econ 4910 spring 2007 environmental economics lecture 2 chapter 6
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ECON 4910 Spring 2007 Environmental Economics Lecture 2 Chapter 6. Lecturer: Finn R. Førsund. 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 - PowerPoint PPT PresentationTRANSCRIPT
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