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Chapter 4
Negative Externalities and Policy
Contents: General Overview
Production Externalities
Policy 1: Externality Tax
Policy 2: Output-reduction Subsidy
Policy 3: Standards
Elasticity Effects on Magnitude of Externalities
Imperfect Competition and Externality Policy
Consumption Externalities
Externalities from Cigarette Smoking
The Economics of Illicit Drugs
General Overview
An externality can only exist when the welfare of some agent, or group of agents,
depends on an activity under the control of another agent. Under these circumstances, an
externality arises when the effect of one economic agent on another is not taken into account
by normal market behavior.
Externalities are a type of market failure. When an externality exists, the prices in a
market do not reflect the true marginal costs and/or marginal benefits associated with the
goods and services traded in the market. A competitive economy will not achieve a Pareto
optimum in the presence of externalities, because individuals acting in their own self-interest
will not have the correct incentives to maximize total surplus (i.e., the “invisible hand” of
Adam Smith will not be “pushing folks in the right direction”). Because competitive
markets are inefficient when externalities are present, governments often take policy action
in an attempt to correct, or internalize, externalities.
Externalities may be related to production activities, consumption activities, or both.
Production externalities occur when the production activities of one individual impose a cost
or benefit on other individuals that are not transmitted accurately through a market. Let us
first examine production externalities, for example, air pollution from burning coal, ground
water pollution from fertilizer use, or food contamination and farm worker exposure to toxic
chemicals from pesticide use. We will then analyze the case of consumption externalities,
which occur when the consumption of an individual imposes costs or benefits on other
individuals that are not accurately transmitted through a market.
Production Externalities
To motivate the concept of a production externality, consider the following
examples:
A farmer takes irrigation water out of a river before it reaches a wildlife refuge.
The farmer’s actions reduce the flow of water reaching the wetland, which
reduces the amount of wetland acreage available to waterfowl. Consequently,
fewer birds are attracted to the refuge, which decreases the utility of
birdwatchers. If farmers had to account for the value of the lost utility to
birdwatchers (i.e., there was a price associated with a reduction in birds), they
would probably reduce the amount of irrigation water they pumped from the
river.
A more common example is the case of a firm polluting an air or water source as a
by-product of production. Examples here include, the production of refrigerators
using CFC’s, a coal-burning electricity plant (NO x
and SO x
), or a paper mill, which
dumps chlorine bleach into a river as a by-product of producing white office paper.
In the Far East of Russia, there is also a huge health issue that is created by gold
mining. The mine-owners use magnesium to separate gold ore from quartz, but do
not recycle the magnesium. Instead they wash it into the river, which is the source
of drinking water for cities in Eastern Russia, such as Vladivostok and Khaborovsk.
Partly as a result of poor water quality, the life expectancy citizens in the Russian
Far East has dramatically decreased
Figure 4.
Production Externalities and the Failure of Competitive Markets
MPC = marginal private cost (inverse of the private supply curve)
MEC = marginal externality cost (suffered due to pollution)
MSC = social cost (vertical sum of MPC and MEC)
Social optimum at B (where MSB=MSC)
Social Benefits = ABQ
O.
Social Costs = OBQ
Social Welfare = ABO.
Free market outcome at C
Social Benefits = ACQ
c O.
Social Costs = OCQ
c
c .
Social Welfare = ABO - BEC.
Deadweight Loss = BEC.
An example of a case where pollution is directly related to output:
Because a competitive economy will be inefficient (will not achieve a Pareto
Optimum) in the presence of externalities, combating externalities is a legitimate arena for
government policy. The policy goal is to move the economy to a socially optimal point such
as point B in Figure 4.1, where MSB (i.e., Demand) equals MSC.
This social optimum may be achieved by any of several policies. We will examine
three policies:
(1) a Tax
(2) a Subsidy
(3) a Restriction, Standard, or Quota
We will find that the choice of policy has implications for the distribution of
economic benefits among producers, consumers and government.
