the basic models1 the basic models of environmental economics finn r. førsund department of...
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The Basic Models 3 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 theoryTRANSCRIPT
The Basic Models 1
The Basic Models ofEnvironmental Economics
Finn R. Førsund
Department of Economics, University of Oslo
THE FOURTH INTERNATIONAL CONFERENCE ON ECONOMIC CYBERNETIC ANALYSIS:GLOBAL CRISIS EFFECTS ON DEVELOPING ECONOMIES,
Bucharest, May, 22-23 2009
The Basic Models 2
Background
What is environmental economics? Building blocs:
Production and consumption 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
The Basic Models 3
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
The Basic Models 4
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 bD d e d d
The Basic Models 5
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
The Basic Models 6
Illustration of the social solution
e
b’,d’
b’ d’
e*
b’* = d’*
The Basic Models 7
The fundamental pedagogical marginal rule Optimal pollution where marginal benefit from
pollution equals marginal damage of pollution Towards policy instruments:
What is behind benefit of pollution? What is behind damage of pollution?
Must disaggregate to formulate prescriptions for policy instruments.
The Basic Models 8
The materials balance
Pollution is generically a problem with joint outputs in economic activities of production and consumption
The first law of thermodynamics tells us that matter cannot disappear
A production/consumption activity using physical inputs must generate residuals
General feature of residuals that they arise from use of inputs in a wide sense
The Basic Models 9
Explaining the benefit function and the purification function of the basic model Factorially determined multi-output
production (Frisch, 1965) in the production sector, with purification
Marketed output: y Pollutants: e Production inputs: xy (K,L,E,M,S) Purification inputs end-of-pipe: xa (K,L,E,M,S)
( ), 0
( )y
y
y f x f
e h x
( ), , 0, 0aa x h a
The Basic Models 10
Options for reducing pollutants Reduced activity level and use of all inputs Substitution among inputs Modification; end-of-pipe purification Change of production technologies of
production, pollution generation and modification f*(xy) > f(xy), h*(xy) < h(xy), a*(xa) > a(xa)
Changing type of product, types of inputs Recirculation of residuals, residuals as goods
Relocalisation of activities
The Basic Models 11
Factorially determined multi-output production Profit maximisation with environmental
constraint
Output price: p Input prices: qy, qa Pollution constraint: eR
. .
( ) , 0 ( ) ( )
y y a a
Ry y a
Max py q x q x
s t
y f x e h x a x e
The Basic Models 12
Profit maximisation, cont. The Lagrangian
First-order conditions
Endogenous variables as function of exogenous variables
( ) ( ( ) ( ) )Ry y y a a y aL pf x q x q x h x a x e
0 ( 0 for 0) , 0 ( 0 for 0)
0 ( 0 for )
y y a ay a
R
L Lpf q h x q a xx x
e e
( , , , ) , ( , , , )R Ry y y a a a y ax x p q q e x x p q q e
The Basic Models 13
The benefit function Environmental restriction is so lax that the
constraint is not binding e* < eR
No purification resources are used. xa = 0
The profit function with binding environmental constraint
* *( ) , 0 ( )y y a ypf x q x e h x
*
,
( ( , , , )) ( , , , )
( , , , ) ( ) ,0
R Ry y a i i y a
i y a
Ry a
pf x p q q e q x p q q e
p q q e B e e e
The Basic Models 14
The relationship between the benefit- and the abatement cost function Minimising production and purification costs
Comparing with the profit maximising case, solving for endogenous variables as functions of exogenous variables we have
,
. .
( ) , ( ) ( )
i ii y a
o Ry y a
Min q x
s t
y f x y e h x a x e
( , , , ) ( ; , , ) , (0, ]o R o Ry a y ac c y q q e c e y q q e e
The Basic Models 15
c’(e,y)
c’(e;yo)
c’
Illustration of cost function
eπEmissions
Marginal costs
emin
The Basic Models 16
The damage function, 1 Utility of environmental services as public
goods
Man-made goods: yi
Environmental services: M = m(e), m’ < 0 Demand for the environmental services,
vertical summation
( , ) , 0, 0(0, ) ( ,0) 0i i i iM iM
i i i
U U y M U UU M U y
1
( , )N
iM ii
U y M
The Basic Models 17
The damage function, 2
Using the relationship between the environmental service M and the emissions e
The coefficient, v, converting “utils” to money may be a function of preferences, income, income distribution and emissions
1
( ) ( , ( ))
( ), 0
N
iM ii
d e vm U y m e
D d e d
The Basic Models 18
Damage functions and standards
Methods of estimating d(e) Direct methods; contingent evaluation, asking
about willingness to pay Indirect methods; hedonic prices, property values,
travel cost method Standards
1( ) ( )S S SM m e M e e m M
The Basic Models 19
c’(e,y)
c’(e;yo)
c’
Illustration of standards
eπEmissions
Marginal costs
emin
eS