Environmental Economics 1

ECON 4910 Spring 2007 Environmental Economics Lecture 2 Chapter 6

Lecturer: Finn R. Førsund

Environmental Economics 2

The Coase theorem

Provided some assumptions are fulfilled, the initial property right to an environmental resource does not matter for the social efficiency of the utilisation of the resource

Maximising profit or utility bargaining between the parties will lead to the same use of the environmental resource independent of the alocation of property rights

Environmental Economics 3

Consider the basic model

Benefit function is associated with a steel mill emitting pollutants

Damage function is associated with a downwind laundry drying clothes outdoors

( ), ' 0, '' 0

( ), ' 0, '' 0

B b P b b

D d P d d

Environmental Economics 4

Behind the benefit function we have the multiple output production function

Pollution without regulation

pollution corresponding to private profit maximisation Pπ = g(x*)

( )

( )

y f x

P g x

. . ( )i iMax py q x s t y f x

Environmental Economics 5

Interpretation of the benefit function The benefit function reflects the costs of

reducing the amount of pollution, P, generated in steel production, i.e. by purification and/or output reduction, from a level equal to the private profit maximisation level Pπ to a lower level

Notice that it is also costly for the steel mill to increase the level of pollution beyond Pπ. The b’(.) – function has a discontinuity

Environmental Economics 6

Allocating property right to clean air The steel mill has the right to pollute The laundry has the right to clean air

Pmin is found by solving d’(P) = 0

P

d’(P)

b’(P)

PπP*PMin

Environmental Economics 7

Asumptions for the Coase theorem No transaction costs Perfect information Agents price-takers Maximize profit (utility) Costless enforcement of agreements No income and wealth effects

Environmental Economics 8

Elements of general equilibrium models of the environment Basic stages:

(1) Extracting/harvesting resources (2) Transformation of resources into products

Residuals as by-products (Primary/secondary residuals if add-on purification is an option)

(3) Environmental impacts of absorption of residuals (4) Evaluation of changes in environmental indicators

Evaluation through utility functions, environment as public good, or damage functions.

Products are also evaluated either through utility functions or benefit functions

Environmental Economics 9

Strands of models according to level of aggregation Aggregated macro level:

General equilibrium and interdependencies most important, skip details about resource creation, production structure, general abatement possibilities.

Micro level of the firm: Detailed production function and purification possibilities,

household production functions Classical externalities models:

Short- circuits the environment, direct representation of residual-generating activities in production and/or utility functions

Environmental Economics 10

Why general equilibrium models Overview of complexities, interdependencies in the

economy and economic - environmental interactions, expose weaknesses of partial analyses

Establish concepts or variables fruitful for empirical work.

Show the type and extension of information needed to implement any optimal solution

Show possibilities for decentralised decision-making Framework for study of distributional aspects of

pollution and pollution abatement

Environmental Economics 11

An aggregated general equilibrium model Model without resource extraction and inputs

Multiple outputs that generate pollutants Environmental services influences by pollutants Environment as a public good

'

'

,

i1 g

i1 g

j jj j1j gj i M

N

ij ij=1

F( ,.., ) 0 , > 0y y F

Z = s( ,.., ) , 0y y s

M = m(Z) , m 0

U ( ,.., ,M) > 0, > 0U x x U U

= yx

Environmental Economics 12

Formulating the social optimisation problem

0

nj

j 1j gjj=1

1 g

1 g

n

ij ij=1

Max ( ,.., ,M)w U x x

subject to

F( ,.., )y y

M m(s( ,.., )) y y

yx

Environmental Economics 13

Solving the model

Simplifying the model by eliminating variables The Lagrangian function

nj

j 1j gjj=1

1 g

1 g

g n

iji ii=1 j=1

L = ( ,.., ,M)w U x x

- F( ,.., )y y

- (-m(s( ,.., )) + M)y y

- yx( - )

Environmental Economics 14

Differentiating wrt all endogenous variables Endogenous variables yi,xij,M Necessary first –order conditions

' ' 'i i i

i

jj i i

ij

nj

j Mj=1

L = - m s + 0F

y

L = (x, M) - 0w U

x

L = (x, M) - 0w U

M

Environmental Economics 15

Interpreting shadow prices

The marginal effect in the optimal solution of changing constraints μi : shadow price on the distribution constraint, if

the shadow price is zero, then giving more of it to a person has no opportunity cost

γ: shadow price on the transformation function, if the shadow price is zero, then there is no cost of production

λ: shadow price on the environmental service function, if the shadow price is zero, then there is no environmental cost of pollution

Environmental Economics 16

Interpreting inequalities

If the first-order conditions hold with inequalities then the endogenous variable in question should be set to zero The supply of good i condition

inequality means that the production and pollution cost is higher than the shadow price the good should not be supplied

The allocation condition of a good to an individual inequality means that the weighted social value of the

good is lower than the shadow price the good should not be supplied to the individual

Environmental Economics 17

Interpreting inequalities, cont.

The environmental service condition inequality means that the weighted social value of the

environmental good summed over all individuals is lower than the shadow price of the environmental good the environmental good should not be supplied

Environmental Economics 18

Standard procedure of solution Assume interior solutions, i.e. all first-order

conditions hold with equality (back to standard Lagrange with equality constraints)

Eliminating two of three Lagrangian parameters

Marginal costs equal to marginal benefits

' ' 'n

j jj M j ii i i

j=1

F (x, M)m s (x, M) w U w U

Environmental Economics 19

Forming MRT and MRS

' ' )' '

' '' ' )

' ')

) )

' '1

)

nj

k=1

nj j

k M j ddd d k=1

nj je e

k M j eek=1

nj

k M d jdk=1

j jj e e

k M g

jj e

(x, M)m s (x, Mw U w UF F

F F(x, M)m s (x, Mw U w U

(x, M)m sw U(x, MU

(x, M (x, Mw U U

(x, M)m sw U

(x, Mw U

Environmental Economics 20

Implementing the solution via competitive markets Profit maximisation to prices pi

Necessary first-order conditions

MRT assuming interior solutions

1

. .g

i i 1 gi

Max p y s t F( ,.., ) 0y y

' 0 , 1,..,i ip F i g

'

'd d

e e

F p

F p

Environmental Economics 21

Implementing the solution, cont. Consumers maximising utility given income,

Ri

Necessary first-order conditions

11

( ,.., , ) . . 0g

jj gj i ij i

i

Max U x x M s t p x R

( , ) 0, 1,.., , 1,..,ji iU x M p i g j n

Environmental Economics 22

Implementing the solution, cont. 2 MRT = MRS

A competitive market system will not realise a Pareto optimum. The environmental costs are left out of the market system. M is a public good, no producer is providing this good and selling it to consumers

' ( , ), 1,.., , , 1,..,

' ( , )

jd d d

je e g

F p U x Mj n d e g

F p U x M