ERE9: Targets of Environmental Policy
• Optimal targets– Flow pollution– Stock pollution
• When location matters• Steady state
– Stock-flow pollutant• Steady state • Dynamics
• Alternative targets
Last week
• Valuation theory • Total economic value• Indirect valuation methods
– Hedonic pricing– Travel cost method
• Direct valuation methods
Environmental & Resource Economics
• Part 1: Introduction– Sustainability– Ethics– Efficiency and optimality
• Part 2: Resource economics– Non-renewables– Renewables
• Part 3: Environmental economics– Targets– Instruments
• Part 4: Miscellaneous– Valuation (next course)– International environmental problems (next course)– Environmental accounting
Pollution• Pollution is an externality, that is, the unintended
consequence of one‘s production or consumption on somebody else‘s production or consumption
• Pollution damage depends on– Assimilative capacity of the environment– Existing loads– Location– Tastes and preferences of affected people
• Pollution damage can be– Flow-damage pollution: D=D(M); M is the flow– Stock-damage pollution: D=D(A); A is the
stock– Stock-flow-damage pollution: D=D(M,A)
Efficient Flow Pollution
• Damages of pollution D=D(M)
• Benefits of pollution B=B(M)
• Net benefits NB=B(M)-D(M)
• Efficient pollution Max NB
0
NB B D B DM M M M M
dM
dB
Maximised net benefits
M*
*
M
D(M)B(M)
D(M)
B(M)
M
Efficient level of flow pollution emissions
dM
dD
Total damage and benefit functions
Marginal damageand benefit functions
Marginal damage
Marginal
benefit
Costs,benefits
0 M
Quantity of pollution
emission per period
M*
B C
A
The economically efficient level of pollution minimises the sum of abatement and damage costs
M’
D
X
Y
Types of externalities
• Area B: Optimal level of externality• Area A+B: Optimal level of net private benefits
of the polluter• Area A: Optimal level of net social benefits• Area C+D: Level of non-optimal externality
that needs regulation• Area C: Level of net private benefits that are
unwarranted• M*: Optimal level of economic activity• M‘: Level of economic activity that maximises
private benefits
Efficient Flow Pollution (2)
• Optimal pollution is greater than zero• The laws of thermodynamics imply that zero
pollution implies zero activity, unless there are thresholds (e.g., assimilative capacity)
• Optimal pollution is greater than the assimilative capacity
• Pollution greater than the optimal pollution arises from discrepancies between social and private welfare
Stock pollutants lifetime
pre-industrial concentration
concentration in 1998
atmospheric lif etime
CO2 (carbon dioxide) ca. 280 ppm 365 ppm 5-200 yr CH4 (methane) ca. 700 ppb 1745 ppb 12 yr N2O (nitrous oxide) ca. 270 ppb 314 ppb 114 yr CFC-11 (chloroflouro carbon-11) zero 268 ppt 45 yr HFC-23 (hydrofluoro carbon-23) zero 14 ppt 260 yr
Sulphur spatially variable spatially variable 0.01-7 days
NOx spatially variable spatially variable 2-8 days
Source: IPCC(WG1) 2001
S1
S2
R4
R3
R2
R1
S: SourceR: Urban area
Stock pollutants with short lifetime: When location matters
Wind direction and velocity
Stock pollutants with longer lifetime: Efficient pollution
• Damages of pollution
• Benefits of pollution
• Stock
• Net current benefits
• Efficient pollution Max NPVNB
• Hamiltonian:
with decay rate 0 1t t tA M A
( ) ( ) ( )t t tH B M D A M A
t
tt
BM
t t
t tt
Dr
t A
( )t tD D A
( )t tB B M
( ) ( )NB B M D A
Steady State
• Static efficiency
• Dynamic efficiency
• Steady state
t
tt
BM
t t
t tt
Dr
t A
BM
DD BArA r M
0 t tM A A M
Steady State (2)
• Marginal benefit of the polluting activity equals the net present value of marginal pollution damages
