# Negative Externalities ```Chapter 4:
Negative Externalities
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
Externalities are a type of market failure
-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.
Externalities may be related to production
activities, consumption activities, or both.
-Production externalities: production activities of one
individual imposes costs/benefits on other individuals that
are not transmitted accurately through a market.
-Consumption externalities: consumption of an individual
imposes costs or benefits on other individuals that are not
accurately transmitted through a market.
Examples of production
externalities






Air pollution from burning coal
Ground water pollution from fertilizer use
Food contamination and farm worker exposure to
toxic chemicals from pesticide use
Irrigation water and consequential decline of
waterfowl population in nearby wildlife refuge
Production of refrigerators using CFC’s
Health issues resulting from gold mining
Production Externalities
Social optimum at B (where MSB=MSC)
MSC Social Benefits = ABQ* O.
Social Costs = OBQ*.
Social Welfare = ABO.
\$
A
MPC
E
B
G
P*
C
PC
PP
MEC
F
H
Free market outcome at C
Social Benefits = ACQcO.
Social Costs = OCQc + OEC = OEQc.
Social Welfare = ABO - BEC.
Deadweight Loss = BEC.
D
Q*
QC
Mathematical Representation of production externalities
The Social Welfare Maximization Problem is:
Max{W(Q)=B(Q)-C(Q)-E(Q)}
Q
where:
Q = Output
B(Q) = Total Social Benefit of Producing Q.
C(Q) = Total Private Cost of Producing Q.
E(Q) = Total External Cost of Producing Q.
W(Q) =Social Welfare Function (Total Surplus From producing Q)
Social Welfare is maximized where Q satisfies the First-Order
Condition (FOC):
WQ=BQ (Q)-CQ (Q)-EQ (Q), which can be rearranged as
BQ(Q) = CQ(Q) + EQ(Q)
Where:
BQ(Q) =the partial derivative of B(Q) with respect to Q=MB
CQ(Q) = the partial derivative of C(Q) with respect to Q=MPC
EQ(Q) = the partial derivative of C(Q) with respect to Q=MEC
Socially optimum output, Q*, occurs when MB = MPC + MEC.
Unregulated competition with
externalities
Under unregulated competition, firms
maximize profits, resulting in the
FOC:BQ(Q) = CQ(Q), or MB = MPC.
When this FOC is solved for Q, call it QC,
we find that QC&lt; Q* whenever MEC &gt; 0.
Because QC Q*, QC is inefficient.
Policies to achieve social
optimum Q*
Three possible policies:
-Tax
-Subsidy
-Restriction, Standard, or Quota
Choice of policy affects the distribution of
economic benefits among producers, consumers
and government.
Targeting: Process of deciding which economic
variable to control to reduce externality.
Ex. Outputs, inputs, or the externality-generating
activity itself (i.e., the pollutant).
Policy 1: Tax-1
Externality Tax: t* = P* - PP=MEC (Q*), where
t* is the required market correction to achieve Q*
units of production. \$
MSC
A
E
MPC
B
P*
PC
PP
F
G
C
H
MEC
D
Q*
QC
Firms treat the tax rate as an additional component
of their marginal private cost; that is, a unit tax of
t* shifts the MPC curve upwards in a parallel
fashion by the distance t*.
Mathematical expression
t* = EQ(Q*) = MEC(Q*).
Private optimization problem:
Max {(Q)=PQ-C(Q)-t*Q}
Q
FOC:
Q(Q)-P-C Q(Q)-t*=0 or, P = CQ(Q) + t*.
Since P = MB at all points along the demand
curve, and t* = EQ(Q*), we can express the private
condition (which is identical to the condition for a
social optimum) under the tax as:
BQ(Q*) = CQ(Q*) + EQ(Q*)
Welfare implications of externality tax
Consumer surplus= ABP*
Producer surplus= OFPP
Government revenue= P*BFPP
\$
MSC
A
MPC
E
B
P*
PC
PP
F
G
C
H
MEC
D
Q*
QC
Policy 1: Tax-2
Production tax: If the government knows
how much pollution is produced per unit of
production output, then it can set a tax on
production output that achieves the same
results as an externality tax. However, the
relationship between pollution and
production output is often very difficult to
estimate with any degree of precision.
Policy 1: Tax-3
Consumption Tax:
Sales tax on polluting goods.
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*).
Q*=Social Optimum output
Pc*=Optimal Consumer price
Ps*=Pc*-t=net producer price
t=consumption tax
Policy 2: Output-reduction Subsidy
Subsidy = P* - PP for each unit of output that is
not produced.
If Q = the current level of output, firms in a
competitiveQindustry have the following
objective: Max.  PQ  C(Q)  (Q  Q)S , and
FOC= Q  P  C' (Q)  S  0
Optimal subsidy level: (i.e., the unit subsidy that
equates the optimal social and private outcomes)
S* = t* = MEC(Q*).
Welfare implications of subsidy
Consumer surplus = ABP*.
Producer surplus = OFBP* + BGHF,where
BGHF = (P* - PP)&middot;(Qc - Q*)].
Government expenditure = BGHF.
\$
MSC
A
MPC
E
B
P*
PC
PP
F
G
C
H
MEC
D
Q*
QC
Problem with subsidy
In the long run, subsidies for pollution
reduction may actually increase pollution
because the subsidy may attract more firms
into the market.
Policy 3: Standards on
Pollution/Output
Command-and-control approach
through production quotas to restrict
output to Q*.
Welfare implications of quotas
Consumer surplus= ABP*
Producer surplus= OFBP* (larger than it is for
Externality Tax)
Government revenue= zero (smaller than it is for
MSC
Externality Tax) \$ A
E
MPC
B
P*
PC
PP
F
G
C
H
MEC
D
Q*
QC
Government allocates Q* Units of pollution
permits to industry
The price of a permit will be P*
The government will not need to pay subsidies
and producers will not need to pay taxes.
It may be desirable from the political economy
perspective
Production Externalities:Example
Inverse demand (D) = Marginal Benefit (MB)= a - bQ
Marginal private cost (MPC)=C(Q) = c + dQ
Marginal externality cost (MEC) = e + fQ
Marginal social cost (MSC) = MPC + MEC = c + dQ + e
+ fQ = c + e + (d + f)Q
Social optimum
The Social Optimum is where MB = MSC
Marginal Benefit (MB)= a - bQ
Marginal social cost (MSC) = MPC + MEC = c + dQ
+ e + fQ = c + e + (d + f)Q
a

