CHAPTER 14: ECONOMICS OF POLLUTION CONTROL
I.
Introduction
A.
Up until this point, we have focused on the flow of resources into the "economic system"
Economic System
outputs
Firms
Households
inputs
extraction
residuals
Natural Life Support System
Air, Water, Wildlife,
Energy
Raw Materials, Amenities
ASSETS
B.
II.
We now want to talk about the flow of wastes back into the system, specifically addressing
two questions
1.
What is the appropriate level of waste flows?
2.
How to allocate the flows? Will the market work?
A Pollution Taxonomy
A.
The damage caused by waste disposal depends crucially upon the environment's ability to
absorb the waste.
B.
DEFINITION: The absorptive capacity refers to the environment's ability to absorb
waste products.
1.
Note: It is not that the system destroys the waste (this would contradict the first
law of thermodynamic). Rather, the system transforms it into a substance not
considered to be harmful to the ecological system, or dilutes it so that the resulting
concentration is not harmful.
14-1
2.
3.
Examples:
a.
Carbon dioxide is absorbed by plant life
b.
Organic pollution in waterways can be transformed into less-harmful
inorganic matter by bacteria in the waterways.
If emissions exceed the absorptive capacity of the system, they will accumulate in
the environment and cause damage.
Absorptive
Capacity of the
Environment
Emissions
Load
C.
Pollution
Accumulation
Pollution
Damage
Classification of Pollutants
1.
By absorptive capacity
a.
DEFINITION: A stock pollutant is a pollutant for which the
environment has little or no absorptive capacity.
Examples:
b.
i.
Nonbiodegradable bottles
ii.
Heavy metals (e.g., lead)
iii.
Some synthetic chemicals (dioxins and PCB's)
DEFINITION: A fund pollutant is a pollutant for which the environment
has some absorptive capacity.
Examples:
i.
Carbon dioxide
14-2
ii.
2.
waste paper products
By Horizontal zone of influence
a.
DEFINITION: The damage caused by a local pollutant is experienced
near the source of the emissions.
i.
b.
Nonbiodegradable plastics
DEFINITION: The damage caused by a regional pollutant is
experienced at greater distances from the source.
i.
sulfur dioxides from coal emissions is believed to be a culprit in
the acid rain problem.
ii.
carbon dioxide
Note: It is possible for a pollutant to be both.
Example: carbon dioxide
3.
By Vertical zone of influence
a.
DEFINITION: A surface pollutant is one whose damage is determined
mainly by the concentration of the pollutant near the earth's surface.
Example:
b.
i.
water pollutants
ii.
plastics
DEFINITION: A global pollutant refers to a pollutant whose damage is
determined by its concentration in the upper atmosphere.
Examples:
4.
III.
i.
carbon dioxide is often cited as a contributor to the greenhouse
effect.
ii.
Chloroflourocarbon emissions are linked to ozone depletion.
The above taxonomy is useful because, as we shall see, different pollutants require
different policies. Failure to recognize these distinctions can lead to flawed,
counterproductive policies.
The Efficient Allocation of Pollution
14-3
A.
As in all previous chapters, the efficient allocation is one that maximizes the present value
of the net benefits.
B.
Different approaches need to be considered in dealing with fund versus stock pollutants.
C.
Stock Pollutants
1.
Question: Can stock pollutants be treated in a static framework?
No. By their very nature, stock pollutants create interdependencies between
decisions made today and the welfare of future generations.
2.
Example:
a.
Consider a good (X) whose production costs are zero and for which
consumers perceive a marginal net benefit of MB = A.
b.
Question: How much will the firm produce?
An infinite amount.
c.
Now suppose the production process also generates a stock pollutant, with
a marginal costs to society of MC = bA for each period exposed to the
pollutant. Suppose further that b = .1.
d.
Should another unit of the good be produced today?
PV[MNB] = PV[MB] - PV[MC]
2
= A - {bA + bA/(1+r) + bA/(1+r) + ...}
2
= A - bA{1 + 1/(1+r) + 1/(1+r) + ...}
= A - bA[1 + 1/r]
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0.6
0.4
0.2
0.0
5.0%
7.0%
9.0%
11.0%
13.0%
15.0%
17.0%
-0.2
-0.4
-0.6
-0.8
-1.0
3.
Stock pollutants have many of the same problems as nonrenewable resources with
rising extraction costs.
a.
b.
