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ENVIRONMENTAL AND NATURAL RESOURCE ECONOMICS
Part 1: PERFECT COMPETITION, EFFICIENCY AND EXTERNALITIES
by Jon D. Harford
(Last updated January, 2005)
(Note: references to Tietenberg are to his book Environmental and
Natural
Resource
Economics,
7th
edition,
published
by
Addison
Wesley.
Perfect Competition without Externalities
(Tietenberg discusses this type of material in Chapter 2 of his
book.)
Perfect competition is an ideal form of a market economy which
represents a simple starting point for analysis of real world
economies.
In perfect competition large numbers of buyers and
sellers exist in each and every market and no one of them believes
he has any influence over price.
In addition, there is no
uncertainty or imperfection in information and all decision makers
are rational.
defined
Rationality for consumers means maximizing a well-
utility
function
subject
to
an
individual
budget
constraint, while rationality for each producer means each firm
maximizes profits by its choice of inputs and output.
For
consumers,
maximizing
utility
subject
to
the
budget
constraint leads to particular choices of consumption goods for
each set of price and budget that the consumer faces.
By varying
the price of one particular good, other things the same, one can
derive a relationship between the quantity of one particular good
chosen and its price.
This relationship is the individual demand
curve of a consumer, a relationship which holds prices of other
goods and income constant.
Assuming that consumption of a unit of a good X by George
affects no one except George, the demand curve of George for good
X can be interpreted as reflecting the marginal benefit of units of
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consumption.
Referring to the demand curve in Figure 1a, it is
seen that at price of $12, George would buy one unit of the good X.
Accordingly, the value to George of the first unit of the good must
be at least $12.
At a price of $11, George would be willing to buy
two units of X.
From this we can infer that the second unit of X
must be worth at least $11.
Continuing in this reasoning it is
seen that the third unit of X must be worth at least $10, the
fourth unit must be worth $9, and the fifth unit must be worth at
least $8.
Accordingly, we would argue that the total of five units
must be worth at least $(12+11+10+9+8)=$50.
The total value of
five units of the X good we shall call the total benefits of that
consumption.
Now suppose George faced a price of $8 for the X good and
accordingly paid a total ($8)(5)=$40 to acquire five units.
The
difference between the amount George spent to acquire the five
units and the total benefits of those units would be called his
consumer surplus. George's consumer surplus is his net benefits of
consuming five units of the good.
That is, net benefits are the
total
costs
benefits
minus
the
consuming the five units.
least ($50-$40)=$10.
total
(his
expenditures)
of
We know that this net benefit is at
The method of refining this estimate is to
take ever smaller increments in the amount of the X good and
calculate
increment.
the
highest
price
associated
with
acquiring
that
If one takes this process to its ultimate limit, one
finds that the total benefits equal the area under the demand curve
up to the quantity consumed.
Therefore, we can conclude that the value of consumer surplus
is the area between the demand curve and the price line over to the
quantity consumed. Marginal benefit is the rate of change of total
benefits with respect to a change in the good consumed.
An
estimate of George's marginal benefit a given unit of X is the
highest price at which that unit is purchased.
Mathematically,
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George's marginal benefit of consuming an infinitesimal amount of
additional good X is the height of his demand curve.
Individual
demand curves are added horizontally (quantity addition) to obtain
the market demand curve for good X.
The total benefit, marginal
benefit, and consumer surplus associated with the market demand
curve for X are calculated in exactly the same fashion as with the
individual demand curve.
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While benefits come from consuming goods, costs come from
producing them. Perfectly competitive firms maximize profits under
conditions in which they take input and output prices as constants.
In the short run this leads to a choice of output in which marginal
cost equals price.
In the long run equilibrium marginal cost and
average cost both equal price.
Thus, at the market output that is
supplied for any given level of price it can be said that output is
being produced at marginal cost.
reflects private costs.
Of course, the supply curve only
That is, costs which the individual firms
see as affecting their profits.
Referring to Figure 1b, one sees that one unit of output will
be produced when the price is $4, thus indicating that the cost to
private producers of the first unit of output is no more than $4.
At a price of $5, suppliers are willing to provide two units of the
good.
This indicates that the second unit of the good costs the
firms no more than $5.
Iterating, it is seen that the third unit
5
costs no more than $6, and the fourth unit costs no more than $7.
If uses the same reasoning, but takes ever smaller increments to
output, it is seen that the area under the supply curve up to the
amount produced is the total private cost of production.
Now suppose that suppliers receive $8 per unit for each of
five units for a total of $40.
indicate
that
the
($4+$5+$6+$7+$8)=$30.
total
Our method of cost accounting would
private
cost
is
no
more
than
However, in the long run under perfect
competition there must be zero economic profit and firms would
therefore have revenues equal to opportunity costs. The difference
in the two views of costs is that our estimate of $30 takes the
view that part of the "costs" of firms are not costs from society's
viewpoint, but economic rents.
Economic rents are those payments
to factors of production above the minimum necessary to keep them
in an industry.
In other words, economic rents are that part of
the payments to factors such as a bricklayer, that is above his
opportunity cost as represented, for example, by the level of wage
he could receive by working in another industry.
The collection of economic rents received by factors of
production
in
an
industry
is
called
the
producers'
surplus.
