Internalizing external effects
Prof. Dr. Carsten Vogt
University of applied sciences Bochum
Summer term 2013
Coase theorem
• Main message: Two parties will always face an
incentive to voluntary internalize an external effect
• External effect will be internalized EFFICIENTLY
• And: Irrespective who gets the property right
• Note: If Coase is right, there is no need for
government intervention.
Coase theorem: a simple example
• Two producers
– Steel plant, exercising an external effect on a
– Fish breeder
• Steel plant gets the property right, i.e. the unlimited
right to pollute the water
• Basic idea of Coase: fish breeder has an incentive to
buy the right to pollute from the steel plant
• Does it work?
Coase: A simple example
• Idea works if both parties are better off
• Two important variables:
– Marginal damage: Damage exercised by the next unit of
pollution
– Marginal abatement costs: Costs of avoiding the next unit
of pollution
• In our example:
– MD: loss of the fish breeder by the next unit polluted
water
– MAC: costs of abating the next unit polluted water
Damages and costs
• MAC: next unit of abatement typically more costly
than the unit before, i.e. MAC are increasing in
abatement
• MD: increasing in pollution, i.e. the next unit of
pollution induces a higher marginal damage than zhe
unit before
MAC and MD
p
Marginal abatement costs
H
MAC  E 
Marginal damage
MDE 
B
G
A
N
M
Q
D
K
0
E2
F
z
C
E*
Source: Sturm/Vogt (2011), p.49
E1
E
E
1. Laisser faire rule
• Fishery proposes, e.g. reduction to E1
• Compensation payment z for every unit pollution
reduced
• Rational for steel plant?
–
–
–
–
Yes, because:
Costs increase by triangle 𝐸1𝐶 𝐸
Total compensation payment: 𝐸1𝐷𝐹 𝐸
Net gain: 𝐶𝐷𝐹 𝐸 > 0
–  steel plant should accept the deal!
1. Laisser-faire rule
• Does it pay for the fish breeder, too?
• Gross gain for the fishery is the damage avoided, i.e.
area 𝐸1𝐴𝐵𝐸
• Costs of the compensation payment: 𝐸1𝐷𝐹 𝐸
• Obviously, 𝐸1𝐴𝐵𝐸> 𝐸1𝐷𝐹 𝐸
• Net gain: DABF>0
• Fish breeder should make the proposal
• Since both are better off with the contract, both will
agree to sign !
1. Laisser-faire rule
• As long as MAC>MD, we can always find a payment z
that makes both parties better off
• Result: fish breeder offers exactly z and steel plant
agrees to reduce emissions down to E*
• Next: what happens, if the fishery owns the property
right?
• Coase: steel plant has an incentive to buy the right to
pollute
2. Polluter Pays rule
• Start: origin
• Steel plant: proposes, e.g., ti increase ist emissions
up to E2
• Offers a compensation payment z for the fishery
• Gross gain for the steel plant: reduction of
abatement costs, i.e. area 0𝐻𝐺𝐸2
• Total compensation payment: area 0𝑁𝑀𝐸2
• Net gain: 𝐻𝐺𝑀𝑁 > 0
• Pays for the steel plant!
2. Polluter Pays rule
•
•
•
•
•
•
•
Does it pay for the fishery?
Total damage increases by: 0𝐾𝐸2
Total compensation received: area 0𝑁𝑀𝐸2
Obviously, 0𝑁𝑀𝐸2>0𝐾𝐸2
Net gain: 0𝑁𝑀𝐾 > 0
Deal pays for the fishery, too!
Both parties can be made better off, as long as
MAC>MD
• Both agree on E*!
Coase theorem: Results
• We have shown:
•  external effect will be internalised voluntary, i.e.
without any coercement by the government
• external effect is internalized efficiently, in the
end, the optimal emissions level E* is realized
• Solution works in case of laisser-faire, as well as
polluter-pays rule
• Thus, all parts of the CT have been proven.
Coase theorem: Intuition
• Very simple intuition:
• In case of external effects, there is an inefficiency
• By removing the ineficiency, a welfare gain is created
• This gain can be used to make both parties better off
Coase theorem: Limits 1
• Transaction costs can be very high in case of many
negotitators
– c.f. climate negotiations for example
• But caution:
– Negotiations are economically only justified if there is a
welfare gain by a Coasian contract
– If transaction costs are higher than the efficiency gain:
there is no positive welfare gain
– Negotiations do not make sense!
Coase theorem: Limits 2
• Assumption of perfect and symmetric information
• Parties have to be informed about heigth of damage
and costs
•  private information!
• Fishery e.g. has an incentive to exaggerate its
damage, because compensation payment depends
on reported damage
• Thus, in case of imperfect information direkt
negotiations (even in case of only two players) will no
longer lead to efficient results!
Coase theorem: Limits 3
• Distributional impacts: differ according to property
allocation rule
• The one who owns the resource gets the
compensation payment
• Laisser faire: steel plant is paid
• Polluter pays: fishery is paid
• Thus:
– Laisser faire favourable for steel plant
– Polluter pays favourable for fishery
Internalization 2: The Pigou Tax
• Simple basic idea: in case of external effects, market
price does not reflect the true cost of production
• „simulate“ the missing costs by imposing a tax
• Effect: Harmful activity becomes more costly
– Producers are forced to take social cost of production into
account
• Therefore, it should decrease
The Pigou Tax
• First: charcaetrizing the social optimum
• What is the optimal environmental taxation from
society‘s point of view?
• Question of weighing costs and benefits (as always!)
• Benefits from environmental protection: avoided
damages (e.g. from emissions)
• Environmental protection costs
• Total cost: 𝑇𝐶 𝐸 = 𝐴𝐶 𝐸 + 𝐷 𝐸
Pigou tax
• Social planning problem:
• 𝑇𝐶 𝐸 = 𝐴𝐶 𝐸 + 𝐷 𝐸
𝑚𝑖𝑛!
𝐸
• First order condition:
𝑇𝐶 ′ 𝐸 = 𝐴𝐶 ′
− 𝐴𝐶 ′
𝐸
𝐸
+ 𝐷′ 𝐸 = 0
= 𝐷′ 𝐸
• In words: marginal abatement costs and marginal
damage have to be equated!
Optimal Pigou tax: Graphical explanation
p
MACE 
MDE 
C
t
*
A
D
0
E3
Source: Sturm/Vogt (2011), p.77
B
E4
E*
E2
E1
E E
Optimal Pigou tax
• E* is the optimal emissions level
• Thus, there exists an optimal level of environmental
damage (sometimes disturbing for other disciplines)
• i.e. it is not worthwhile to drive emissions down to
zero
• Simply too costly
• Optimum emissions level can be implemented by a
tax rate set at the level of marginal damage and
marginal abatement costs in optimum
Optimal Pigou tax: Implementation
• How does a single firm adapt to the tax rate?
MACi Ei 
p
t
C
*
A
B
D
0
Ei1

