Chapter 4: Negative Externalities

1
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

2
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.

3
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 CFCs
• Health issues resulting from gold mining

4
Production Externalities
MSC

A
MPC
E
B
MEC
G
P
C
PC
H
F
PP
D
Q
QC
5
Mathematical Representation of production
externalities

• The Social Welfare Maximization Problem is
• MaxW(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)
• WQBQ (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 QMB
• CQ(Q) the partial derivative of C(Q) with
  respect to QMPC
• EQ(Q) the partial derivative of C(Q) with
  respect to QMEC
• Socially optimum output, Q, occurs when MB MPC
  MEC.

6
Unregulated competition with externalities

• Under unregulated competition, firms maximize
  profits, resulting in the FOCBQ(Q) CQ(Q), or
  MB MPC.
• When this FOC is solved for Q, call it QC, we
  find that QClt Q whenever MEC gt 0. Because QC
  ?Q, QC is inefficient.

7
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-generatin
  g activity itself (i.e., the pollutant).

8
Policy 1 Tax-1

• Externality Tax t P - PPMEC (Q), where t
  is the required market correction to achieve Q
  units of production.
• 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.

9
Mathematical expression

• t EQ(Q) MEC(Q).
• Private optimization problem
• Max ?(Q)PQ-C(Q)-tQ
• Q
• FOC
• ?Q(Q)-P-C Q(Q)-t0 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)

10
Welfare implications of externality tax

• Consumer surplus ABP
• Producer surplus OFPP
• Government revenue PBFPP

11
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.

12
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).
• QSocial Optimum output
• PcOptimal Consumer price
• PsPc-tnet producer price
• tconsumption tax

13
Policy 2 Output-reduction Subsidy

• Subsidy P - PP for each unit of output that is
  not produced.
• If the current level of output, firms in a
  competitive industry have the following
  objective , and
• FOC
• Optimal subsidy level (i.e., the unit subsidy
  that equates the optimal social and private
  outcomes) S t MEC(Q).

14
Welfare implications of subsidy

• Consumer surplus ABP.
• Producer surplus OFBP BGHF,where
• BGHF (P - PP)(Qc - Q).
• Government expenditure BGHF.

15
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.

16
Policy 3 Standards on Pollution/Output

• Command-and-control approach through production
  quotas to restrict output to Q.

17
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
  Externality Tax)

18
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
  PBFPP 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.

19
Elasticity Effects on the Magnitude of
Externalities
MSC
Q
MPC
D Inelastic
PC, QCCompetitive price quantity PI,
QISocially optimal price quantity, when D is
inelastic PE, QESocially optimal price
quantity, when D is elastic
Pl
PE
PC
D elastic
P
Ql
QC
QE
20
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.

21
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!

22
Imperfect Competition and Externality Policy
High MSC
Low MSCsmall MEC High MSClarge MEC Unregulated
competitionQc MonopolyQm

A
MR
Low MSC
MPC
B
D
Qc
Q
Qm
Qlow
Q High
23
Low MSC

• Optimal output, Qlow, 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.

24
High MSC

• Optimal output, Qhigh, is smaller than the
  monopoly output, Qm.
• In monopolistic market with high MSC, the optimal
  policy may be to impose tax, Tthe distance AB.
  If this tax is imposed, MPCt will intersect MR
  at Point B, which produces the optimal amount.

tax
25
Production ExternalitiesExample

• 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

26
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

27
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
• 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
• t MEC(Q)

28
Unregulated Monopoly

• Monopolist sets MPCMR, 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
• ? ?
  ?
• Setting MPC MR

2
(
)
R

aQ
-
bQ
R

a
-
bQ
Q
29
Unregulated Middleman

• Unregulated middleman sets MR MO, where MO
  (marginal outlay) is the derivative of Outlay
• MRa-2bQ
• Marginal private cost (MPC)C?(Q) c dQ
• Outlay MPC(Q)Q(c dQ)Q ? MO c 2dQ
• Setting MR MO
• a-2bQcdQ ?
• Price that middleman pays producers -substitute
  QD into the equation for MPC
• ?
• Price that middleman charges consumers-
  substitute QD into the equation for inverse
  demand

P


P
c
dQ
C

-
?
P
a
bQ
30
Consumption Externalities

• We now turn to consumption externalities.
• Consumption externality exists when one
  individuals consumption imposes costs on other
  individuals that are not transmitted through a
  market.

31
Graph of consumption externalities

• MSCMarginal social cost of production (0
  production externality)
• MECconsMarginal External Cost of consumption
• MPBconsMarginal Private Benefit Individual
  Demand
• MSBconsMarginal Social Benefit MPBcons
  MECcons
• Socially optimal outcome Q, Pc, Pp
• Inefficient outcome under unregulated
  competitionQcomp,Pcomp

MSC prod
Pc
MEC cons
P comp
Pp
MPB cons
MSB cons
Q
Q comp
Q
32
Externalities from 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)
• Estimated Annual external costs of smoking
• 35 billion (medical cost)
• 20 billion (lost work)
• 5 billion (fires, smoke, odor damage)
• 60 billion (total cost)

Activity Annual deaths
Smoking 400,000
Drinking 150,000
Drugs 30,000
33
Policies to control cigarettes

• A cigarette tax or tobacco tax.
• 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 of externality cost / 30
  billion packs).

34
Policy consequences

• Producers Restriction on quantities may benefit
  producers or distributors if elasticity of demand
  is smaller than 1.
• Government Tax revenues can be used to
  compensate victims of smoking damages, or it can
  be used in lieu of other distortionary taxes
  (such as income taxes and sales taxes) to support
  government programs.
• Unintended Consequences May strengthen the case
  for the legalization of drugs.

35
The Economics of Illicit Drugs

• Should there be a drug legalization policy
  similar to the one for cigarettes?
• Proposals
• ? Legalize illicit drugs.
• ? Ban advertisement and sale to minors.
• ? 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.

36
Economic impacts of drug policy

• 1. Legalization of drugs would shift income from
  the illegal network of drug traffickers to
  government (taxes) and legal marketers
  (pharmacies).
• 2. 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.
  
• 3. Costs of crime enforcement may go down.
• 4. Consumer prices (inclusive of taxes) may go
  down and quantity may go up. There may be higher
  health costs associated with drug addiction.