Before we begin our analysis, we should briefly discuss the targeting of externality
control policies. Targeting refers to the process of deciding which economic variable (e.g.
output quantity or input price) should be regulated in an attempt to control the externality.
Each policy mentioned in the preceding paragraph can be targeted in several ways. Typical
targets include outputs, inputs, or the externality-generating activity itself (i.e., the pollutant).
In most cases, targeting the externality-generating activity itself, or its associated price, is the
most efficient approach, because targeting outputs or inputs (or their prices) creates
distortions in the relative prices of goods and thus generates other economic inefficiencies
(in a general equilibrium).
Policy 1: Externality Tax ("Pollution Tax") or Output Tax
Production Tax: Suppose the government establishes an Externality Tax of t* = P* -
P
P
. It is easy to show that a tax of t* is the required market correction to achieve Q*
units of production. This fact can be seen graphically in figure 4.1 when we realize
that the firm treats the tax rate as an additional component of its marginal private
cost; that is, a unit tax of t* shifts the MPC curve upwards in a parallel fashion by
the distance t. The optimal tax (i.e. the one that achieves Q) is clearly t* =
MEC(Q*).
The welfare implications of the Externality Tax are:
Consumer surplus= ABP*
Producer surplus = OFP
P
Government revenue= P*BFP
P
If the government knows how much pollution is produced per unit of production
output, then the government can set a tax on production output that achieves the same results
as an externality tax. In practice, however, the relationship between pollution and production
output is often very difficult to estimate with any degree of precision.
Keep in mind that the government revenue from either type of tax not only corrects
the externality, it also gives the government the opportunity to reduce other, distortionary
taxes (such as income taxes or sales taxes) in the economy, thereby eliminating other
deadweight losses in the economy. This is the so called Double Dividend of environmental
taxes. Such spillover benefits from one market to another can be computed using general
equilibrium models.
We can easily show that the appropriate externality tax, t*, needed to bring
unregulated competition in line with the social optimum by:
t* = E Q
(Q) = MEC(Q)A unit tax of t* results in the following private optimization
problem:
Max Q PQ C Q t Q
Q
which yield the FOC:
π Q ( Q ) = P − CQ ( Q ) − t *= 0
or,
P = C
Q
(Q) + t*
Since P = MB at all points along the demand curve, and since the regulator has set t* =
E
Q
(Q*), we can express the private condition (which is identical to the condition for a social
optimum) under the tax as:
B
Q
(Q*) = C
Q
(Q*) + E
Q
(Q*)
Consumption Tax: It is also useful to show the equivalence of a tax on production and a
sales tax on the consumption of the polluting good. When a sales tax is
implemented in place of a production tax, the residual demand curve for firms in the
market shifts downward to represent the net price of each unit sold. The net price,
or Net Marginal Benefit (NMB), is the Marginal Benefit of consumers less the level
of the sales tax (NMB = D - t*).
Figure 4.
Q*= social optimum output, P c
= optimal consumer price
P
s
= P
c
- t = net producer price, t = externality
Policy 2: Output-reduction Subsidy
The second policy consists of a subsidy to producers for reducing pollution or for
reducing output. Example: The government pays a subsidy = P* - P
P
for each unit of
output that is not produced.
Elasticity Effects on the Magnitude of Externalities
P
c
, Q
c
= Competitive price and quantity in the market
P
i,
Q
i
= socially optimal price and quantity when demand is inelastic
P
e
, Q
e
= socially optimal price and quantity when demand is elastic
The answers to important policy questions often depend on the magnitudes of key
elasticities. Figure 4.3 shows that the elasticity of demand affects the degree of inefficiency
associated with a production externality. When demand is inelastic, the socially optimal
level of production, Q i
, is not too far from the competitive level of production, Q c
. In the
extreme case of infinitely inelastic demand, demand may be vertical at the point Q c
, so that
the unregulated and regulated outcomes coincide. Under conditions of highly inelastic
demand, the inefficiency associated with a production externality may be small, so that it
may not be worth regulating the externality. Under highly elastic demand conditions,
however, the socially optimal level of production, Q e
, is farther away from the competitive
level, Q c
. In this case, the inefficiency associated with the production externality may be
relatively large, so that regulation may be desirable.