Producers' surplus is represented by the area between the price
line, the supply curve, and the vertical axis, up to the quantity
produced.
The
producers'
surplus
can
be
considered
the
net
benefits of production to the supply side, just as consumer surplus
can be consider the net benefits of consumption to the demand side
of the market.
It is one of the remarkable things about perfect competition
is that it is perfectly efficient given certain conditions.
Some
of the conditions for its efficiency are merely the conditions for
its existence.
These include perfect information by all parties
about all prices and products, no uncertainty, that economies of
scale disappear at output levels small compared to the market
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demand at a price that reflects average cost, and that goods have
attributes that make private ownership possible.
An additional
condition for the efficiency of perfect competition is that there
are no externalities or third-party effects.
Since the subject of
environmental economics is basically one of applying the notion of
externalities to problems such as pollution and congestion, we will
have much more to say about this subject.
For now, let us turn to
Figure 2 to illustrate how perfect competition produces efficiency
under the ideal circumstances indicated.
By efficiency, it is
simply meant that overall benefits minus costs are maximized.
In
the Figure, it is seen that output Q* clears the market and that
area N is consumer surplus, and area M is producer surplus.
The
total benefits of the production and consumption of Q* is the sum
of producers' and consumer surplus.
Now suppose that we consider
the costs and benefits of expanding output to Q1.
One cannot know
how the benefits and costs would fall on various parties without
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describing the policy that would bring about such and increase in
output, but we can know what the effect on net benefits would have
to be.
Specifically, the increase in benefits associated with
greater consumption of the good would be represented by area G,
while the increase in production cost associated with the increased
output would be (G+H).
This implies that net benefits would go
down by an amount equal to H.
One can perform a similar analysis
to demonstrate that a reduction in output would also reduce net
benefits because consumption benefits would be decreasing faster
than the reduction in production costs. Under the circumstances
assumed, no form of government intervention can improve efficiency.
A POLLUTION EXTERNALITY: THE OUTPUT DIMENSION
We now consider a situation in which a perfectly competitive
industry produces pollution in direct proportion to the amount of
output it produces.
In other words, it is assumed that the ratio
of pollution (Z) to output (Q) is a constant equal to w=(Z/Q).
This pollution creates an external cost to society.
For example,
it z were an air pollutant, the external cost would be manifested
in an increased incidence of respiratory ailments in the general
population, reduced visibility, and damage to the surfaces of
buildings,
cars,
and
clothing.
Assuming
that
pollution
is
proportional to output makes it legitimate to plot these external
costs as a function of output.
Since they can be plotted as a
function of output, they can be placed within the same type of
diagram that we use for supply and demand.
We define marginal social cost (MSC) as the sum of marginal
private cost (MPC) and the marginal external cost (ME)
a unit of output.
created by
MPC is represented, for reasons we have already
discussed, by the supply curve.
Since marginal external cost is a
cost that is in addition to the private cost for the same unit of
output, we derive marginal social cost by the vertical addition of
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ME and MPC.
The result of this vertical addition are combined with
the supply and demand curves in Figure 3.
The diagram indicates
that the private market will yield and equilibrium output of Q0.
However, the efficient level of
output will be at Q*, where
marginal social cost equals the marginal benefits of the good.
Thus, the existence of a pollution externality implies that the
unregulated market will produce an excessive level of the good.
Given the goal of efficiency, how would a regulatory authority
design a policy to achieve the efficient level of output?
In the
present simple setting of perfect competition and the assumption of
an all-wise government, the answer is relatively simple.
The
private market will internalize the cost of pollution if it is made
to
pay
a
price
(external)cost.
for
the
pollution
equal
to
its
marginal
Specifically, the government would set a constant
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tax of T per unit of output, where T=ME*, and ME* is the level of
marginal external cost at the efficient output level. This tax and
its effects are illustrated in Figure 3. (Refer also to Figure 4.4
in Tietenberg, 7th edition.)
With most supply and demand curves the tax will cause the
price that demanders to pay to go up and the price that suppliers
receive to go down.
In other words, the tax creates a wedge
between the supply and demand prices, causing both sides of the
market to bear some of the burden of less favorable prices for
their sides of the market.
This is necessary because output must
be reduced and still maintain an equilibrium in the market where
neither
shortage
nor
surplus
exists.
In
basic
terms,
suppliers and demanders are made worse off by the tax.
both
Those who
buy and sell a good are not likely to wish it to be taxed even if
there is an externality.
Before quantifying losses to suppliers
and demanders, we turn to the basic point that there is a net gain
from this pollution tax.
In Figure 3 the area labeled A represents the net gain to
society of imposing the ideal pollution tax.
This area is derived
by subtracting the loss of benefits from output reduction from Q0
to Q* from the savings in social cost from that same reduction in
output.
This area represents a dollar number whose relative size
may not be especially large in comparison with the taxes collected!
You may well wonder if the cost of the tax does not indicate that
our calculation of net gain is incorrect and too optimistic.
However, the tax collected is not a social cost.
It represents a
transfer of resources from the private sector to the government.
These resources can presumably be returned to the general public in
the form of reduced levels of other taxes or increased spending on
goods provided by the government.
A real social cost of a
pollution tax would exist if there were administrative costs of
collecting these taxes.
