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