In some cases, depending on the value of the demand elasticity, producer profit may
actually increase under pollution regulation. In figure 4.3, if demand for the final product is
inelastic, then a regulation that decreases production, such as a quota/standard designed to
reduce pollution, will move producers towards the monopoly level of output. In such a
case, producers may actually desire regulation, because the increase in market price
associated with a lower level of production may actually increase producer surplus. The
more inelastic the demand is, the higher are producer revenues under regulation and firms
are more likely to gain increased profit under pollution regulation.
Imperfect Competition and Externality Policy
Figure 4.
High MSC
Low MSC
MPC
D
M
R
Qm Q*low
w
Q*high Qc Q
$
A
B
In figure 4.4, we can consider two cases:
One in which MSC is relatively low (i.e. MEC is small); low MSC
One in which MSC is relatively high (i.e. MEC is large); high MSC
In both cases, unregulated competition produces too much output, at point Qc
Under a monopoly, however, the unregulated monopolist may produce either too much or
too little from a social perspective. In the case of “low MSC”, the optimal output, Q* low
, is
larger than the monopoly output, Qm. Hence, under a monopolistic market structure,
externality control regulation may not be warranted. In fact, the optimal policy may be to
subsidize the polluting monopolist to produce more of the polluting good.
In the case of “high MSC”, the monopolist produces “too much” output from a
social perspective, because Q* high
< Qm. The optimal tax policy for monopoly, in this case
is t* = the distance AB. In that case, MPC + t* will intersect the Marginal Revenue curve at
point B, which causes the monopolist to produce the optimal amount.
In markets with externalities, a monopoly market structure is preferable to
unregulated competition whenever the monopolist produces “too much” output.
So that the result of regulated competition,
B
Q
(Q*) = C
Q
(Q) + t,
where:
t* = MEC(Q*) = e f
a - c - e
d + f + b
e(d b) f(a c)
d f b
produces the socially optimal allocation.
Unregulated Monopoly
A profit-maximizing monopolist sets MPC = MR, where MR (marginal revenue) is
the derivative of R (total revenue) and total revenue is R = P(Q)Q, or, recognizing demand:
R = (a - bQ)Q ⇒ R = aQ - bQ
2
⇒ MR = a - 2bQ
Then, setting MPC = MR:
c + dQ = a - 2bQ ⇒ Q
M
a - c
d + 2b
P = a - bQ ⇒ P
M
= a -
ba - bc
d + 2b
Compare the monopoly solution with the social optimum. Under what conditions
will the monopoly solution coincide with the social optimum?
Unregulated Middleman:
The unregulated middleman seeks to set MR = MO, where MO (marginal outlay) is
the derivative of Outlay, which is defined as: Outlay = MPC(Q)Q.
Thus, the objective function of the middleman is:
{ }
Max a bQ Q c dQ Q
Q
which has the following FOC:
π Q = a − 2 bQ − c − 2 dQ = 0
Note: This can also be solved by calculating the marginal outlay:
Outlay = (c + dQ)Q ==> MO = c + 2dQ,
then, setting MR = MO:
MR = a - 2bQ = c + 2dQ ⇒ Q
D
a - c
2(b + d)
The middleman finds the price (s)he will pay producers by substituting Q
D
into the
equation for MPC:
P
P
= c + dQ ⇒ P
P
= c +
d
a - c
b + d
The middleman finds the price (s)he will charge consumers by substituting Q
D
into
the equation for inverse demand (D):
P
C
= a-bQ ⇒ P
C
= a-
b
a-c
b+d
Compare the middleman solution with the social optimum. Under what conditions
will the middleman solution coincide with the social optimum?
