1. Environmental Economics1 ECON 4910 Spring 2007 Environmental Economics Lecture 6, Chapter 9 Lecturer: Finn R. Førsund

2. Environmental Economics 2 Illustration of spatial dimension Spatial configuration: transport from source to receptor Key variable: transfer coefficient a ij a kij Transfer coefficient Source i (Point, Mobile, Diffuse) Environmental receptor, j i

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

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

5. 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 over time, may be calculated as averages over several time periods

6. 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

7. Environmental Economics 7 Illustration of river pollution Receptor j Source i Downstream Estuary

8. 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 located above the receptor

9. 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

10. 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

11. Environmental Economics 11 The case of polluting a river Must look at pollution caused by source i: R i is the set of receptors downstream 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 when investigating marginal effect of source i

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

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

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

15. 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 and receptor

16. 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 independent of location of source

17. 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

18. 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

19. 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

20. 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

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

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

23. 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 Marginal costs of uniform reductions will in general differ from common marginal cost of the optimal solution

24. Environmental Economics 24 Efficiency of tradable permits e1*e1* -c 1 ’ e1e1 -c 2 ’ -c 1 ’, -c 2 ’ e R = a(e 1 o +e 2 o ) e1oe1o e2oe2o e2e2 e2*e2*

25. Environmental Economics 25 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 q 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