1. Trading and Efficiency
© 1998, 2006 Peter Berck

2. Topics Marginal Cost of abatement and Bid for Permits
Efficient Allocation of Emissions among firms
Cap and Trade Program
Coase Theorem

3. MCA
Let
E be current emissions
E0 be initial emissions
E0-E is abatement
C(Q,E)
Costs go down when emissions go up.
Reducing emissions from E to E-1 is abating emissions by one unit.
MCA = C(Q,E-1) – C(Q,E)
Called Marginal Cost of Abatement

4. Abating 4 Units of Clean Air
Technique (20,50) costs 180 and is least
cost way to make Q* using 20 units of air
P other stuff = 2.

5. MCA
MCA = ( )/4

6. Profits and Small Q Change
Suppose we start with P = MC(Q)
What happens to Profit if we add a little amount, L, to Q?
Change Profit = P (Q+L – Q) –
[C(Q+L) – C(Q)]
= L {P – [C(Q+L) – C(Q)]/L }
= L {P – MC} = 0

7. Firm’s Bid for Clean Air Services
Profits as a function of TBES (E)
p(P,E) = P Q(.) - C(Q(.),E)
where Q(.) is the supply function
Firms will bid the amount of additional profits they could make from one additional unit of air (E+1) to receive one additional unit of air.
Bid(E) = p(P,E+1)-p(P,E)

8. Bid in terms of Cost Bid(E) = p(P,E+1)-p(P,E)
= P(Q –Q) + C(Q, E) - C(Q, E+1)
(true if “1” is small relative to Q)
Bid(E) = C(Q(.), E) - C(Q(.), E+1)
The amount that total cost decreases when the firm is allowed to use one more unit of clean air (pollute one ton more)
If the firm makes a small change in Q because of the change in E, it will not change profit—see previous slide.

9. MCA and Bid Bid(E) = C(Q(.), E) - C(Q(.), E+1) MCA = C(Q,E-1) – C(Q,E)
So Bid and MCA are the same
Ok so MCA(E+1) = Bid(E)…discrete approximation
A firm will pay its cost savings for the right to pollute.
The graph of an isoquant with a TBES shows how we would calculate MCA.

10. Bid as a function of TBES
Bid = change in total cost/change in pollute
Bid
tons of S emitted (units of air used up)

11. MCA as a function of Abatement
Costs more to clean up a ton as more tons cleaned up.
MCA
tons of abated

12. Fixed Amount of Air: Two Firms
Read firm 1 from right
Read firm 2 from left
Point splits total between the firms.
$/unit
Total Tons To be Emitted
Firm 1 emissions
Firm 2 emissions
tons of S emitted (units of air used up)

13. How much Air to each? Intersection minimizes total cost
Treating firms the same has losses
50/50 split
Bid 1
Bid 2
tons

14. Dead Weight Loss
50/50 split
Bid 1
Bid 2
tons

15. Losses
Older studies show that the total cost of achieving clean air is much higher with a uniform TBES than it would be with TBES set for each firm.
California appears as the exception
Spent much more on regulation than other states
Assume the regulators learned.

16. Cap and Trade
One way to get the firms to the intersection point is to give each of them a pollution allotment and let them trade.
So long as they don’t trade allotments that they don’t have (fraud) the total amount of pollution remains constant
Acid rains section of CAA is a Cap and Trade Program as is RECLAIM

17. Avoiding loss
Trading.
let plants within a firm
let firms within an airshed
Jointly meet standards
Firm with higher MCA at the standard buys right to pollute from firm with lower MCA
Both have more money
Pollution is same.

18. However
When two firms trade the spatial distribution of the pollution will be different.
Trading can be a mechanism to inflict pollution on the poor.
Trading can lead to pollution in places that are more sensitive--have more people and more health damage

19. Optimal Pollution
Figure Marginal Cost and Marginal Benefit of SOx Emissions Abatement

20. Zero Pollution
The shaded area is the deadweight loss if all 9.1 million tons of S0x are abated.

21. Zero Abatement
Figure Deadweight Loss if Emissions are 9.1 Million Tons

22. Coase
Coase’s contribution was to recognize that trading is costly, sometimes prohibitively so.
We call the following the Coase theorem:
When trading costs are low enough, it does not matter which firms originally get the rights to pollute. The costs and pollution will be the same. But not the amounts of money the firms get (the ones with the permits get more money.)

23. Coase
But Coase’s real contribution was to say that without trading one could get either of the DWL figures.
Giving the rights to the polluter causes a lower DWL in the figures than giving the rights to the breathers.
Of course, rights allocations in between do better than either.