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

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

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

The tax solution The source decision problem The first order condition

A simple version of the RAINS model The problem formulation

The Lagrangian

The necessary first order conditions

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

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

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

Solutions The Lagrangian First order conditions

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

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

Cost effective solutions Uniformly mixed Non-uniformly mixed

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

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