In the present analysis we are ignoring
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such administrative costs, but recognition of such costs would not
necessarily argue against the use of pollution taxes, since all
taxes have such costs.
The area A+Y1+Y2 represents the reduction in external cost due
to the reduction in output from Q0 to Q*.
Since the vertical
distance between the MSC curve and the Supply curve represents
marginal external cost, the area between these two curves over the
range of output reduction represents the reduction in external
costs.
The area (V1+V2) represents tax revenue raised, which is a
pure transfer.
The areas (V1+Y1) and (V2+Y2) represent the losses
of consumer and producer surpluses due to the tax. Subtracting the
loss of surpluses from the reduction in external costs and the gain
in tax revenue leaves the area A as the net benefit associated with
bringing output down to the efficient level.
In discussing the uses of the pollution tax, we deliberately
did not state that these taxes should be used for compensation of
pollution victims.
The reason is that under present assumptions,
such compensation cannot improve efficiency and might well harm
efficiency. Compensation for pollution damage will harm efficiency
if such compensation reduces the incentive for individuals to keep
the overall costs of pollution to them as small as possible.
For
example, if someone could live far away from a pollution source and
make $50000 a year and have no medical costs or close to the
pollution source and make $52000 but pay for $3000 in medical costs
to counteract the effects of pollution, then efficiency dictates
that the person should live far away from the pollution.
However,
if the person were compensated for such pollution-related medical
costs, he would live near the pollution source.
In conclusion, under the present assumptions a tax per unit of
output equal to marginal external cost at the efficient level of
output with no compensation to victims of pollution will yield an
efficient market equilibrium.
The tax corrects the essential
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problem that the free market under-prices the output that creates
the pollution.
How much of the tax is passed on to consumers and
how much is absorbed by suppliers is of no importance as far as the
efficiency of the situation is concerned. The important feature is
that the tax reduces the output to the efficient level.
WHEN POLLUTION CAN VARY INDEPENDENTLY OF OUTPUT
We now consider the issue of pollution under the assumption
that pollution can be varied independently of output.
This is
clearly possible with most types of air and water pollution.
Various filtering processes on smokestacks can reduce emissions of
air pollutants.
Various changes in processes and in-factory
systems for recovering wastes can reduce the pollutants going into
our waterways.
However, all of these reductions in pollution
releases, holding output constant, require an extra expenditure of
money by the firm or person responsible.
To model the situation, consider Figure 4 where the horizontal
axis is measured in units of pollution (z), and all curves are
drawn holding the firm's output at q0. (See also Figure 15.2 in
Tietenberg, 7th edition in reference to the Figures 4 and 5 in these
Notes.) Figure 4 has both a right and left vertical axis.
The left
vertical axis hits the horizontal axis at the point of zero
pollution releases.
The right vertical axis hits the horizontal
axis at a point indicating the level of pollution that the firm
would release if it had no financial incentive to restrict its
pollution output.
This level of pollution is labeled z0, and is
the level of pollution which minimizes the cost to the firm of
producing a given output.
The vertical axes both measure concepts
in terms of dollars per unit of pollution.
Starting at the right axis and moving left, the level of
pollution released is declining.
Accordingly, the measure of
pollution eliminated is the horizontal distance from the right axis
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to the level of pollution actually released, which is algebraically
(z0-z).
The curve labeled mcz is the marginal cost of pollution
reduction curve.
Presumably, mcz starts at a zero level at z0,
since the cost of pollution control is at a minimum at that point.
MCZ rises as one moves from right to left and the amount of
pollution reduction is increased.
It is generally accepted that
for many pollutants the marginal cost of pollution reduction rises
extremely
rapidly
as
one
approaches
one
hundred
percent
elimination, and the mcz curve is drawn to reflect this.
The area
under the mcz curve from the right axis over to the amount of
pollution actual released can be interpreted as the total cost of
pollution control.
If pollution were reduced to level z*, then the
area labeled e would be the total cost of pollution control.
The curve md is the marginal damage curve and it is a function
of the actual pollution released.
The height of this curve
indicates the increase in damages to society from one more unit of
pollution.
At the aggregate level, this curve may be rising,
constant, or falling, although a rising curve is likely to be the
most common case for the pollution from an industry of firms.
Because each firm is a small contributor to the total pollution, md
is taken as constant.
Since we are discussing the issue currently
on the scale of a single firm, it is appropriate to assumed that md
is roughly constant.
The area under the md curve from the left
axis up to the actual level of pollution represents the total
damages from pollution released.
Within the context of this
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diagram, efficiency in the choice of pollution, or equivalently, in
the
choice
of
pollution
control,
is
characterized
by
the
minimization of the sum of pollution control costs plus pollution
damages.
In fact, total damages and total external cost are the same
concept.
However, marginal damage has the units of dollars per
unit of pollution, while marginal external cost has the units of
dollars per unit of output, so the marginal concepts do not have
the same units and one needs separate terms to keep them straight.
One may further view marginal damage as a measure of the marginal
benefit of getting rid of pollution, and the reduction in pollution
damages from eliminating a certain amount of pollution as the
benefits of that action.
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From the viewpoint of the firm the md curve does not matter in
any direct sense.
The firm will only be induced to engage in
pollution control if there is some direct financial incentive to do
so. Before deciding on what financial incentive to create, one has
to know what one would like to accomplish.
