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:
– Stock-damage pollution:
– Stock-flow-damage pollution:
D=D(M); M is the flow
D=D(A); A is the stock
D=D(M,A)
Economic activity,
residual flows and
environmental damage
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
NB B D
B
D


0

M
M M
M M
Efficient level of flow pollution emissions
D(M)
B(M)
D(M)
B(M)
Total damage and
benefit functions
Maximised net
benefits
M
dD
dM
*
dB
dM
M*
Marginal damage
and benefit functions
M
The economically efficient level of pollution minimises the sum of
abatement and damage costs
Costs,
benefits
Marginal
X
benefit
Marginal damage
A
Y
D
C
B
0
M
M*
M’
Quantity of pollution
emission per period
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
CO2 (carbon
dioxide)
CH4
(methane)
N2O (nitrous
oxide)
CFC-11
(chloroflouro
carbon-11)
HFC-23
(hydrofluoro
carbon-23)
concentration
in 1998
atmospheric
lifetime
ca. 280 ppm
365 ppm
5-200 yr
ca. 700 ppb
1745 ppb
12 yr
ca. 270 ppb
314 ppb
114 yr
zero
268 ppt
45 yr
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
Stock pollutants with short lifetime:
When location matters
Wind direction
and velocity
R1
R2
S1
S2
R4
S: Source
R: Urban area
R3
Stock pollutants with longer lifetime:
Efficient pollution
• Damages of pollution
Dt  D (At )
• Benefits of pollution
Bt  B (Mt )
• Stock
At  Mt   At with decay rate 0    1
• Net current benefits
NB  B (M )  D (A)
• Efficient pollution
Max NPVNB
• Hamiltonian: H  B (M )  D (A)  t (Mt  At )
Bt
  t
Mt
t
Dt
 r t 
 t
t
At
Steady State
• Static efficiency
Bt
  t
Mt
• Dynamic efficiency
t Dt
r t  

 t
t At
• Steady state
0  Mt  At  A  M 
B
 
M
D
D
B

A
r  
     

A
r 
M
Steady State (2)
•
•
•
•
D
B
A

M
r 
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
Steady State (3)
D
B
D B
B
D 1 B
B r

A




r 


M
r 
A M
M
A  M M 
A
M


D 1 D

M  A

D
B

M M
1  r 





Distinguish
four cases:
r=0
r>0
imperfectly
persistant
pollutant
perfectly
persistant
pollutant
>0
A
B
=0
C
D
Steady state: Case A
• Case A
r  0,   0
• Equation collapses to
D
B

M M
• 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
D D 1 B


M A  M
Steady state: Case A (2)
dD
dM
dB
dM
*
M*
M̂
In the steady-state, A will have reached a
level at which A*=M*
M
Steady state: Cases A and B
dB 
r
1  
dM 

dD
dM
dB
dM
**
*
M*
M**
Case A:
r  0,   0
Case B:
r  0,   0
M̂
M
Steady State: Cases C and D
•
•
•
•
Case C: r  0,   0
Case D: r  0,   0
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
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




U  U (C , E )

Q  Q (R , K , E )


• E is an index for environmental pressure E  E (R , A)
• V is defensive expenditure

F  F (V )
The optimisation problem
maxW 
Ct ,Rt ,Vt

 t
U
(
C
,
E
(
R
,
A
))
e
dt
 t t t
t=0
subject to
St  Rt
At  M (Rt )   At  F (Vt )
Kt  Q (Kt , Rt , E (Rt , At ))  Ct  G (Rt ) Vt
• Current value Hamiltonian:
H  U (Ct , E (Rt , At ))  Pt ( Rt )  lt (M (Rt )  At  F (Vt ))
wt (Q (Kt , Rt , E (Rt , At ))  Ct  G (Rt ) Vt )
• Control variables: C, R, V
• State variables: S, K, A
• Co-state variables: P, w, l
Static Efficiency
H  U (Ct , E (Rt , At ))  Pt ( Rt )  lt (M (Rt )  At  F (Vt ))
wt (Q (Kt , Rt , E (Rt , At ))  Ct  G (Rt ) Vt )
H
 UC  w  0  UC  w
C
H
 UE ER  P  wQR  wQE ER  wGR  lMR  0
R
H
 w  lFV  0  w  lFV
V
Dynamic Efficiency
H  U (Ct , E (Rt , At ))  Pt ( Rt )  lt (M (Rt )  At  F (Vt ))
wt (Q (Kt , Rt , E (Rt , At ))  Ct  G (Rt ) Vt )
H
P 
 P  P  P
S
H
w 
 w  w  w  wQK
K
H
l
 l  l  l    UE EA  wQE EA
A
Shadow Price of Resource
H
 UE ER  P  wQR  wQE ER  wGR  lMR  0 
R
wQR  P  wGR  UE ER  wQE ER  lMR
• 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!
Optimal time paths for the
variables of the pollution model
Pt+wGR-UEER-wQEER-lMR
Pt+wGR-UEER-wQEER
Units of
utility
Pt+wGR-UEER
Stock damage
Production
flow damage
Utility flow
damage
Gross
price
Marginal
extraction
cost
Pt+wGR
Pt = net price
Net price

time, t
A competitive market economy
where damage costs are
internalised
Units of
utility
Stock damage tax
Pollution flow damage tax
Utility damage tax
Pt+wGR= Gross price
Social
costs
Marginal
extraction
cost
Private
costs
Pt = net price
Net price

time, t
Efficient Clean-up
H
 w  lFV  0  w  lFV
V
• 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
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