Microeconomics 2nd Edition by Douglas Bernheim

Exercise 3

Suppose a paper mill earns $500,000 when it pollutes a river, and that it can invest in abatement. We'll use A to stand for the amount invested; the more it invests, the less pollution there is. The effects of pollution are confined to a single farmer, who earns (in dollars)
Assume that bargaining is frictionless and that the parties will split the gains from any agreement equally. What agreement will the mill and the farmer negotiate if the mill has the right to pollute What if the farmer has the right to the level of water quality that would be achieved with an abatement investment of $250,000