From the viewpoint
efficiency, the best level of pollution control is given by the
release of z* amount of pollution because that is where marginal
damage
of
pollution
pollution (md=mcz).
equals
the
marginal
cost
of
eliminating
At higher levels of pollution, the cost of
getting rid of another unit of pollution is less than the damage it
causes;
at
levels
of
pollution
lower
than
z* ,
the
cost
of
eliminating one more unit of pollution is greater than the damage
caused by that unit of pollution.
A financial incentive to reduce pollution could come in the
form of a pollution tax of amount t.
For given output (therefore
given revenue), the firm will desire to minimize the sum of
pollution taxes and pollution control costs, where the pollution
control costs are a function of how much pollution is reduced below
z0, and the pollution tax costs are going to be t times the amount
of pollution still released.
The solution to the firm's problem is to eliminate pollution
down to the point where the marginal cost of pollution control just
equals the rate of tax (t).
One can see this by noting that if the
cost of getting rid of one more unit of pollution is less than the
tax one would have to pay on it, then the firm's overall financial
burden is reduced by getting rid of that unit of pollution.
On the
other hand, if the cost of getting rid of another unit of pollution
is greater than the tax on that unit, then the firm will be better
of by paying the tax on that unit.
If the tax is set at the level of t*, then the firm will
choose to produce pollution at the level of z*, and incur t*z*
amount of pollution taxes and an amount equal to area e in control
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costs.
The pollution taxes reflect the size of the remaining
damages from the release of z* level of pollution by the firm.
The
area g is interpretable as the net benefit of inducing the firm to
eliminate the release of (z0-z*) amount of pollution.
That is,
potential damages of (e+g) have been eliminated, while control
costs of amount e have been incurred.
This diagram can be scaled up to the industry level with only
minor changes.
The scaling up involves the horizontal addition of
pollution levels from all firms, which requires an alteration of
the scale on which the horizontal axis is drawn.
To reflect the
larger scale, capital letters are used for the corresponding
concepts previously denoted with small letters.
In many cases,
this alteration of scale will imply that the aggregate marginal
damage (MD) curve should be drawn in an upward sloping fashion.
Figure 5 reflects the diagram drawn at an industry scale.
The
areas G and E are industry level of analogues of areas g and e from
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17
Figure 4.
G represents the net benefits of the efficient level of
industry pollution control, while E represents the control costs of
all firms.
With MD upward sloping, the total pollution tax
payments will exceed the area representing total damages form
remaining pollution. This latter concept is represented by area R.
As with the tax per unit output, there is a presumption that
the proceeds of the tax revenue are distributed in a way that is
independent of one's behavior or status as victim or polluter. The
tax revenue is a transfer of purchasing power to the government for
its redirection, and does not represent a social cost.
On the
other hand, both of these taxes effect output because of the
effective upward shift in supply (as viewed from the demand side)
caused by the financial burden of these taxes.
To relate these two
one has to keep in mind that T is a tax per unit of output and t is
a tax per unit of pollution.
At z* pollution and Q0 output, the tax
burden per unit of output would be (t*z*/Q0).
As we explore in more detail in the Appendix to this Chapter,
the pollution tax, by placing an a burden on extra output because
of its association with pollution, not only gives the proper
incentives to reduce pollution for a given output level, it also
gives the proper incentives for the industry to reduce output to
the efficient level.
Furthermore, in those cases where the ratio
of pollution to output can be varied, the pollution tax is superior
in efficiency to the output tax. Other things the same, efficiency
will be improved the most the more directly the policy is aimed at
discouraging the actual agent of the externality.
THE POLLUTION STANDARD APPROACH
(See
Tietenberg,
7th
edition,
pages
348-352
for
relevant
discussion.)
While many economists have long sung the virtues of the
pollution tax approach, it has been rarely used in practice.
More
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commonly, regulators are told to set pollution standards on firms.
The actual content of these regulations can be complicated for many
practical
reasons
measurement.
involving
difficulties
of
monitoring
and
We will address some of these issues later on.
For
now we take the simple view that a pollution standard is a
limitation on the absolute amount of pollution that a firm may emit
in a given period of time.
It is also assumed that the regulator
can costlessly monitor and enforce such a standard just as it has
been
assumed
that
the
pollution
tax
can
be
costlessly
and
accurately collected.
The theoretical issue at hand is whether such an approach can
achieve the efficiency associated with the pollution tax approach.
In terms of the ideal model, the answer is basically no.
In terms
of Figure 4, it is certainly possible to assume that the regulator
sets the pollution standard of the firm at the level z* and thereby
duplicate the pollution released under the tax approach for a firm
producing a given output. However, no taxes are being collected on
the remaining pollution.
This implies that the costs to the firm
do not reflect the damages remaining from the pollution still not
eliminated.
Therefore, the remaining pollution still creates a
truly external cost and the firms' average and marginal costs of
output will not reflect all costs to society.
Accordingly, the
market's equilibrium price for the good will be too low and output
will be too high compared with the efficient level.
Clearly, efficiency will be improved by the use of pollution
standard relative to doing nothing.
The reduction in pollution
associated with each output level does produce a net benefit.
