Two local firms, A and B, are responsible for all of the pollution in Dirty Lake.Currently, firm A emits 8 tons of noxious pollutants into the lake each year and firm B emits 6 tons for a total of 14 tons of pollutants. The EPA's SuperFund has targeted DirtyLake for clean up. Specifically, the EPA wants to reduce the total amount of pollutants in Dirty lake by 10 tons per year, i.e., reduce the amount of pollutants from the current 14 tons down to only 4 tons. The marginal costs of clean up for the two polluters are given respectively by:

MCA= 75 + 20XAand MCB= 125 + 30XB

where the MCs are the marginal costs of abatement (i.e., of not emitting a ton of pollution) and the Xs are the number of tons of pollutants abated / not emitted per year.

Now, suppose that the EPA decides to auction pollution permits, each allowing the holder to emit one ton of pollutants into DirtyLake each year. Because it wants to limit the amount of pollutants to 4 tons, it limits the number of permits to 4. Assume (1) that the auction is blind; that is, each firm bids once and does not know what the other firm bids and (2) no firm emits without a permit.

1. What is the most that firms A and B, respectively, would offer for the first permit auctioned off? Who would buy it?
2. Do the above analysis for the second, third and fourth permits. How many does each polluter buy? How much pollution does each eliminate?
3. What is the cost of the pollution clean up using the permit approach? Exclude the cost of the permits themselves, since these are just transfers within society. How does this compare to the total cost of the emissions tax approach?
4. Suppose that, before the permit auction takes place, firm A and firm B convince the EPA that the most equitable way to allocate the permits is to give each of them 2. If the two polluters can bargain costlessly, would this equal allocation be stable, or would it likely be modified? Explain.