c

e
c  e  dQ  fQ  a  bQ &THORN; Q* 
df b
P*  a  bQ&THORN;
 ba  bc  be 
P*  a  

 df b 
Numerical Example
Scenario
a (demand
intercept)
c (supply
b (demand intercept d (supply
slope)
)
cost)
20
2
Q (quantity)
Competition
5.33
P( Price)
9.33
4
1
Consume
t( tax) r surplus
0.00
28.44
e (m
extern. f (m extern.
intercept)
cost)
2
0.5
producers Environment Government
Total
surplus
surplus
revenue surplus
14.22
-17.78
24.89
tax
4.00
12.00
4.00
16.00
8.00
-12.00
16.00
28.00
Subsidy
4.00
12.00
-4.00
16.00
40.00
-12.00
-16.00
28.00
permit
4.00
12.00
0
16.00
24.00
-12.00
0.00
28.00
a equals
Competition
24
6.67
13.33
0.00
35.56
31.11
-24.44
tax
5.14
13.71
4.57
26.45
13.22
-16.90
23.51
46.29
Subsidy
5.14
13.71
-4.57
26.45
60.24
-16.90
-23.51
46.29
permit
5.14
13.71
0
26.45
36.73
-16.90
0.00
46.29
42.22
Unregulated vs. Regulated Competition:
Unregulated competition: B Q(Q) = C Q(Q), MB = MPC
Marginal Benefit (MB)= a - bQ
Marginal Private Cost (MPC)=C(Q) = c + dQ
ac
a  bQ  c  dQ &THORN; Q C 
ba  bc
C
P  a  bQ &THORN; P  a 
b d
Regulated competition: B Q(Q*) = C Q(Q*) + t*
Impose tax t* = MEC(Q*) for regulated competition.
Marginal Externality Cost (MEC)= e + fQ
Q* at social optimal = Q*  a  c  e
b d
df b
 a-c-e 
t* = MEC(Q*) = e  f  d + f + b  =
e(d  b)  f(a  c)
dfb
Quotas v. externality taxes
Producers prefer quotas to externality taxes
because they gain a larger share of social surplus.
If quota is transferable, producers will bid against
each other for the quota rights until the quota price
equals P*- PP.
-Whoever initially had the legal rights to the transferable
quota will earn quota rents equal to P*BFPP by selling the
quota rights.
-Buyer of the rights will be have surplus= PPFO.
*Note: producer surplus is the same as it is under an
externality tax. The quota rents is the same as
government revenue under the externality tax.
Elasticity Effects on the
Magnitude of Externalities
MSC
Q
MPC
D Inelastic
PC, QC=Competitive price &amp; quantity
PI, QI=Socially optimal price &amp;
quantity, when D is inelastic
PE, QE=Socially optimal price &amp;
quantity, when D is elastic
Pl
PE
PC
D elastic
QE
Ql
QC
P
Elasticity and regulation
When demand is inelastic, the socially optimal
level of production, Qi, is not too far from the
competitive level of production, Qc. Therefore, the
inefficiency associated with a production
externality may be small, and it may not be worth
regulating the externality.
When demand is elastic, the socially optimal level
of production, Qe, is farther away from the
competitive level, Qc. In this case, the
inefficiency associated with the production
externality may be relatively large, and regulation