• Benefits of pollution are current only• Damages of pollution are a perpetual
annuity• The decay rate ( ) acts as a discount rate
DB AM r
Steady State (3)
1
1
1
M D DA
M A
DB D B B D B B rA rM r A M M A M M
D B rM M
imperfectly persistant pollutant
perf ectly persistant pollutant
>0 =0 r=0 A C r>0 B D
Distinguish four cases:
Steady state: Case A
• Case A
• Equation collapses to
• In the absence of discounting, an efficiency steady-state rate of emissions requires that– the marginal benefits of pollution should equal the
marginal costs of the pollution flow – which equals the marginal costs of the pollution
stock divided by its decay rate
0, 0r
D BM M
1D D BM A M
M*
*
M
dM
dBdM
dD
M̂
Steady state: Case A (2)
In the steady-state, A will have reached a level at which A*=M*
Steady State: Cases C and D
• Case C:• Case D:• The pollutant is perfectly persistent• In the absence of assimilation, the
steady state can only be reached if emissions go to zero
• Clean-up expenditures might allow for some positive level of emissions
0, 0r
0, 0r
Efficient Stock-Flow Pollution• Pollution flows are related to the extraction and use of
a non-renewable resource– For example, brown coal (lignite) mining
• What is the optimal path for the pollutant?• Two kind of trade offs
– Intertemporal trade-off– More production generates more pollution
• Pollution damages through – utility function
– production function
• E is an index for environmental pressure
• V is defensive expenditure
( , )U U C E
( , , )Q Q R K E
( )F F V
( , )E E R A
The optimisation problem
• Current value Hamiltonian:
• Control variables: C, R, V• State variables: S, K, A• Co-state variables: P, ,
, ,t=0
max ( , ( , )) dt t t
tt t t
C R VW U C E R A e t
t tS R
( ) ( )t t t tA M R A F V
( ,( , , ) )) (t tt t t tt tK Q K R C G RE R A V
subject to
( , ( , )) ( ) ( ( ) ( ))
( ( , , ( , )) ( ) )t t t t t t t t t
t t t t t t t t
H U C E R A P R M R A F V
Q K R E R A C G R V
Static Efficiency
( , ( , )) ( ) ( ( ) ( ))
( ( , , ( , )) ( ) )t t t t t t t t t
t t t t t t t t
H U C E R A P R M R A F V
Q K R E R A C G R V
0C C
HU U
C
0R R R R RE E
HU E P Q Q E G M
R
0V V
HF F
V
Dynamic Efficiency
( , ( , )) ( ) ( ( ) ( ))
( ( , , ( , )) ( ) )t t t t t t t t t
t t t t t t t t
H U C E R A P R M R A F V
Q K R E R A C G R V
HP P P P
S
K
HQ
K
A AE E
HU E Q E
A
Shadow Price of Resource
• Gross price = Net price + extraction costs + disutility of flow damage + loss of production due to flow damage + value of stock damage
• Flow and stock damages need to be internalised!
0R R R R RE E
R R R R RE E
HU E P Q Q E G M
RQ P G U E Q E M
time, t
Units ofutility
Pt = net price
Pt+GR
Stock damage
Pt+GR-UEER
Pt+GR-UEER-QEER
Pt+GR-UEER-QEER-MR
Net price
Production flow damage
Utility flow damage
Marginal extraction cost
Gross price
Optimal time paths for the variables of the pollution model
time, t
Units ofutility
Pt = net price
Pt+GR= Gross price
Stock damage tax
Net price
Pollution flow damage tax
Utility damage tax
Marginal extraction cost
Private costs
A competitive market economy where damage costs are internalised
Social costs
Efficient Clean-up
• The shadow price of capital equals the shadow price of stock pollution times the marginal productivity of the clean-up activity
• Ergo, environmental clean-up (defensive expenditure) is an investment like all other investments
0V V
HF F
V
Alternative Standards
• Optimal pollution is but one way of setting environmental standards and not the most popular
• The main difficulty lies in estimating the disutility of pollution
• Alternatives– Arbitrary standards– Safe minimum standards– Best available technology (not exceeding
excessive costs)– Precautionary principle