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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
Externalities, Pollution, and Policies for the Optimal Level of Pollution
One way to look at externalities like pollution is to consider the cost and benefits
of the pollution (a negative externality.)
To see how energy pollution affects society’s welfare and to investigate what
policies we may use to mitigate environmental problems, we begin our analysis
with Figure 8.1. D equals the demand or the marginal benefits in the oil market.
MCpv represents the private marginal costs of the private supply curve. Assume
that the production and transportation of oil creates oil spills and other pollution.
With the included external costs of such pollution, the supply curve representing
private and external costs or all social costs would be MCsc.
The private market allocation would be where D=MCpv at Ppv and Qpv.
At the private market solution, Qpv, the true social costs are greater than the
benefits with the area abc representing the social losses in this case.
If we could internalize the externality, then the social costs would equal the private
costs and the market price and quantity would be Psc and Qsc.
Acknowledgements: These notes come an upcoming version of Carol Dahl’s book.
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
Externalities, Pollution, and Policies for the Optimal Level of Pollution
One way to look at externalities like pollution is to consider the cost and benefits
of the pollution (negative externality.)
We often approach thinking about equalizing the
Marginal Benefits to the Polluter to Marginal Damages to sufferer of pollution
Marginal Costs of Pollution Abatement to Marginal Benefits from Abatement
See the diagram 8.2 below.
The left hand side or the benefit side we see that the marginal benefits are high for
the first units of pollution. This suggests that it is very difficult to emit almost no
pollution. However, as the amount of pollution increases it becomes increasingly
easier to not emit or to clean up the pollution.
Alternatively, the cost of not polluting the initial (or any) amount is very difficult.
The Marginal Abatement cost is very high as more pollution is abated. The
marginal abatement cost falls as the pollution restrictions are eased.
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
On the right hand side a small amount of pollution may cause no damage. The
natural environment is able to absorb or has some tolerance for pollution.
However, as the pollution increases we exceed the carrying capacity of the
environment and marginal damages or the damage of the last unit of pollution gets
larger as the pollution increases. Thus, the environment becomes less able to cope
as pollution increases.
Alternatively, the Marginal Benefits from Abatement are very low initially, but rise
as the level of pollution gets larger.
Property Rights, Pollution, and Outcomes: Introduction to Coase Theorem
Coase in the 1930s noted that given
• well defined property rights,
• with no party having excessive market power, and
• in the absence of transaction costs,
an optimal level of pollution would be arrived at by bargaining between polluter
and sufferer no matter who had the original property rights.
Transaction costs in this context include the money costs as well as the time and
effort required to conduct the transaction.
If those who suffered the damages of the pollution have the rights to the water, the
pollution will be at B. With less pollution than B, they will suffer no damage and
so won’t mind the pollution. However, with more pollution than B, they will suffer
damages and won’t permit the pollution.
If the polluters have the rights to the water, the pollution level will be at D. Since
they don’t benefit from pollution beyond D, they will not pollute more than D.
Since there are benefits for all pollution less than D, they will pollute up to point
Alternatively, if property rights are not well defined, the pollution level would
likely be at D as well as those having no recourse will not be able to stop the
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
Property Rights, Pollution, and Outcomes: Introduction to Coase Theorem
From an economic point of view, the optimal quantity of pollution or what
economists would call an efficient level of pollution is at point C. At pollution
levels less than C, the benefits of pollution are greater than costs, so society
benefits from pollution. After C the costs are greater than the benefits, so society
loses if we pollute more than C.
If the polluter is large and the one suffering the damages is also large, the two are
likely to get together and negotiate an optimal solution. For example, suppose the
polluter is a coal mine whose runoff makes a local river more acidic. A refinery
downstream uses the water in its processes. But when the water is acidic, it has to
be cleaned up or it corrodes the refinery equipment. Suppose that initially the coal
mine or the polluter has the property rights and pollution is at D. For the last unit
of pollution, the refinery would be better off if it paid anything less than EA to get
the coal mine not to pollute.
Similarly for the next to the last unit of pollution, there is some payment from the
refinery to the coal mine to not pollute that would make both the refinery and the
coal mine better off. Through negotiation the firms could come to some payment
schedule that would make them both better off until we reach point C. For less
pollution, there is no payment between them that would make them both better off.