What is done today has a permanent effect on all future generations.
i.
Emitting pollutant ⇔ extracting resources
ii.
MC of emission on society increases as stock of pollutant
increases ⇔ MC of extraction increases as stock of resource
decreases.
In fact the efficient solution is the same.
i.
The quantity of X produced over time should decline as the
marginal cost of damage increases. This will lead to a reduction
in the amount of pollution.
ii.
The price of X should increase over time to reflect the increased
social cost of pollution.
14-5
c.
D.
iii.
Resources committed to pollution control should increase over
time.
iv.
Eventually, a steady state will be reached where additions to the
stock of pollutants would cease, with emissions controlled instead.
Technological change can modify the efficient allocation by:
i.
Developing ways of recycling the pollutant
ii.
Developing ways of making the pollutant less harmful.
Fund Pollutants.
1.
Fund pollutants are to stock pollutants what renewable resources are to
nonrenewable resources.
a.
If emissions of fund pollutants exceed the absorptive capacity of the
system, then the pollutant will accumulate.
This is similar to the regenerative capacity in renewable resources.
b.
If the emissions are less than the absorptive capacity, no problem exists.
However, as in renewable resources, one has to be concerned with what
processes are allowed to contribute to using up the renewable resource:
"absorptive capacity."
2.
Suppose a product is going to be produced (i.e. fix the output level), generating Q0
units of pollutants without abatement. What is the efficient amount of pollution
emissions versus pollution control.
14-6
Marginal
Damage
Cost
Marginal
Cost of
Control
MC
Q0
a.
There are two marginal cost curves, both of which are increasing.
i.
The marginal cost of pollution damage is increasing.
•
ii.
b.
Quantity of
Pollution
Emitted
small amounts of pollution have only minor effects.
The marginal cost of pollution control is increasing. It is harder
to control all emissions than the first portion of emissions.
Question: Is zero the efficient level of fund pollution?
*
i.
Not necessarily. In this diagram, the optimal level is Q .
ii.
If damage costs are high enough, however, it can be efficient.
14-7
Marginal
Damage
Cost
Marginal
Cost of
Control
MC
TCd
Q*
c.
IV.
Quantity of
Pollution
Emitted
We would generally expect the optimal level of pollution to vary by region
and by types of pollution.
The Market Allocation of Pollution
A.
B.
V.
TCc
Question: Does the market naturally lead to the optimal allocation of pollution
emissions?
1.
No, due to the common property aspects of air and water.
2.
Pollution is an externality.
The argument for government intervention in this case is particularly strong.
Cost Effective Policies.
A.
B.
Efficient policies of achieving Q*
1.
Impose a legal limit
2.
Taxing pollutants
3.
The amount of information needed in order to determine the efficient level of
pollution is enormous and existing estimates are uncertain.
Cost effective policies
14-8
C.
1.
Instead that we focus on how to achieve a predetermined level of pollution
reduction in the most cost-effective manner.
2.
There are two types of pollutants to consider in this respect.
a.
DEFINITION: A uniformly mixed fund pollutant is one whose damage
depends upon the total amount of the pollutant entering the system.
b.
DEFINITION: A non-uniformly mixed fund pollutant is one whose
damage is relatively sensitive to where emissions are injected into the
system.
Uniformly Mixed Fund Pollutants
1.
In this case the focus can be on minimizing the total pollution level and ignoring
distributional impacts.
2.
What is the cost effective allocation of control responsibility for uniformly mixed
fund pollutants?
a.
The cost of achieving a given reduction in emissions will be minimized if
and only if the marginal costs of control are equalized for all emitters.
MC1
MC2
MC2
30
30
MC1
20
20
10
10
0
b.
0
q1
0
5
10
15
q2
15
10
5
0
In the graph we have two sources of pollution, with a goal of reducing
emissions by 15 units. For a more formal example, suppose we start with
two firms, with firm 1 initially emitting 20 units of pollution and firm 2
initially emitting 50 units of pollution. Suppose we want to control that
pollution down to a total of 55 units of pollution?
E1 = 20
E2 = 50
14-9
Goal: reduce total emissions to 55
Question: How should the pollution control be allocated between the
two firms?
We need to know the relative costs of pollution control. Suppose
MC1 = q1
MC2 = 2q2.