Ei* t *
Increase emissions
and pay the tax
Source: Sturm/Vogt (2011), p.79
Ei Ei
Reduce emissions
and save the tax
Optimal Pigou tax: Implementation
• Does the industry as a whole meet the target?
• Example: two firms, i and j
p
MDE 
MACE 
t*
MAC j E j 
MACi Ei 
0

Ei* t *
Ei

E *j t *

E* t *
Source: Sturm/Vogt (2011), p.80
Ej
E E
Optimal Pigou tax: Implementation
• Result:
• Single firms adapt according to 𝑀𝐴𝐶𝑖 𝐸𝑖 ∗ 𝑡 ∗
and 𝑀𝐴𝐶𝑗 𝐸𝑗 ∗ 𝑡 ∗
= 𝑡∗
= 𝑡∗
• Aggregated, the optimal emissions level is realized:
• 𝐸𝑖 ∗ 𝑡 ∗ + 𝐸𝑗 ∗ 𝑡 ∗ = 𝐸 ∗ 𝑡 ∗
• Principally, the government can correct the market
failure by a well-designed optimal Pigou tax!
Pigou tax: Problems
• Optimal tax rate: requires information !
• Planner must know:
– MAC
– MD
• Is private information
• Rational agents will not truthfully display it!
• Realistically, planner will not be able to calculate
optimal tax rate
•  no taxation at all?
Pigou tax: Problems
• No. Wrong tax is better than no tax!
p
MDE 
MACE 
t2
t
*
B
A
E
C
D
F
t1
0
E2 t 2 
Source: Sturm/Vogt (2011), p.82

E* t *
E1 t1 
E E
Emissions trading
• Environmental goods: no market price
• Pigou: tax instead of a price
• Further possibility: create markets for
environemental goods
• Markets for environmental goods do not evolve
because these are public goods
• So how can we create a market for environmental
goods, like, e.g. clean air or clean water?
Emissions trading: the basic idea
•
•
•
•
Underlying environmental goods are public in nature
But: emissions are private goods
Thus: emission permits can be traded in a market
Prerequisites:
– Government defines total amount of permits allocated to
the market as a whole
– Decision about allocation rule (e.g. auctioning versus
grandfathering)
– Installation of a system of measurement, control and
sanction
Emissions trading: how it works
p
MACi
 
MACi EiIA
MAC j
A
p
C



 
MAC j E IA
j
D
0
E j  p
B
EiIA
E IA
j

MACi Ei  p   MAC j E j  p
Ei  p
Ei
Ej
E
Emissions trading: results
Two important features:
– Emissions trading meets the ecological target (provided
controls and sanctions)
– Emissions trading is cost efficient, i.e. the (arbitrary)
reduction target is realized at minimum cost
• Plants with lower abatement costs will undertake the
abatement
– Difference to command and control: under C&C even
plants with high MAC are forced to abate!not efficient.
Tax and permits: comparison
• Trading: government fixes the amount of permits,
emissions‘ price emerges in the market
• Tax: government fixes the price, amount of emissions
emerges
•  if we want to implemet some target for sure,
emissions trading might be better.
• Uncertainty? If damages and/or costs are uncertain,
government makes mistakes either in the amount of
permits allocated or in setting the tax rate
– What are the consequences of mistakes connected with both
instruments?
Tax and permits: comparison
p
MAC
MD
t*
A B
t1
0
E * E1
E2 E
E
Tax and permits: comparison
• If MAC is steeper than MD: tax leads to smaller
welfare loss (given same percentage mistake)
• IF MD is steeper than MAC: vice versa
(Weitzman 1974)