which there is a univocal relation between the production level of Q and the consumption of the environmental good E.
    • Therefore, the standard can be viewed as the minimum acceptable level E* under which it is not admitted to go and, therefore, as the maximum level Q* the polluter is allowed to produce.
    • For production levels lower than Q*, the polluter does not bear any cost for polluting. If production exceeds Q*, the polluter has to pay a sanction (a fine) of amount M.
Environmental standards - 2

If the standard has also an economic (allocative) purpose (achieving the social optimum) it should be fixed at QS and the minimum (and efficient) sanction at MS. The sanction acts as the Pigouvian tax in allocative terms, while it has no distributional implications (no polluter pays principle, no over-taxation)

As for the environmental tax, the sanction is a cost for the polluter. Therefore, a standard exclusively satisfying a “technical” objective Q* implies a minimum sanction of M*.

It must be taken into account, however, that the sanction is not certain any time the standard is exceeded (violated). It depends on how difficult and costly controlling activities are. The polluter will thus behave on the base of the expected sanction (or the actual sanction), that is, MP = p MS, where p is the probability of being sanctioned upon violation of the standard. If p = 0.5, the actual sanction is 1/2 MS and the standard will be not respected (QP)unless the sanction is raised to 2MS







a synthesis of alternative instruments source silvestri
A synthesis of alternative instruments (Source: Silvestri)

PROS (+) and CONS (-)

C&C = Command and Control

optimal intertemporal intergenerational use of environmental natural resources
Optimal intertemporal (intergenerational) use of environmental-natural resources

So far, the problem of optimal allocation of an environmental good E (i.e., of pursuing the maximum net social benefit) has been worked out by comparing CURRENT costs and benefits associated to the use of this good.

This static representation, however, does not fit the actual concerns related to the use of many natural resources where costs and benefits differently occur anddistribute over time

We need to make explicit that these resources behave as stock that can be used either in the current period or in next periods. Therefore, choices about resource use have an inherent dynamic (intertemporal) dimension.Such dimensionconcerns two different aspects:

How future generations will use/demand this resource

How the resource stock evolves over time

The allocation problem thus becomes to find TODAY the optimal exploitation/extraction rate. Such optimal resource exploitation substantially differs for the two different kind of natural resources:

NON-RENEWABLE (EXHAUSTIBLE) RESOURCES: fossil energy, mineral resources, etc.

RENEWABLE RESOURCES: forestry resources, fishery resources, water resources etc.

future generations and the problem of discounting
Future generations and the problem of discounting

In principle, the idea of optimality can be maintained: maximization of the Net Social Benefit. Now, however, the “society” is the aggregation of current and next generations and its net benefit is the difference between the flow of benefits B(E)tand of costs C(E)t over time:

Algebraic summation of such benefits and costs, however, incur the problem of comparing monetary values over different periods of time. This problem is tackled by comparing the current value of benefits and costs, therefore by discounting all values at the discount rate r.

Therefore, the maximization of the current (discounted) intertemporal net social benefit (SB0) (thus achieving the optimal allocation of E across generations/periods) is expressed as:

  • Is there a market or a rights’ negotiation mechanism allowing this optimal solution to be achieved?
    • Here, market-negotiation can not be afforded for the simple reason that some generations can not express their preference now; therefore, transactions can not be carried out.
    • Present generation, therefore, may tend to impose a too-high (egoistic) value of r. As a consequence, appropriate policy measures should aim at restoring this hypothetical optimal transaction among generations by fixing an appropriate value for r (intergenerationalcoordination).

This is evident in the case of exhaustible resources:

Under this circumstance, the resource is available in an absolutely scarce quantity, the stock QT. Therefore, the problem in resource management is to decide how much of QT has to be extracted (used) by the present generation and how much has to be left to the next generations.

Any generation will obtain a net benefit B(Q)t from resource extraction. Due to absolute scarcity, quantity used by time t generation is definitively missed for time (t+n) generations. Therefore, B(Q) t+n becomes an opportunity cost associated to B(Q)t; in other words, it is the option value of the resource itself.

Without an intergenerational coordination, in any period t there will be tendency to over-utilize the resource to the level Q* for which Bm(Q*)t = 0.

At such exploitation rate, however, there will correspond an opportunity cost for the following periods whose discounted value is B(Q*)t+1/(1+r). A generation that is not aware of this implicit cost implicitly assumes a very high discount rate that makes this opportunity cost negligible. Therefore, the discount rate in such context is somehow a measure of the degree of “egoism” of present generations with respect to future generations.

Let’s consider this problem of intergenerational coordination in an oversimplified situation (model): one good (E) and only two generations (t = 1, 2)

Optimal intertemporal extraction of exhaustible natural resources - 1

If we wish to define the optimal allocation of the given stock QT between the two generations the problem to be solved is:

Optimal intertemporal extraction of exhaustible natural resources - 2

QT - Q1 = Q2 (expresses the extraction of second generation)

  • It can be easily found that the optimal solution is that level of current (generation 1) use Q1 such that:
  • The intuitive explanation is that any further unit of current exploitation would generate an additional benefit for generation 1 that is lower than the discounted value of the benefit subtracted (opportunity cost) to generation 2.

