1. A General Model of Pollution Control
Topic 3
A General Model of Pollution Control

2. Learning Objectives
After this topic you should be able to Understand that a trade-off exists between environmental damages and pollution abatement costs Illustrate and explain the notion of marginal damage functions and why they are useful Illustrate and explain the notion of marginal abatement functions Illustrate and evaluate the social efficient level of pollution emissions Apply the equi-marginal principle to the problem of pollution control

3. First, some important questions
What is the appropriate level of environmental quality we ought to try and achieve?
How do we allocate reductions in emissions over many polluters?
How are benefits and costs of environmental programs distributed across society?

4. Pollution Control: Our Simple Model
Pollution Control: Two Aspects
Damages
Abatement Costs
In general the greater the level of pollution the greater the level of damages and the greater the abatement costs

5. Damage Functions
A damage function describes the relationship between pollution and damage
A marginal damage function shows the changes in damages stemming from a one unit change in emissions or ambient concentrations
The height and shape of a damage function depends on the pollutant and circumstances involved

6. Damage Functions Fig 1b Fig 1a (euro/per week))
Damages (euro/per week)
Both show thresholds
Emissions
(tons /per week)
Emissions
(tons/perweek)

7. Marginal Emission Damage Functions
Fig 2 Anatomy of MD functions
€ per ton/year
MD2 28
MD1 a 12 b e2 e1
Emissions (tons per year)

8. Damage Functions Two emission damage functions shown
Consider MD1 and MD2
What are marginal damages at e1?
What are total damages at e1?
What is the difference between the two functions?
What causes the MD function to shift?
Population change
Different time horizon

9. Abatement Costs
Costs of reducing the quantities of residuals being emitted or of lowering ambient concentrations
Marginal abatement cost functions are the costs associated with lowering emitted residuals by one unit
Quantities of pollution on the horizontal axis
Monetary value on vertical axis
Marginal Costs must be read from right to left
The origin = uncontrolled emission levels (ē)

10. Abatement Costs Fig 3a Fig 3b € per year € € c2 c c1 a MAC x b e ē ē e
Effluent
Tons/year
Effluent
Tons/year

11. Marginal Abatement Costs
MAC1 lies below MAC 2
What are the marginal costs associated with an emission level e?
What are the total abatement costs associated with MAC 1 and MAC2?
What might cause MAC to shift right or left
Different production technology
Technology change

12. Socially Efficient Level of Emissions
To complete the model and find the socially efficient level of emissions we need to bring together the marginal damage functions and marginal abatement costs
The socially efficient level of emissions is where these are equal
At this point social costs are minimised
There is a trade off between the two
Does this make sense?

13. The Efficient Level of Emissions
Fig 4: Efficient level of Emissions
MAC € MD
Area a depicts total damages
Area b are total abatement costs
Total social costs = a + B w a b
Emissions (tons/year) ē e* ē

14. Socially Efficient levels of emissions
What causes the MD function to shift?
Population changes
If MD shifts to the right or left what happens to the socially efficient emission levels?
What causes the MAC to shift?
Technology
What happens to e* of this occurs?
Implications for public policy?

15. Enforcement Costs Reducing emissions is not free
Fig 5
Reducing emissions is not free
Enforcement costs raise the marginal cost
The vertical distance between the MAC and MAC+E are the enforcement costs € MD
MAC +E
MAC e1 e2
Emissions

16. The Equi-Marginal Principle
If there are multiple sources of particular type of pollutant with differing marginal abatement costs and if it is desired to reduce aggregate emissions at the least possible cost, then emissions from the various sources must be reduced in accordance with the equi-marginal principle
Example- see Table 1

17. Example
The Table shows explicit abatement costs of each of two firms emitting a particular residual into the environment
Each emits 12 tons/week if no effort is made to control emissions (total emissions 24 tons/week)
Public Policy is to reduce overall emissions to half of its present level
Two Strategies
Equi-proportionate strategy
Equi- marginal strategy
Which strategy is socially optimal?

18. Strategies to reduce emissions
Table 1:Marginal Abatement Costs
Emissions (tons/wk)
MAC
Source A (€000)
Source B
(€000) 12 11 1 2 10 4 9 3 6 8 7 5 14 20 25 31 38 24 58 94
Strategy 1: Equi-Proportionate Cutbacks
MAC A = 6K
MAC B = 20K
TACA = 21K
TACB= 56K
Overall TAC = 77K/per wk
Strategy 2: Equi- Marginal strategy
Equalise MAC across 2 firms
When A = 4 tons and B =8
TACA= 39
TACB = 22
Overall TAC = 61

19. Equi-Marginal Principle
The Emission reduction plan that follows the equi-marginal rule gives emission reductions at minimum cost
So for any particular amount of money devoted to effluent reduction the maximum quantitative reduction can be obtained by following the equi-marginal principle
Public policy should NOT be designed under the rule of equi-proportionate reductions at various sources

20. Summary
The model of pollution control is based on a trade-off between environmental damages and pollution abatement costs The socially efficient level of pollution is where marginal damage costs are exactly equal to marginal abatement costs & total social costs are minimised at this point The efficient level of emissions are subject to change because the real word is dynamic Equalising MAC’s minimises the social cost of reducing emissions

21. Required Reading
Field & Field, Environmental Economics: An Introduction, chapter 5