Practice Problem 4.1:
Assume an econometrician provides you with the following parameter estimates for
the economic model presented in this example:
a = 50
b = 1
c = 0
d = 1
e = 0
f = 1.
Find (1) the social optimum, (2) the unregulated competition result, (3) the unregulated
monopoly result, and (4) the unregulated middleman result.
Answers to Practice Problem 4.1:
(1) Social Optimum:
Q
a - c - e
d + f + b
⇒ Q = 14.28, P
= a -
ba - bc - be
d + f + b
⇒ P = $35.
(2) Unregulated Competition:
Q
C
a - c
d + b
⇒ Q = 25 P
C
= a -
ba - bc
b + d
⇒ P = $
(3) Unregulated Monopoly:
Q
M
a-c
d+2b
⇒ Q=16.66 P
C
= a-
ba-bc
d+2b
⇒ P=$33.
(4) Unregulated Middleman:
Optimal tax on consumption externality: t* = MEC(Q*)
P*cons = optimal consumer price
Pprod = Pcons - t* = net price received by producers at production quantity Q*
Externalities from Cigarette Smoking
Health Costs Associated with Smoking:
Smokers' health costs shared by society.
Cost of family support (in case of early death).
Risk to nonsmokers (second-hand smoke).
Estimated Death Toll (1989):
Activity Annual Deaths
Cigarettes 400,
Alcohol 150,
Drugs 30,
Estimated Annual external costs of smoking:
$ 35 billion (medical cost)
$ 20 billion (lost work)
$ 5 billion (fires, smoke, odor damage)
$ 60 billion (total cost)
Policy alternatives to control cigarettes:
(1) A cigarette tax or tobacco tax.
(2) A standard/quota to restrict quantities of cigarettes and tobacco.
Approximately 30 billion packs of cigarettes are smoked annually. If marginal externality
cost = average externality cost, then the tax should be $2.00 per pack ($60 billion / 30
billion packs).
Policy consequences:
(1) Producers: Restriction on quantities may benefit producers or distributors if
elasticity of demand is smaller than 1.
(2) Tax Shifts Benefit the Government: Tax revenues can be used to compensate
victims of smoking damages, or it can be used in lieu of other, distortion taxes
(such as income taxes, sales taxes, etc.) to support government programs.
(3) Unintended Consequences: May strengthen the case for the legalization of
drugs.
The Economics of Illicit Drugs
If cigarette smoking is legal, why should illegal drugs not be legal? It is
interesting to many economists that our society has chosen to regulate illicit drugs
differently than cigarettes. Some economists, including Milton Friedman and Gary Becker,
have argued for a drug legalization policy similar to the policy for cigarettes.
The Proposal of the Following:
(1) Legalize illicit drugs.
(2) Ban advertisement and sale to minors.
(3) Institute a tax on drugs.
Benefits:
Increased government revenue.
Reduced government costs (fewer prisoners and less drug enforcement).
Reduced crime.
Costs:
Increased addiction.
Legalization may induce more to try.
Economic Impacts:
- Legalization of drugs would shift income from the illegal network of drug
traffickers to government (taxes) and legal marketers (pharmacies).
- Drug producers may be better off if drug cartels behave like the middlemen, since
eliminating drug trafficker middlemen may result in increased quantity and
higher producer prices. Hence, poor coca farmers in developing countries, for
example, may benefit from legalization.
The costs of crime enforcement may go down.
Consumer prices (inclusive of taxes) may go down and quantity may go up.
There may be higher health costs associated with drug addiction.
Economic analysis of the proposal requires assessment of:
Market structure under current arrangements.
Market structure after legalization.
Externality cost of health and crime.
Demand for drugs when they are legal and illegal.
We can assess these items by developing answers to questions such as: Is the
current marketing network competitive? monopolistic? monopolistic competitive?
middlemen? Analytical tools we have developed in this lecture may help us to answer these
questions.