may be desirable.
Unexpected result of regulation?!
If demand is inelastic, pollution regulation
may increase producer profit.
-regulations that decrease production, such as a
quota, will move producers towards the monopoly
level of output. This decrease in turn will raise the
market price of the final product and increase
producers revenues.
The more inelastic the demand, the higher
the producer revenues under regulation!
Imperfect Competition and
Externality Policy
High MSC
\$
A
MR
Low MSC=small MEC
High MSC=large MEC
Unregulated competition=Qc
Monopoly=Qm
Low MSC
MPC
B
D
Q*
High
Qm
Q*low
Qc
Q
Low MSC
Optimal output, Q*low, is larger than the monopoly output, Qm.
In monopolistic market with low MSC, the optimal policy may be to
subsidize the polluting monopolist to produce more of the polluting
good.
High
MSC
\$
M
R
A
Low MSC
MPC
B
D
Q* Qm
High
Q*low
Qc
Q
High MSC
Optimal output, Q*high, is smaller than the monopoly output, Qm.
In monopolistic market with high MSC, the optimal policy may be to
impose tax, T*=the distance AB. If this tax is imposed, MPC+t* will
intersect MR at Point B, which produces the optimal amount.
High
MSC
\$
M
R
Low MSC
A
B tax
MPC
D
Q*
Qm
High
Q*low
Qc
Q
Unregulated Monopoly
Monopolist sets MPC=MR, where MR (marginal
revenue) is the derivative of R (total revenue), R= P(Q)Q
Demand = P(Q)= a – bQ
Marginal private cost (MPC)=C(Q) = c + dQ
2
 R  ( abQ) Q  R aQ bQ  MR  a  2bQ
Setting MPC = MR:
ac
d  2b
c  dQ  a  2bQ &THORN;
QM 
P  a  bQ &THORN;
ba  bc
M
P  a  

 d  2b 
Unregulated Middleman
Unregulated middleman sets MR = MO, where MO
(marginal outlay) is the derivative of Outlay
MR=a-2bQ
Marginal private cost (MPC)=C(Q) = c + dQ
Outlay =MPC(Q)Q=(c + dQ)Q  MO = c + 2dQ
Setting MR = MO:
D  ac
Q
a-2bQ=c+dQ 
2(b  d)
Price that middleman pays producers -substitute
QD into the equation for MPC:
d a c
P
P P  c  dQ  P  c  2 b  d
Price that middleman charges consumerssubstitute QD into the equation for inverse demand:
C a b ac
C 
P

P
a bQ
2 ad
Numerical Example
Scenario
a (demand
intercept)
b (demand
slope)
c (supply
intercept)
20
2
4
d (supply e (m extern. f (m extern.
cost) intercept)
cost)
Q (quantity)
P( Price)
t( tax)
1
Consumer
surplus
Competition
5.33
9.33
0.00
28.44
14.22
-17.78
tax
4.00
12.00
4.00
16.00
8.00
-12.00
16.00
28.00
Subsidy
4.00
12.00
-4.00
16.00
40.00
-12.00
-16.00
28.00
permit
4.00
12.00
0
16.00
24.00
-12.00
0.00
28.00
Monopoly
3.20
13.60
0.00
10.24
25.60
-8.96
Middleman
2.67
14.67
7.11
Middlemen
profits
24.89
-7.11
producer
price
6.67
2
0.5
producers Environmen Government
surplus
t surplus
revenue
21.33
Total
surplus
24.89
26.88
0.00
producers
profits
24.89
3.56
```