1. ECON 4910 Spring 2007 Environmental Economics Lecture 6, Chapter 9
Lecturer: Finn R. Førsund
Environmental Economics

2. Illustration of spatial dimension
Spatial configuration: transport from source to receptor
Key variable: transfer coefficient aij i
Transfer coefficient
Source i
(Point,
Mobile,
Diffuse)
akij
Spatial dimension of environmental problems of interest, will influence the optimal solution
One solution to a local pollution problem may be to move either the source or the victims
Transport from source to environmental receptor of interest, air, water, dilution, retention, deposition on the way
Environmental receptor, j
Environmental Economics

3. Spatial dispersion of pollutants
Non-uniform dispersion
ei = vector of secondary or remaining discharges of pollutants from source i
eki = discharge of pollutant of type k from source i
Msj = environmental service of type s measured by indicator at receptor j
Environmental Economics

4. Non-uniform dispersion of pollutants
Introducing transfer coefficients
The unit transfer coefficient akij is a pure reorganisation of the environmental function summing up the amount of a pollutant reaching the environmental receptor
Environmental Economics

5. Non-uniform dispersion of pollutants, cont.
Marginal impact on environmental services is depending on the location of the source i
The transfer coefficient may also depend on level of emission of other substances if physical interactions
Special case of constant transfer coefficient
Must also consider the time dimension
Environmental Economics

6. One-directional diffusion of pollutant
Pollution of a river, simplifying to one pollutant and fixed transfer coefficients
Ordering the sources along the river starting upstream of receptor j
The transfer coefficient of source most upstream must be the smallest due to retention
Define retention: falling to the bottom, eaten up, worked on by bacteria, aquatic life, sedimentation
Environmental Economics

7. Illustration of river pollution
Downstream
Source i
Receptor j
Define retention: falling to the bottom, eaten up, worked on by bacteria, aquatic life, sedimentation
Environmental Economics

8. One-directional diffusion of single pollutant, cont.
Marginal impact from source i to the same receptor j gets successively larger for sources downstream
Dissolved oxygen and organic waste
Environmental Economics

9. The social solution, non-uniform dispersion
The social optimisation problem adopting monetary evaluation of environmental services
Assuming the monetary evaluation of the same service level is independent of receptor
First-order condition
Marginal purification cost equal to marginal evaluation of the environment
Environmental Economics

10. Implementation using a Pigou tax
Firms minimise costs plus tax payment
First-order condition
Comparing the social solution and the market solution yields the optimal tax
Tax rate function of the dispersion of the pollutant and the impact on environmental services
Environmental Economics

11. The case of polluting a river
Must look at pollution caused by source i:
Ri is the set of receptors polluted by source i
Load in receptor j is also coming from all upstream sources, but by assuming additivity of load these effects can be neglected
Environmental Economics

12. Environmental Economics
River pollution, cont.
The first-order condition in the social solution
Simplifying to the same biological effect and monetary evaluation of the environmental sevice
Environmental Economics

13. Implementing using a Pigou tax
Finding the optimal tax rate
The tax rate becomes smaller the further downstream the location of the source
Environmental Economics

14. Uniform dispersion of pollutants
Uniform dispersion implies that all transfer coefficients are equal and typically equal to 1
Environmental Economics

15. Uniform dispersion of pollutants, cont.
Marginal effects
The marginal effect is independent of source, i.e. location, but depends on type of pollutant
Environmental Economics

16. The social solution, uniform dispersion
The social optimisation problem (simplifying to one pollutant and one environmental service)
First-order condition
Marginal purification cost equal to total marginal evaluation of change in environmental service
Environmental Economics

17. Implementing the social solution using a Pigou tax
Finding the optimal tax rate
The tax rate is independent of source implying the same marginal purification cost for all sources and equal to the total marginal monetary evaluation of the environmental service
Environmental Economics

18. Tradable emission permits
Trade in permits can be used when
the social solution is derived from setting environmental standards because the damage function is not known
Damage function known, but certainty of achieving the desired pollution level is preferred
Trade in permits to a common trading price can only be socially optimal if the pollutant is uniformly dispersed
Environmental Economics

19. Tradable emission permits, cont.
Modelling one receptor, one pollutant , multiple sources
Policy problem: how to distribute emission permits on the sources in order to achieve the environmental standard to least cost
Policy options
Auction the permits
Giving them free, following e.g. a grandfathering principle
Environmental Economics

20. Tradable emission permits, cont.
Finding the restriction on total emission
If the dose-response functions are known, goals for environmental services, , will determine the total emission restriction
Environmental Economics

21. Tradable emission permits, cont.
How to set the firm-specific quotas
Grandfathering: uniform reduction
Least cost allocation
Environmental Economics

22. Least cost allocation, cont.
The Lagrangian
First-order condition
Environmental Economics

23. Least cost allocation, cont.
The least cost solution: Marginal purifications costs should be equal for all firms
Comparison with uniform reduction solution
Environmental Economics

24. Market implementation of emission permits
Giving quotas free, allowing free trade
A firm can keep a permit or sell it to other firms
Assume a market with a price for quotas
Analogy with the Coase theorem
Assume an auction ending with a competitive price q:
min sum of purification cost and outlay on quotas, same solution as above
Environmental Economics