1. Term paper 4910 spring 2004 Spatial environmental model
Key variable: transfer coefficient aij
aij
Transfer coefficient
Source:
Point
Mobile
diffuse
Environmental receptor

2. Ambient standard Deposition of a residual (pollutant)
Environmental service
Damage function

3. No monitoring of individual discharges
The social problem
The first order conditions

4. The tax solution
The source decision problem
The first order condition

5. A simple version of the RAINS model
The problem formulation

6. The Lagrangian

7. The necessary first order conditions

8. Economic interpretation
Marginal cost
min  c’
Σλjaij
interior
max e
emin e* e0
Discharge

9. Marginal purification costs
Marginal costs vary between sources due to the different transfer coefficients
The foot index for source i on the rhs implies that marginal costs vary

10. Ambient standards and pollution permits for each receptor
Quota for each source
The cost minimisation problem for a source

11. Solutions
The Lagrangian
First order conditions

12. Implementing the social solution
Shadow price on ambient standards equal to permit prices

13. Uniformly and non-uniformly distributed pollutants
General problem formulation
Uniform mix: multiple recipients
Non-uniform mix: only one recipient

14. Cost effective solutions
Uniformly mixed
Non-uniformly mixed

15. Ambient standards and permit trade
Uniform mix case, source problem
Optimality condition

16. Ambient standards and permit trade, cont.
Non-uniform mix case: source problem
Optimality condition