In
fact, the extra control costs incurred because of the standard to
imply an upward shift in the supply curve and some reduction in
equilibrium output. However, the reduction in output is simply too
small to attain efficiency because of the absence of a tax to
reflect the remaining pollution damage.
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Some would argue that while a pollution tax may be superior
under certain ideal circumstances, in the "real world" the standard
approach is better.
However, there is at least one practical
informational problem that offers an additional argument for the
tax
approach.
One
might
suppose
that
the
regulator
has
a
reasonably good idea about the MCZ curve for the aggregate of
firms, but not very good information regarding the individual mcz
curves of firms.
All the regulator needs to know to set the
pollution tax at the appropriate level is the aggregate MCZ and MD
curves.
Individual firms responding to that common tax will all
equate their individual marginal costs of pollution control to that
tax.
This is efficient in that the aggregate costs of pollution
control will be at the minimum necessary to eliminate a given total
of pollution.
On the other hand, for a regulator to set a standard for total
pollution that can be enforced, it must set standards on individual
firms.
To achieve the same efficiency as the pollution tax all
those standards must be set so that the marginal cost of pollution
control is the same for all firms.
This is because any differences
in the marginal cost of control between two firms implies that the
total cost of pollution reduction could be lowered by having the
firm with the higher marginal cost reduce pollution one unit less
and the lower marginal cost firm reduce pollution by one unit more.
However, achieving equal marginal cost of control for all firms
using the standard approach requires the regulator to have detailed
knowledge of the control cost relationships of each and every firm.
Without this knowledge, the regulator is likely to use some rule of
thumb for deciding on emission reduction responsibilities.
One
such rule would be to have all polluters reduce their pollution by
X%.
While such a rule may sound reasonable, it is not likely to
lead to the reduction of pollution at the least total cost.
In
fact, such a percentage reduction rule requires that the regulator
20
be able to properly choose base levels from which to measure
pollution reduction as well as measure actual pollution itself.
Another practical consideration favoring the use of pollution
taxes is that the revenue raised can be used to substitute for
revenue from taxes that cause inefficient distortions in behavior.
An important example of a tax causing undesirable changes in
behavior is the income tax.
The income tax is applied to earnings
in the market, but not to the real income created when one does
chores for one's self such as washing the car, repairing one's
home, or cooking one's meals.
Nor does the income tax system count
the value of leisure as income.
This means that the income tax
encourages the substitution of non-market work and leisure for
efforts which create market income.
Such substitution effects
create a burden of taxation that is in excess of the direct burden
as measured by the taxes raised.
The pollution tax creates net benefits because of the changes
in behavior that it creates.
If the tax revenue could be used to
reduce taxes like the income tax, one might expect that it would
have the additional benefit of reducing some the inefficiency
associated with those taxes.
As it turns out, it is true that the
presence of other taxes does affect the amount of additional tax
one would place on pollution to achieve efficiency.
issue is complicated.
However, the
For example, suppose there are two private
goods produced, one is polluting, and there is a uniform rate of
tax on both goods that raises revenue for a public good.
If we now
consider raising the tax on the polluting good and lowering it on
the non-polluting good in order to raise the same revenue, it is
not always the case that the rate of tax on the polluting good will
be higher than that on the non-polluting good by an amount equal to
or greater than the marginal pollution damage caused by the good.
The reason is that pre-existing taxes distort the labor-leisure
choice and this distortion may be worsened by an adjustment in the
21
tax scheme.
SUBSIDY APPROACHES
At one time, some economists suggested that a subsidy per unit
of pollution eliminated would provide an equivalent incentive to a
pollution tax.
s*=t*.
Such a subsidy would be set at level s* such that
from the viewpoint of the firm, it would pay to reduce
pollution to z* for a given output level, since they would receive
more in subsidy than it would cost them in control cost for each
unit removed down to that level of pollution.
Below z*, the
subsidy would be less than the marginal cost of control (mcz), and
therefore those units would not be removed.
Subsidies sound nicer than taxes, so such an approach might
have
some
appeal.
However,
this
subsidy
approach
would
be
generally poor way to reduce pollution. In the first instance, any
subsidy implies the existence of taxes on something else in order
to fund the subsidy, so one does not really escape the need to
impose a tax. Furthermore, while the subsidy per unit of pollution
reduction does provide a positive incentive to reduce the level of
pollution for a given level of output, it provides the wrong
incentives when it comes to the output dimension of the pollution
problem.
A subsidy per unit of pollution reduction would more than
remove any burden of pollution control cost from the firm and not
add any burden for the remaining pollution still emitted. In fact,
the firm would presumably make a "profit" on removing the early,
less costly, units of pollution.
This means that the firms' net
cost of production would be lower than it was without any pollution
regulation at all. Therefore, since price will reflect average and
marginal cost in the long run, output will be priced below marginal
social cost and will tend to be larger than it was without
regulation. In an extreme case, where pollution relative to output
22
is lowered very little and output expands a great deal, total
pollution might actually increase from such a policy.
In fact, a subsidy per unit of pollution eliminated has not
been tried. However, subsidization of some portion of the costs of
pollution
control
has
been
tried.
Tax
laws
have
allowed
accelerated depreciation of some pollution control equipment.
At
one time the Federal government subsidized the construction of
waste water treatment plants.
