# Trading and Efficiency © 1998, 2006 Peter Berck. Topics Marginal Cost of abatement and Bid for Permits Efficient Allocation of Emissions among firms Cap.

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

Reminder… A Pareto improving exchange is one that makes at least one party better off and no party worse off. Market transactions (without externalities) between willing buyers and sellers are pareto improving. A redistributive tax is not. (Makes Larry Ellison worse off and John on the corner better off.)

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

How much to pay for added E Firm has rights to emit E and is offered rights to emit E+1. Would pay added profits for added E This is the bid for E In a market those with highest bid get the E

Firm’s Bid for Clean Air Services Profits as a function of effluent standard (E)  (P,E) = P Q(.) - C(Q(.),E) where Q(P,E) 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,E+1)-  (P,E)

Q is a function of E P = MC(Q,E) Supply function is Q(P,E) – Increase in P – Increase in E P MC(Q,E+1) MC(Q,E) Q(E+1)Q(E)

Bid in terms of Cost Bid(E) =  (P,E+1)-  (P,E) = P(Q(P,E+1) –Q(P,E)) + C(Q(P,E), E) - C(Q(P,E+1), E+1) true if “1” is small relative to Q Approximately the same as Bid(E) = = P(Q(P,E+1) –Q(P,E)) + C(Q(P,E), E) - C(Q(P,E), E+1) +C(Q(P,E), E) – C(Q(P,E+1), E)

Simplifying C(Q(P,E), E) - C(Q(P,E), E+1) Is Marginal cost of abatement Negative of the change in cost from adding a unit of emission +C(Q(P,E), E) – C(Q(P,E+1), E) MC is (change in cost from one more unit of Q) MC * (Q(P,E)- Q(P,E+1)) is change in cost from (Q(P,E)- Q(P,E+1)) of Q. Notice it is a negative number

Putting it together Bid(E) = P(Q(P,E+1) –Q(P,E)) + C(Q(P,E), E) - C(Q(P,E), E+1) +C(Q(P,E), E) – C(Q(P,E+1), E) Bid(E) = (P – MC )(Q(P,E+1) –Q(P,E)) + MCA = MCA Firm’s will pay their marginal cost of abatement in order to get another unit of emissions

Bid as a function of emissions Bid = change in total cost/change in pollute Bid tons of E 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 left Read firm 2 from right Point splits total between the firms. \$/unit tons of E emitted (units of air used up) Total Tons To be Emitted Firm 1 emissionsFirm 2 emissions

How much Air to each? Bid is marginal cost emissions Area under bid is avoided costs Tons emitted 10 \$10000 20 \$7000

Bids for two firms. Bid 1 Tons emitted Bid 2 50/50 split

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

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

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 Meredith Fowlie does this with Cars and Powerplants and finds big losses from making powerplants too clean and cars not clean enough

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

Right Amount of Pollution MCA and Marginal benefit of Abatement the same. Or: Bid (firms marginal benefit from pollution) = Marginal damage from pollution Same thing.

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

Coase

Zero Pollution The shaded area is the deadweight loss if all 9.1 million tons of S0 x 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.

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