Similarly we could start at B and make the same arguments why the firms should
end up at C.
However, transaction costs are often very high. Take the example of a refinery
polluting a low income neighborhood. Although the residents as a whole may
suffer more damages than the refinery gains by polluting, it may be difficult and
costly to organize and negotiate a better solution with the refinery. Further, they
may not have access to any market where they can convert the health damages they
will suffer into the cash to make payments to the refinery. In such a case we think
markets will fail and most economists agree that the government should intervene.
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
Pollution Policies for Optimal Level of Pollution
Four different policies could be implemented in the above case. The government
1) set a pollution standard permitting pollution at level C,
2) set a unit tax on pollution of AE,
3) sell pollution permits equal to AC, or
4) set a unit subsidy on clean up or abatement of AE.
Setting standards and enforcing them tends to be the way that U.S. environmental
policy has been implemented and is called command and control. If the regulation
were obeyed the firm would pollute C and abate or no longer pollute amount CD.
The polluter’s losses would be the cost of abatement or area CFD in Figure 8.2.
The last three more market oriented policies, often called incentive based policies,
include a tax on pollution, selling pollution permits, or a subsidy to help abate
Back in Figure 8.2, if a unit tax equal to AE were set, then the optimal level of
pollution would also occur. For pollution before C, the benefits are greater than the
tax. It is beneficial to pollute and pay the tax. After C, the benefits of pollution are
less than the tax, and therefore they are better off not polluting. The production
decision under unit taxes is given by:
Q S  0 when Costs  MC + unit tax
Q S = 0 when Costs = MC + unit tax
Q S  0 when Costs  MC + unit tax
The distribution effects of the policy indicate the gains and losses from the policy.
The total tax the polluter would pay would equal AEFC and the cost of abatement
would be CFD. If pollution had been at D before the policy, the benefits to society
would be equal to FGD.
For pollution permits, the government would have to give out or sell permits
equal to AC. If they auctioned off permits, firms (and consumers or conservation
groups ) would have to buy them in order to pollute. If the price of permits was
less than AE, then firms would want to pollute up to the point where the permit
price was equal to the marginal benefits of pollution. Before that point, pollution
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
would yield more benefit than the permit would cost, so firms would want to buy a
permit and pollute more. However, if they wanted to pollute more than AC, there
would not be enough permits, and the price of permits would be bid up:
Similarly if the price of permits were higher than AE, firms would want to pollute
too little. They would buy fewer permits than AE. With excess permits on the
market, the price of permits would be pushed down. Thus, the market should push
the permit price to the same level as the optimal tax.
Q S  0 when Costs  MC + Permit price
Q S = 0 when Costs = MC + Permit price
Q S  0 when Costs  MC + Permit price
The distribution effects are the same as in the tax case if the government auctions
off the permits. If the government gives away the permits the polluter only loses
CFD from the policy and the government receives no revenues. The distribution
effects are the same as for the comand-and-control system.
The third incentive would be to subsidize the polluter not to
pollute. Suppose the subsidy was AE or we paid a firm AE for each level of
pollution that they abated.
a. Explain why this policy would get us the optimal level of pollution.
b. What would this policy cost the government?
c. Although all policies, if properly enforced, could get us to the optimal
level AC, they have different income distribution effects. Compare the costs
to the firm of all four policies – a standard, a tax, a marketable permit, and
a subsidy.
Economists do not favor a subsidy policy, or having victims pay to reduce
pollution, but rather recommend the “polluter pays principle.” Another term for
this is “source based pollution taxes or fees.”
Although having victims or the government pay to reduce pollution could in
principle get us to a social optimum, economists believe that having the polluter
pay is likely to be more efficient for a couple of reasons. Victims are usually a
more diverse group than polluters. Thus, collecting fees from them has higher
transaction costs and there are incentives for each victim to want to free ride and
let others pay.
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
Also if either the government or victims pay polluters to not pollute, it could cause
polluters to exaggerate how much they would like to pollute to increase their
It could also lower costs in polluting industries and encourage entry into the
industry, which would further raise the desired level of pollution and the subsidy
costs to the taxpayers.
