Trading and Efficiency © 1998, 2006 Peter Berck

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

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

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.

MCA MCA = (180-160)/4

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

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)

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.

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.

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

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

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)

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

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

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.

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

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.

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

Optimal Pollution Figure 12.1. Marginal Cost and Marginal Benefit of SOx Emissions Abatement

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

Zero Abatement Figure 12.3. Deadweight Loss if Emissions are 9.1 Million Tons

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.)

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.