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ECON 4910 Spring 2007 Environmental Economics Lecture 12 Summing up Lecturer: Finn R. Førsund

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Content of course

Background Environmental policy International issues Dynamic issues Valuation

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Background

What is environmental economics? Building blocs:

Production of man-made goods and generation of pollutants

Production of environmental services Interaction economic activity and the environment Evaluation of man-made and environmental

goods

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Tools for dealing with the building blocks Production and generation of pollutants

Multi-output production theory Production of environmental services and

interaction pollutants – the environment Knowledge about natural environments and

effects of deposition of pollutants Evaluation of environmental goods

Externalities Public-good theory

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The basic social-choice model Social choice: how much environmental

protection, trade-off marketed goods – environmental services

Benefit to the production sector from pollution and damage of pollution to consumers

B = benefit, e = pollution, D = damage

( ), ' 0, '' 0

( ), ' 0, '' 0

B b e b b

D d e d d

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The basic social-choice model, cont. The social optimisation problem

Necessary first order condition

Second order sufficient condition

'( ) '( ) 0b e d e

( ) ( )PMax B D b e d e

''( ) ''( ) 0b e d e

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Illustration of the social solution

e

b’,d’

b’ d’

e*

b’* = d’*

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Explaining the benefit function and the purification function of the basic model Factorially determined multi-output

production in the production sector

Marketed output: y Pollutants: e Production inputs: x1 (K,L,E,M) Purification inputs: x2

1 2 1 2

1 2 1 2

( , ), 0, 0

( , ), 0, 0

y f x x f f

e h x x h h

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Factorially determined multi-output production, cont. Profit maximisation with environmental

constraint

Output price: p Input prices: q1, q2

Pollution constraint: eR

1 1 2 2

1 2 1 2

1 2

. .

( , ) , ( , )

( , ) R

Max py q x q x

s t

y f x x e h x x

h x x e

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Profit maximisation, cont. The Lagrangian

First-order conditions

Endogenous variables as function of exogenous variables

1 2 1 1 2 2

1 2

( , )

( ( , ) )RL pf x x q x q x

h x x e

1 1 1 2 2 21 2

0, 0L L

pf q h pf q hx x

1 1 1 2 2 2 1 2( , , , ), ( , , , )R Rx x p q q e x x p q q e

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The benefit function Environmental restriction is so lax that the

constraint is not binding e* < eR

No purification resources are used. x2 = 0

The profit function with binding environmental constraint

* *1 1 1 2 1( ,0) , 0 ( ,0)pf x q x e h x

2*

1 1 2 2 1 2 1 21

1 2

( ( , , , ), ( , , , )) ( , , , )

( , , , ) ( ) ,0

R R Ri i

i

R

pf x p q q e x p q q e q x p q q e

p q q e B e e e

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The damage function

Utility of environmental services as public goods

Man-made goods: xi

Environmental services: M Demand for the environmental services,

vertical summation

( , ) , 0, 0i i i iM iMU U x M U U

1

( , )N

iM ii

U x M

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The damage function

Willingness to pay Marshall demand functions

Indirect utility function in money

Max utility for given income, environmental services

1

( ; ) . .

( , , )

n

x i ii

i i

Max U x M s t p x y

x m p y M

1( ( , , ),.., ( , , ); ) ( , , )nU U m p y M m p y M M v p y M

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Willingness to pay, cont.

Hicks demand functions

Expenditure function

Min. expenditure for given income, environmental services E

1

. . ( ; )

( , , )

no

x i ii

oi i

Min p x s t U x M U

x h p U M

1

( , , ) ( , , )n

o oi i

i

E p h p U M E p U M

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Willingness to pay, cont.

Compensating surplus

Difference in expenditure keeping the old utility level Uo when the environment improves from Mo to M1

Question to the consumer: what are you willing to pay for an environmental improvement

1 1( , , ) ( , , ) 0,o o o oCS E p U M E p U M M M

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Willingness to pay, cont.

Using the indirect utility function

The consumer is willing to pay the compensating surplus and will remain on the old utility level

Equivalent surplus

Difference in expenditure keeping the new utility level when the environment improves

1( , , ) ( , , )o o ov p y M v p y CS M

1 1 1 1( , , ) ( , , ) 0,o oES E p U M E p U M M M

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Willingness to pay, cont.

Question to the consumer: what will you accept in payment for forgoing an environmental improvement

Using the indirect utility function

To accept the old environmental service the consumer must have a compensation giving him the same utility level as the improved environment would have given

1( , , ) ( , , )o o ov p y ES M v p y M

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Methods to find willingness to pay Revealed preferences

Utilising complementarity between environmental service and market goods

The travel cost method finding demand for visiting sites

Hedonic regressions; isolating environmental differences

Household production; household produce their own environmental services

Stated preferences Asking people; constructed markets and

contingent valuation

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Environmental policy Is public regulation necessary?

Property rights; the Coase theorem Market failure: public bads and externalities

Regulating policy instruments for pollution Command and control Economic incentives

Pigouvian fees, emission fees Marketable permits

Regulation with unknown control costs Unobserved emissions, audits

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The Coase theorem

e

b’,d’

b’ d’

e*

b’* = d’*

d(emin)=0 eπ

Property right polluterProperty right pollutee

Pollutee can payPolluter to cut back

Polluter can payPollutee to acceptmore pollution

Bargaining solution

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Unknown costs: The Weitzman rule

e

D’(e)-E{c’(e)}

e*

t*

-cH’

-cL’

eH(t*)eHeLeL(t*)

Social loss if Husing t*

Social loss if Lusing t*

Social loss using e* if L and if H

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International issues

Transboundary pollution Global warming Stratospheric ozone depletion Acid rain

Type of pollutants Uniformly distributed: deposition

Non-uniformly distributed: deposition Deposition depends on location

1

N

ii

e

1

N

i ii

a e

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Policy models for economic efficiency Minimising costs for given environmental

deposition targets The RAINS model

Future projection eio

Deposition target dj*

1

*

1

min

( ) . .

,

( ) , 1,..,

No

i i ii

N

ij i j ji

o oi i i i

Min c e e s t

a e b d

e e e e i N

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Policy models for economic efficiency, cont. Ideal Kyoto protocol

1

*

1

min

( ) . .

,

( ) , 1,..,

No

i i ii

N

ii

o oi i i i

Min c e e s t

e d

e e e e i N

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Tradable emission permits

Trade in permits can be used when The social solution is derived from setting

environmental standards because the damage function is not known

Damage function known, but certainty of achieving the desired pollution level is preferred

Trade in permits to a common trading price can only be socially optimal if the pollutant is uniformly dispersed

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Efficiency of tradable permits

e1*

-c1’

e1

-c2’

-c1’, -c2’

eR = a(e1o +e2

o)

e1o e2

o

e2

e2*

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Stock pollution

Damage from accumulated waste

Cannot achieve an interior steady-state solution without decay of accumulated pollution Decay:

Formulating a dynamic optimisation model for an infinite horizon and solving using optimal control theory. Steady state illustration by phase diagram

0

( ), 0t

t t t tD D e dt D

0 0

t t

t t te dt A e e dt