Lecture notes 1, 4910 spring 2005, FRF Spatial environmental models

1
Lecture notes 1, 4910 spring 2005, FRFSpatial
environmental models

• Spatial configuration
• Key variable transfer coefficient aij

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 Nj

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, dj

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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