We can better appreciate this result graphically :

Optimal intertemporal extraction of exhaustible natural resources - 3

Optimal intergenerational allocation of stock QT under a non-null discount rate. The higher is r, the larger is the use of current generation (Q1), the lower the amount left to generation 2 (Q2)

Optimal intergenerational allocation of stock QT only when the discount rate is null (r = 0; no intertemporal preference).




Optimal use of current generation (Q1) under an infinite discount rate (r=∞) expressing the lack of intergenerational coordination








Optimal intertemporal exploitation of renewable natural resources
  • For these resources, the problem of the optimal dynamic exploitation has not only and simply to do with intergenerational coordination (a “fair” distribution across generations). Before dealing with optimality, in fact the issue is to pursue sustainability in the use of the resource. Its available quantity X, in fact, is not absolutely scarce (a stock QT) as it depends on a natural accumulation process, usually based on biological processes, i.e. on a growth function.
  • In the (classical) case of biological population, this growth typically follows a logistic function. According to this function the the resource (for instance, a forest) stops growing at a given maximum level of the stock X representing its dynamic biological equilibrium:
  • This function also implies that at any time t the resource stock growth (Xt+1=Xt+1 – Xt) depends on the initial level of the stock itself Xt:
Sustainable exploitation of renewable natural resources - 1
  • If the resource growth is Xt+1 = f(Xt), it will be evidently possible to use (extract or exploit) in the unit of time such level (quantity) of the resource itself, Yt = Xt+1 = f(Xt), without affecting the initial available stock for any following period, that is maintaining the initial stock constant at Xt. This level of use Ytis called sustainable equilibrium (or sustainable exploitation) as it allows the resource stock to remain stable over time.
  • Any exploitation level Y>YMAXcan never be sustainable regardless the initial stock as this is never able to regenerate the same amount of the resource. On the contrary, for any Y






  • These two sustainable equilibria, however, are not equivalent. The equilibrium corresponding to the smaller steady stock (X1) is an unstable sustainable equilibrium: even a little movement of the stock from X1 will cause a permanent departure from the equilibrium (YMAX; XMis unstable, too). On the contrary, in X2 we have astable sustainable equilibrium (the stock will spontaneously return to the equilibrium value after a little deviation).
Sustainable exploitation of renewable natural resources - 2
  • Beside stability, is (Yt; X2) also more economic efficient compared to (Yt;X1)? To deal with economic efficiency in this context we have to introduce the cost associated to resource exploitation. The exploitation level Y evidently has a cost according to this sort of production function Y=g(X,E), where E indicates the exploitation effort, a synthetic measure of production inputs used for exploitation.
  • It is reasonable to assume that Y/E>0 but also that E/X<0, namely, for a given exploitation level Y the effort must increase as the stock decreases:
  • If c is the unit cost of E, it is easy to see how the more efficient (i.e., lower cost) solutions correspond to the higher stock levels (the stable ones)
  • It is also interesting to notice that this result has a lot to do with the access regime for the resource. Let’s consider two opposite access regimes:

- Free Access

- Exclusive Access





E3 >

E2 >


Sustainability and optimal exploitation

free access vs. exclusive access rights - 1

  • The free access regime (regime LA) means that there is no cost associated to the access. Still a cost must be borne for extracting the resource (c for any unit of effort, E). The exploitation under free access will thus continue (increase) until revenues are greater than exploitation costs, that is, until Y(E)>cE. exploitation will stop when Y(E)/E=c. Let’s represent the revenue Y(E)=f(X) and the cost cE in the same diagram:







  • Under free access, the consequent sustainable exploitation (YLA;XLA) is unstable and, above all, is clearly inefficient as the same exploitation(YLA)can be obtained with a stable stock (X*) and a much lower cost (cE*0). Collectively, however, they are not able to understand that a greater aggregate profit could be obtained with a lower level of exploitation.
Sustainability and optimal exploitation:

free access vs. exclusive access rights - 2

  • To make the exploitation stable and efficient (optimal) it is thus necessary to introduce forms of coordination. The easiest way is to assign an exclusive property right on the resource to a single individual (regime P). He/She decides the level of exploitation Y(E). If he/she is rational, as under free access, he/she aims at maximizing the profit given by Y(E) - cE. Therefore, the optimal solution will be the level for which: Y/E = Yl = c.

The Tragedy

of the Commons

Yl =c




  • Under assignment of exclusive access rights, the consequent exploitation (YP; XP) will be stable and optimal, much better than under LA (XP>XLA, YP>YLAand EP
Sustainability and optimal exploitation:

the access tax

  • Assigning (or privatizing) access rights, however, does not necessarily conflict with freedom of access. The same result obtainable under exclusive rights, can be achieved by allowing access to the resource upon the payment of an access price (or tax) t. Therefore, a viable compromise between freedom and coordination is to assign exclusive access rights to a public authority that then sells these rights at price t for unit of E to individuals willing to have access to the resource.


EP· t*

  • Therefore, the access is not free but it is free the participation to the “market” of access rights. Therefore, any individual allowed to extract the resource has to bear a unit cost (c+t*) and exploitation will continue until Y(E) = (c+t). As the optimality condition is Yl(E) = c, the optimal access tax should be fixed at: t* = YP(E)/EP - Yl(E). This optimal access tax will “convince” free and non-coordinated individuals to stop at YP. The public authority will also obtain an access tax revenue (t*x EP) to be invested on the resource itself or on compensating individuals discouraged by the tax and, thus, that lost benefits.