By themselves, these cost subsidies
fall short of providing a positive incentive to reduce pollution
unless some of the benefits of treatment are internalized by those
receiving the cost subsidy.
Some internalization of the benefits
may have existed with the local governmental entities that received
the construction grants for waste water treatment since the local
population would presumably have gained something from improvement
in the water quality of nearby rivers and lakes.
We will analyze
this issue further when we discuss actual policies used in the area
of water pollution.
For an ordinary firm, it my be assumed that no internalization
of the benefits of reducing pollution would occur.
However, if
enforcement
because
of
pollution
standards
is
a
problem
of
limitations on the ability of the regulator to impose fines, then
a subsidy of costs may aid in ensuring the compliance of the firm
with the standard.
A firm weighing the cost of controlling
pollution against the fines and other penalties that might be
applied if the firm is discovered violating the standard, may be
swayed in the direction of compliance if some of the control costs
are paid for by cost subsidies.
Note that with this type of
subsidy, the firms' costs of production will always be more than it
would be with no regulation since the only way to receive a subsidy
is to incur some privately borne control costs.
Thus, the cost
subsidy approach does not have the potential for adverse output
effects that the subsidy per unit of pollution reduction has.
23
POLLUTION TAXES WITH NON-UNIFORMLY MIXED POLLUTANTS
(See also Tietenberg, 7th edition, pages 353-360)
The
previous
discussion
of
pollution
taxes
and
other
approaches to controlling pollution has assumed that the pollutant
is uniformly mixed into the medium into which it is released. For
example, with air pollution it is being assumed that emissions from
any polluting source have the same effect on the concentration of
pollution at every location at which a person might experience it.
This assumption is certainly factually incorrect, although for some
purposes it may be not too far wrong. However, if the pollution
levels around a source of pollution are much higher than they are
further away from the source and if all sources are not located in
a similar manner in their geographical relationship to the victims
of pollution, then the level of marginal damage per unit of
emissions is likely to vary across sources of pollution.
In this
case, the natural extension of the previous reasoning is to have
each source face an emission tax equal to the marginal damage that
its emissions cause at the efficient level of control.
To see how the emission tax would relate to the source’s
impacts on the victims, one has to consider both the number and
location of the victims as well as the way in which emissions
translate into pollution concentration levels at the sites of the
victims.
Suppose there are two sources of pollution, where the
source is designated generically by i=1,2.
Suppose for the moment
that there is only one location for the victims.
One may think of
the appropriate Pigovian tax per unit of emissions on source i as
being determined by ti=(mdc)ai, where mdc stands for marginal damage
per unit of concentration and ai is the rate of change of air
pollution concentration with respect to a unit of emissions from
source
i.
The
ai
is
sometimes
referred
to
as
the
“transfer
coefficient.”
In this formulation it is still true that the marginal damage
24
per unit of concentration is the same for both sources 1 and 2
since they are both affecting the same population in the same
location. Clearly, if source 1 is much closer to the receptor
victims of pollution, then its transfer coefficient will be higher
than for source 2 and the rate of tax per unit of emissions should
be correspondingly higher.
In a competitive market, a firm would
presumably only locate at a site with a higher rate of pollution
tax if there were some offsetting reduction in cost in another
aspect of its operations.
Now suppose that there are two locations, A and B, for the
victims of pollution.
These locations will vary in their distance
from each of the pollution sources.
In addition, the number of
individuals at locations A and B may not be the same.
Therefore,
to calculate the marginal damage of pollution emissions from a
source i one must consider its distinct transfer coefficients for
locations A and B, where these can be denoted as aiA and aiB.
Furthermore, one must consider the population levels at A and B,
denoted as NA and NB.
In this case the Pigovian pollution tax on
source i will be calculated as ti=(NAaiA+NbaiB)(mdcp), where (mdcp)
is defined to be the marginal damage per unit of concentration per
person, where this is assumed to be the same for all persons.
Thus, the Pigovian tax is calculated to account for the number of
people affected times the rate at which the concentration of
pollution increases with an increase in emissions at the location
of the particular groups.
Now if the transfer coefficients are
such that a1A=a2A and a1B=a2B, then the taxes on the two sources will
be the same.
However, in general one would expect that sources
located in different places will yield different marginal damage
per unit of pollution emissions. Furthermore, if the pollution
damage per unit of emissions is not the same, efficiency is no
longer served by equality of marginal cost of emission control
across sources of pollution.
Of course, firms will not be induced
25
to have equal marginal cost of emission control if the Pigovian
taxes vary from source to source depending upon location.
Administrative costs of having taxes or standards that vary
according to location may make the net benefits of such an approach
less than the costs.
In this case one gets into the area of
“second best” regulatory policy.
Second best resource allocation
is what occurs when efficiency is pursued with some limitation or
constraint on what one can achieve due to problems of insufficient
regulatory knowledge, ability, or other limitation. In a case like
the one being discussed a uniform Pigovian tax that produced the
most efficient outcome given the fact that different sources of
pollution create different marginal damage per unit of emissions
would be called a second best Pigovian tax.
Roughly speaking, a
second best uniform tax would be a weighted average of the first
best set of locationally differentiated taxes.
