1. ECON 4910 Spring 2007 Environmental Economics Lecture 3, Chapter 7 -9
Lecturer: Finn R. Førsund
Environmental Economics

2. Micro environmental economics model
Costs of production and of reducing discharge of pollutants at source
Dose - response relationship of natural environments, production of services
Environmental Economics

3. Derivation of the cost function
Factorially determined multi output model of Frisch
Profit maximisation given prices with no pollutant restriction
Environmental Economics

4. Derivation of the cost function, cont.
Cost minimisation with restriction on emission
The Lagrangian
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5. Derivation of the cost function, cont.1
First-order conditions
Interpretation of shadow prices:
λ: cost of decreasing the emission constraint
γ: cost of increasing output
4 equations to solve for x1,x2, λ, γ as functions of exogenous variables
Inserting in the factor outlay yields the cost function c(yo,q1,q2,eR)
Environmental Economics

6. Standard simplification of the model
Separating production costs and purification costs, dropping subscript i
g(y)= primary pollutant, e= secondary pollutant
Only one type of pollutant
End of pipe purification
Environmental Economics

7. Abatement and purification
Abatement: reduction of pollutants discharged to the environment with endogenous output level.
Purification: reduction of pollutants discharged to the environment with exogenous output.
Environmental Economics

8. Modelling options general case
“Damage” functions: evaluation of environmental services of type s provided by receptor j
Environmental standards
Environmental Economics

9. Social optimisation problem
Damage function and single environmental service, polluter, pollutant, and constant output:
Environmental Economics

10. Social optimisation problem, cont.
First-order condition
Marginal damage equal to marginal cost
Several polluters: must make assumption about nature of dose-effect relations
Damage from total sum of pollutants
Environmental Economics

11. Illustration of the social solution
-c’, D’ D’
-c’ e
d’=0
emin eo e*
Environmental Economics

12. The environmental standards approach
The social optimisation problem
The Lagrangian for the problem (problem written as a maximisation problem)
Environmental Economics

13. The environmental standards approach, cont
First-order condition
Interpretation of shadow price
Increasing environmental service increases the purification cost
Environmental Economics

14. Environmental Economics
Regulating pollution
Command and control
Technology standards
Economic incentives
Tax on pollutants, the Pigou tax
Subsidies
Refunds
Tradable permits
Environmental Economics