Lecture notes 1 4910 spring 2005 FRF Spatial

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

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

Uniformly distributed pollutants n Uniform mix: multiple recipients

Non-uniformly distributed pollutants n Non-uniform mix:

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

The spatial social problem n General social problem formulation with damage function

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

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

The pollutant tax solution n Source decision problem n 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 n

Ambient standard n Environmental service of receptors n Damage function n The physical ambient standard is the level of deposition of pollutants, dj

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

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

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