The
problem
of
pursuing
second
best
policies
repeatedly in discussing environmental policies.
comes
up
A second best
problem that is quite different from the one just discussed is
addressed in the section on the monopoly polluter. The inability of
regulators to vary the pollution tax from times when pollution is
higher to when pollution is lower creates a problem of a similar
second best nature to the one just discussed. Unfortunately, it is
hard to make general statements about the nature of second best
policies since there are a huge variety of possible limitations on
the ability of regulators to attain the first best allocation.
In
all cases, one has to carefully assess the benefits and costs of
each available policy compared with the alternatives.
ZONING AS A COMPLEMENTARY APPROACH TO CONTROLLING EXTERNALITIES
(There is virtually no reference to zoning in Tietenberg.)
Zoning rules determine what kinds of activities can be placed
in what locations.
Some areas are zoned for single family homes
26
only.
Other areas are zoned for commercial and industrial use.
Minimum lot sizes may be set for houses.
Minimum amounts of open
space between a commercial building and the street may be set.
The
unique aspect of zoning in comparison with the previous discussion
of pollution taxes and standards is its emphasis on the spatial
arrangement of actions that may cause externalities.
While, as just discussed, pollution taxes in particular, and
externality taxes in general, can account for differences across
locations in the marginal damage caused by pollution, there is a
coordination issue that may be more easily addressed by zoning
regulations than by Pigovian taxes.
For example, it may be clear
that houses and steel mills should be located in separate places.
However, exactly which place each activity should be located may
not be clear.
It may be useful to have a zoning plan that states
that houses will be in the east part of the jurisdiction, and steel
mills will be in the western part, so that a potential homeowner
does not guess incorrectly where the steel mill is going to be
built. Thus, zoning is most uniquely aimed at arranging activities
so that the total external cost or damage from a given amount of
different activities is at its lowest level.
To be more concrete,
a zoning regulation is trying to locate the polluting activities in
places where the exposure resulting from the pollution emissions
will be as low as possible, other things being the same.
Of
course, other things are seldom the same. Restricting the location
of particular types of firms may increase the overall cost of those
firms producing a given amount of output and pollution.
there will be trade-offs.
Thus,
One simple trade-off may be between
locating the polluting firm farther away from a population center
while at the same time increasing its costs of delivering its
product to that population center.
Of course, if the amount of land area allowed for a certain
activity
also
raises
the
cost
of
particular
types
of
firms
27
operating
and
will
tend
to
limit
both
output
and
pollution.
However, when one restricts land area for an activity, one is
restricting
the
use
of
only
a
single
input
into
production.
Restricting a single input, particularly when that input is not one
closely associated with the negative externality, is unlikely to be
the most efficient way to limit the total amount of an externality
creating activity.
THE MONOPOLY POLLUTER AS A SECOND BEST PROBLEM
(Tietenberg, 7th edition, discusses monopoly on pages 76-78, but
does not include an externality problem.)
We have heretofore assumed that all the markets are perfectly
competitive, and that the pollution problem in the market we
analyze is the only imperfection in the economy.
real world is far more complicated than this.
Of course, the
A general rule of
thumb in trying to attain the first best level of efficiency, is
that the government needs as many instruments of control over the
economy as there are sources of deviations from efficiency.
When
the regulator has fewer instruments of control than necessary to
produce a first best efficient solution, we are said to be a
situation of seeking a second best optimum.
Among the countless reasons why one might be in a situation of
seeking the best "second best" solution to externality problem is
that it may be prohibitively expensive to observe, and therefore
directly regulate, some sources of pollution.
The regulator might
then seek indirect ways of controlling the pollution through the
regulation of the uses of certain types of inputs which may be
strongly related
to the pollution releases.
Or the regulator may
specify that certain technologies must be used, or in other cases,
certain technologies may be prohibited. These types of regulations
do occur and we may suppose that they do so in response to certain
problems of measurement and observability of pollution.
We will
28
explore these types of issues in more detail when we discuss actual
regulatory policies in use.
For the present, it is worthwhile to explore a relatively
simple problem in seeking second best efficiency which illustrates
the potential for surprising outcomes.
Consider an unregulated
monopoly which produces an output by a process which simultaneously
creates a pollutant in fixed proportion to the output.
The
unregulated monopolist will maximize profits by setting marginal
revenue (MR) equal to marginal private cost (MPC), of which the
latter is assumed to be constant.
Because the marginal revenue
curve is below the demand (D) curve, the monopolist will charge a
price above its marginal private cost.
The marginal social cost (MSC) curve is drawn so that it hits
29
30
the demand curve at exactly the monopoly price.
This is merely
fortuitous, and not in any way a necessary feature of the example.
However, the implication of this particular situation is that the
monopolist is setting output exactly at the efficient level.
A
pollution tax would, in fact, cause the monopolist to reduce output
below the efficient level.
In other words, the monopolist's
tendency to charge a price above marginal (private) cost works in
this case to reduce output by the amount desired.
In a sense, the
monopolist is (accidently) charging (and collecting) the right
level of pollution tax.
Thus, in this case the effects of the two
problems of monopoly and pollution simply cancel each other out as
regards efficiency.
Of course, the curves may be drawn so that the monopolist's
price is higher than marginal social cost, in which case some
regulation designed to lower price would be necessary to produce
efficiency.
If the monopolist's price were to be below marginal
social cost then a policy would be called for which raised the
price charged to the consumer.
