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)

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

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*

r

1dM

dB

M*

*

M

**

M**

dM

dBdM

dD

M̂

Steady state: Cases A and B

0, 0r

0, 0rCase B:

Case A:

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