Where qi denotes the quantity of pollution controlled by firm i. Our goal
is:
(E1 - q1) + (E2 - q2) = 55
or
q1 + q2 = 15
or
q2 = 15 - q1
We have a second piece of information (cost effectiveness):
MC1 = MC2
or
q1 = 2q2 = 2(15 - q1) = 30 -2q1
⇒
3q1 = 30
⇒
q1 = 10
⇒
q2 = 5.
Graphically, we have:
14-10
MC1
MC2
30
30
20
20
10
10
0
0
3.
q1
0
5
10
15
q2
15
10
5
0
How to Achieve the Optimal Allocation? Cost-Effective Pollution Control Policies
a.
General Points
i.
ii.
The cost of pollution control for the same pollutant can be
expected to vary by industry and within industries, depending
upon
•
The size of the operation
•
The age of the plant
•
etc.
The best source of information on the costs of pollution control
will likely lie with the plant managers.
•
b.
It is not realistic to expect industries to convey accurate
information on pollution control costs. They will tend to
overestimate the costs.
Alternative policy I: emission standard
i.
DEFINITION: An emissions standard is a legal limit on the
amount of a pollutant that an individual source is allowed to
emit.
ii.
This is referred to in the literature as the "command and control
approach."
iii.
Using the figure below, it is clear that a uniform standard is not
cost-effective in this case.
14-11
MC1
MC2
30
30
20
20
10
10
TC1
TC2
0
0
q1
0
5
10
15
q2
15
10
5
0
iv.
c.
It is unlikely that the government would be able to determine the
cost-effective allocation. It does not have the necessary
information to do so.
Alternative Policy II: emission charge
i.
DEFINITION: An emissions charge is a fee, collected by the
government, levied on each unit of pollution emitted.
MC1
30
20
MC1
10
T
0
q1
ii.
0
5
10
15
How would the firm choose to control its pollution level faced
with an emissions charge of T?
The firm should move to where the MC of control equals the
emissions fee.
iii.
Suppose we now look at both firms.
14-12
MC1
MC2
30
30
20
20
10
10
0
0
q1
0
5
10
15
q2
15
10
5
0
•
iv.
v.
d.
We can get to the efficient allocation of pollution control
by setting the right level of T (T=10).
It is better tan emission standards in a number of ways:
•
The firms now control in the least cost manner relative to
each other, without the government knowing the costs of
pollution control for each firm.
•
An iterative method can be used to achieve the efficient
allocation by comparing the pollution abatement goal
with actual impacts.
•
Firms have an incentive to adopt new technologies in
pollution control, while standards create incentives for
firms to hide new control technologies.
The problem with emissions charges is that finding the efficient
level can be costly and time consuming.
Alternative policy III: transferable emission permits
i.
ii.
DEFINITION: Under a transferable emissions permit system,
all sources are required to have emissions permits matching
their actual emissions, with each permit
(a)
specifying how much the firm is allowed to emit and
(b)
being freely transferable.
Under this system the control authority issues exactly the number
of permits needed to produce the desired emissions level.
14-13
iii.
Severe monetary sanctions are imposed upon sources polluting in
excess of the amount allowed by its permits.
iv.
Example:
•
Consider our earlier example where 15 units of pollution
are to be controlled.
MC1
MC2
30
30
20
20
P2
10
P1
10
0
0
q1
0
5
7.5
10
15
q2
15
10
7.5
5
0
•
D.
What will the equilibrium price be?
v.
Notice that trading yields the most cost-effective allocation of
clean-up among the two firms.
vi.
Initial allocation of permits does not affect efficiency: it only has
distributional consequences.
Non-uniformly mixed fund pollutants
1.
Non-uniformity complicates the problem considerably.
2.
Total emissions is no longer the sole source of concern. We must also consider the
emissions site and its impact on concentration levels at other sites.
3.
It is easy to see why in many cases location does matter, especially when the
absorptive capacity of alternative locations differ.
4.
This whole problem leads to considering ambient standards.
5.
DEFINITION: Ambient standards are legal ceilings placed on the concentration
level of specified pollutants in the air, soil and water.
6.
The target concentration levels are measured at what are called receptor sites.
14-14
7.
The single receptor case.
a.
Location of the emissions source matters relative to the receptor site.
b.
River example:
1
c.
DEFINITION: A transfer coefficient, ai, measures the constant amount
that the concentration at the receptor will rise if source i emits one more
unit of pollution.
d.
