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.

Suppose the EPA were to use an effluents tax approach (a tax on pollution) to clean up the lake.

1. At what dollar amount per ton of pollutants should the tax be set?
2. How many tons of pollutants would be eliminated by each polluter and at what cleanup cost? What would the total cost of the clean up be (don't include the taxes since they are a transfer within society)?
3. How much tax revenue would the EPA collect?