3 Externalities: There is a railroad company R and a wealthy farmer F operating in the Midwest. There are sparks S emanating from the trains which cause damage for the farmer. Profits are R = 40S S 2 F = 200 10S. (a) What is S if the railroad company chose it unilaterally? What would it be if the farmer could choose it? (b) Which value of S maximizes joint profits? (c) What is the loss in potential joint profits if the railroad / the farmer chose S unilaterally? (d) Find the bargaining range when the property rights belong to the railroad / the farmer? (e) Which tax on S (paid by the railroad company) would result in the socially optimal quantity if the two did not negotiate and the railroad company maximized its profits?