Having the polluter pay also appeals to society’s sense of fairness. The higher costs
will be reflected in higher goods prices in polluting industry, causing consumers to
pay the full cost of the product.
Varying Pollution Benefits or Abatement Costs
The third reason to not favor standards is that pollution control benefits are not the
same for all polluters. To see why, remember that the benefits of pollution are the
benefits of not cleaning up pollution or the costs of abatement. For example,
let the benefits of pollution above be MBQ = 10 – 2Q.
The optimal quantity of pollution (Q) from the firms point of view would be where
the marginal benefits of pollution would be 0 = 10 – 2Q or Q = 5.
If the firm abates (A) then quantity of pollution would be Q = 5 – A..
Since the cost of abatement is the benefit from polluting
10 – 2Q = 10 – 2(5 – A) = 2A.
Now let’s look at control from a different angle and focus on these costs of
abatement across two firms. Let the amount we need to abate be the distance CD
from Figure 8.2.
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
Suppose that Figure 8.4 below represents the costs of SO2 abatement for two
electric power producers that are polluting in the above diagrams.
The costs of abatement are the costs of stack gas scrubbers and other pollution
control devices as well as any foregone output that results from abatement. These
costs are a reflection of the benefits in the above pollution model.
In the figure, read the amount abated for firm one from the left hand axis and the
amount abated for firm two from the right hand axis. The horizontal axis represents
the amount that the law requires to be abated and is the optimal amount of
abatement or the amount CD from Figure 8.2.
Suppose the allocation of abatement is at point “a” with firm 1 abating A1 and firm
2 abating A2. Notice at this allocation, the cost for firm 1 to abate the last unit is
“ab” and for firm 2 it is “ac.
It would be cheaper for society, if firm 1 abated more and firm 2 abated less. This
would be true until we arrived at the point where MC1 crosses MC2. Beyond that
point it would be more expensive for firm 1 to abate than firm 2. Thus, from a
social point of view, if the government set the same standard for both firms at “a”,
the losses would be “cbd”.
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
The government could set the abatement rate for each firm with firm 1 required to
abate more than firm 2, or if it knew cost it could pick a tax rate to get the optimal
level of abatement for each.
This would, however, require that the government know the abatement cost for
each firm. Since such information is proprietary it is unlikely that the government
could get the targets or the taxes right. Each firm has an incentive to try to inflate
abatement costs so as to be required to abate less. In addition, it would seem
politically difficult to impose different standards on different firms.
For these reasons, economists tend to favor marketable permits. Based on early
work in the 1960s John Krutilla and Allen Kneese at Resources for the Future.
Such permits require that the government make a decision on the optimal level of
pollution. Once that is decided, permits to pollute are auctioned off.
If the price of permits is too low, firms will want to pollute too much resulting in a
shortage of permits and their price will be bid up. Similarly too high a price will
result in a surplus of permits. The market will determine the price of the permits.
Then firms with low abatement costs will abate more and firms with high
abatement costs will abate less as is socially efficient.
Note again that to make auctions truly competitive all stakeholders should be
permitted to bid for the licenses to permit. Thus polluters (say firms), consumers
(those harmed), and conservation groups should be permitted to participate in the
market. This may yield a better estimate for the value of the negative externality
and its impacts on society.
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Rough Notes Externalities and Optimal Pollution Policies Spring 2016
Permits vs Pollution Standards or Command and Control
Early U.S. pollution regulations favored pollution standards or the command and
control approach. However, with the high cost of this approach and the urging of
economists, more and more market incentives have been introduced into the
Argument for using marketable permits comes from the SO2 regulations in the
Clean Air Act of 1990. This act set up a market for SO2 emission permits
beginning in 1995. Permits were tried on a local basis back in the 1970s and 1980s
in southern California.
Before the act was passed, estimates of compliance cost, which would determine
permit price, were between $170 and $1000 dollars a ton with a few even higher.
Once implemented in 1995, permits averaged around $80 per ton. (Economic
Report of the President 1997 ). Thus, by allowing firms to decide on their own
abatement strategy – the costs of the program were much lower than expected.
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