The cost effective allocation will be achieved when the marginal cost of
concentration reduction (not emissions reduction) are equalized.
e.
Example
i.
Suppose we have two firms, both of which incur a marginal cost
of emissions reduction of
MC1 = MC2 = q
for reducing their emissions by q units.
ii.
Suppose that firm 1 has a transfer coefficient of 1 and firm 2 has
a transfer coefficient of 0.5.
•
That is, firm 1's reduced emissions reduce concentration
at the receptor site on a 1:1 basis.
•
On the other hand, it takes firm 2 twice as much
emissions reductions as firm 1 to have the same effect on
the receptor site concentration.
Source 1 (a1 = 1)
Emissions Reductions
1
2
MC of Emissions
Reduction
1
2
Concentration
Reductions
1
2
14-15
Marginal Cost of
Concentration Reduction
1
2
3
4
5
6
7
3
4
5
6
7
3
4
5
6
7
3
4
5
6
7
Source 1 (a1 = 0.5)
Emissions Reductions
1
2
3
4
5
6
7
MC of Emissions
Reduction
1
2
3
4
5
6
7
•
iii.
Concentration
Reductions
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Marginal Cost of
Concentration Reduction
2
4
6
8
10
12
14
In an effort to reduce concentration at the receptor site by
5 units, we would want firm 1 to reduce emissions by 4
units and firm 1 to reduce emissions by 2 units.
Mathematically, our problem is:
•
a1q1 + a2q2 = 5
⇒
q1 + 0.5q2 = 5
⇒
q1 = 5 - 0.5q2
•
We also want cost effectiveness, requiring equalization of
MC of concentration reduction (not emission reduction)
14-16
MCc1 = MC2 c ,
where MCc =
MCe
a
⇒
MC1 MC2
=
a1
a2
⇒
q1 q 2
=
1 0.5
⇒
q1 = 2q 2
•
Combining this with our goal, we have:
5 − 0.5q2 = 2q2
⇒
5 = 2.5q2
⇒
q2 = 2
⇒
q1 = 2q2 = 4
iv.
Graphically, we have:
MCc1
f.
MCc2
30
30
20
20
10
10
0
a1q1 0
1
2
a2q2
4
3
5
0
Policies
14-17
3
2
4
1
5
0
8.
i.
Ambient standard
ii.
Ambient Charges
•
A source pays ti per unit emitted, where ti = aiF, where F
is a fee used to adjust the level of pollution controlled.
•
In our example, we would want to set F = $4.
•
An iterative process can be used, in much the same way it
was used under emissions charges. Notice, however, that
the government now needs considerably more
information, namely the transfer coefficient.
iii.
An ambient permit system can be designed as well.
iv.
The ambient permit entitles the owner to cause concentration to
rise at the receptor site by a specified amount, rather than
allowing emissions to rise.
•
The higher the transfer coefficient of the firm, ceteris
paribus, the more permits the firm is going to want.
•
The higher the transfer coefficient, the smaller the amount
of emissions legitimately allowed to the firm by the
permit.
The Many Receptor Case.
a.
This represents a simple generalization of the single receptor case.
b.
Ambient charges can be set for each receptor at:
Tij = aijF
c.
In essence, each firm pays:
Ti =
N
∑aF
ij
j
j =1
d.
VI.
Ambient permits can be set for each receptor site.
Question: What are the distinctions among standards, permits, and charge systems?
A.
Standards are not only information intensive or likely no cost effective, but they also are
less likely to encourage innovation in pollution control
B.
Permit systems adjust automatically, while the charge system must iterate to a solution.
14-18
C.
Problems for charges versus permits:
1.
2.
D.
Charges do not react to changes in the number of sources.
a.
Adding sources will not change the permit result, just the value of the
permits being traded.
b.
Adding sources will increase pollution in the absence of changes in the
charge system.
Charges will not react to inflation unless they are modified. Permits will
automatically adjust.
Permits will not enable technological change in pollution control to alter the overall level of
pollution, but a charge system will.
MC1
30
MC1
20
MC’1
10
T
0
q1
E.
5
10
15
The two systems differ in the cost of being wrong.
1.
A.
0
Permit systems lead to certainty in the total level of pollution emissions. This is
important when the marginal damage function is steeply sloped.
Charges lead to certainty in the marginal control costs. This is important when the
marginal control cost function is steeply sloped.
14-19