However, the nature of the tax that
would create this result would have to be calculated in manner
differently from simply setting it equal to marginal external cost
at the efficient output level.
Exactly how one would compute such
a tax would require a discussion more complex than the importance
of the example would warrant.
But the reader should be convinced
the most efficient policy toward a negative externality in a second
best world may depart substantially from a simple application of a
pollution tax.
31
APPENDIX
THE INTERACTION OF POLLUTION AND OUTPUT WITH A POLLUTION TAX
(Tietenberg, 7th edition, does not address in any significant way
the
interaction
of
the
pollution
and
output
dimensions
in
discussing the effects of pollution taxes, standards and other
approaches to controlling pollution externalities.)
The effects of imposing a pollution tax extend to the output
dimension.
The pollution tax adds to the costs of the firm by
causing the firm to incur pollution control costs and by imposing
the pollution tax itself.
This will add to the marginal and
average cost of producing output by each firm and therefore affect
the supply curve and equilibrium price and output.
Figure
meant
costs
to
illustrate
how
the
concepts
of
control
is
(E),
remaining pollution damages (R), and the net benefits of pollution
control
(G)
can
be
translated
from
Figure
5
to
the
output
dimension.
Holding output constant at Q0, the same level as in the Figure
5, we have designated two marginal social cost curves, MSC0 and
MSC*.
The higher curve (MSC0) represents the marginal social cost
of output when pollution is uncontrolled; that is, when each firm
incurs no control cost in order to reduce pollution.
In this case,
amount of pollution per unit of output is presumably quite high.
Marginal external cost is therefore at a level corresponding to
ME0=(MD)w0, where w0 represents the ratio of pollution to output
with uncontrolled pollution.
The lower curve (MSC*) represents
marginal social costs with a level of pollution control which
equates the marginal costs of control with the marginal damage of
pollution.
Thus, ME*=(MD)w*, where w* is the ratio of pollution to
output when pollution is controlled at an optimal level for any
given output.
The difference in heights between these two marginal social
cost curves represents the difference in marginal social cost of
32
output
under
no
control
and
optimal
control
of
pollution.
Incrementing these differences over all the units of output up to
Q0 gives a net reduction in social cost at that amount of output
that exactly corresponds to the net benefit of pollution reduction
33
34
in Figure 5, which is designated in Figure 7, as well as in Figure
5, by the letter G.
The
two
(lower)
curves
in
Figure
7
are
marginal private cost curves (MPC0 and MPC*).
identifiable
as
The lower curve
(MPC0) is the supply curve under the assumption that no control
cost is incurred.
The higher curve (MPC*) is the supply curve
under the assumption that the firm incurs the pollution control
costs necessary to equate marginal damage to the marginal control
cost, but does not pay any pollution tax.
In other words, MPC* is
the supply curve under the imposition of an ideal standard at each
level of output on firms.
Accordingly the difference in the
heights of the two curves represents the difference between the
cost of adding another unit of output when the firms do not have to
control
pollution
and
when
they
pollution to the efficient degree.
have
to
control
additional
The area between the two MPC
curves up to the output level Q0 thus represents the pollution
control costs designated in this Figure 5 and Figure 7 as area E.
By construction, it follows that the difference in the heights
of
MPC*
and
MSC*
represents
the
marginal
external
cost
when
pollution is controlled to level at which marginal damage equals
the marginal cost of control at every level of output.
words,
MSC*=MPC*+ME*,
where
ME*=(MD)w*.
Accordingly,
In other
the
area
between MPC* and MSC* up to the output Q0 therefore represents total
external cost, which is the same as total damages, remaining after
efficient pollution control has taken place.
In Figure 5 and in
Figure 7, this area is represented by R.
In Figure 8, these curves have been reproduced with the
purpose being to indicate graphically the nature of the area
representing
the
net
gain
from
comparison with doing nothing.
using
the
pollution
tax
in
This is not simply the area G as
previously represented, because the reasoning leading to the area
G ignored the effect of the pollution tax on output.
Taking Q0 as
35
36
the market output when there is no regulation, the output that will
result when there is a pollution tax will be determined by the
intersection of the MSC* and demand curves.
This will yield the
output level labeled Q*.
The overall increase in net benefits from the pollution tax
will
be
the
result
of
lowering
the
marginal
social
cost
of
producing the output Q0 and the reduction in excessive output
created by the effective upward shift in the supply curve to
reflect the true marginal social cost of output.
This mixture of
areas like G in Figure 5, and A in Figure 3, leads to the area M+J
in Figure 8, where M+J includes all of the areas indicated by M or
J.
The net gain indicated by area M+J is larger than G because of
the favorable reduction in output created by the pollution tax.
Given the definitions of the curves, the net benefits of using
a pollution standard approach can be calculated by recognizing that
the equilibrium quantity in the market will be determined by the
intersection of the MPC* and demand curves.
This output is labeled
Qs and is somewhat larger than optimal because MSC* is higher than
the demand price at that output.
However, the relative loss from
using a standard rather than a tax is not particularly large in
this diagram.
It amounts to the area J defined by the gap between
the demand (marginal benefit) curve and the (lower) marginal social
cost curve (MSC*) between the outputs Q* and Qs.
All the area M
(not including J) would be the net benefit of using a standard
approach relative to no regulation.