1. Trading and Efficiency
© 1998 Peter Berck

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

3. Bid in terms of Cost Bid(TBES) = p(P,TBES+1)-p(P,TBES)
Bid(TBES) = C(Q(.), TBES) - C(Q(.), TBES+1)
The amount that total cost decreases when the firm is allowed to use one more unit of clean air (pollute one ton more)
Result depends upon envelope theorem: that the changes in Q(.) do not matter.

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

5. 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)

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

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

8. 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
Still don’t know what the most recent work says
Assume the regulators learned.

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

10. 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