1. Lecture notes 1, 4910 spring 2005, FRF Spatial environmental models Spatial configuration Key variable: transfer coefficient a ij a ij Transfer coefficient Source (Point, Mobile, Diffuse) Environmental receptor

2. The Generic model of spatially distributed pollutants Source abatement cost function Deposition of pollutants in the environment

3. Uniformly distributed pollutants Uniform mix: multiple recipients

4. Non-uniformly distributed pollutants Non-uniform mix:

5. Structured transfer: river pollution At receptor j: a ranking of transfer coefficients starting upstream at source 1 and ending at nearest source N j

6. The spatial social problem General social problem formulation with damage function

7. The spatial social problem, cont. The general first order condition Non-uniformly mixed: Source marginal abatement cost equal to social marginal damage weighted with transfer coefficients. NB! In general different marginal costs between sources.

8. Cost effective solutions, cont. River pollution Uniformly mixed Marginal abatement cost equal for all sources and equal to total marginal damage

9. The pollutant tax solution Source decision problem The tax on pollutants is source specific, and should be set equal to the weighted marginal damage in the optimal case. Uniform distribution: tax rate equal for sources

10. Ambient standard Environmental service of receptors Damage function The physical ambient standard is the level of deposition of pollutants, d j

11. Environmental policy in practice Formulating limits for dj; dj* Social problem: The Lagrangian (Economists’ mathematical manual; Kuhn – Tucker, maximisation)

12. Environmental policy in practice, cont. First order conditions Interpretation: Marginal abatement costs equal to shadow prices on ambient constraints weighted with transfer coefficients

13. Environmental policy in practice, cont. Interpretation of shadow price  Envelope theorem Shadow price positive for binding constraints