A large golf resort (G) uses fertilizer and pesticides to keep its courses green. Their clients prefer very green courses, so their profits are increasing in the quantity of fertilizer g used. Its benefit of using g units of fertilizer 4000g and the marginal benefit is 4000. The golf resort's cost is 40g2 and its private marginal cost is 80g.

The golf resort is located near a bay where people fish and runoff from the golf courses harm the fish. For simplicity, assume that all fishing is done by people who have a fishing guide (F) and that the guide and golf resort are the only parties involved (Note: this is a gross simplification)

G's social marginal cost is 80g + 1000. The guide can sell one-day fishing trips at a price of 800 per unit f. The cost of f units is 2f2 + 1000g with marginal cost of 4f. G and F wish to maximize their total benefits less their total costs.

Part A: Assuming no steps are taken to mitigate the externality, what are their choices of g and f, and resulting net benefits/profits?

Part B: Now suppose that G can take steps to reduce the runoff from its courses. For G, these steps change its cost to 50g2, with private marginal cost of 100g, but has no effect on its benefit or marginal benefit. Doing so, changes F's cost to 2f2 + 100g and its marginal cost to 4f. So this changes G's social marginal cost to 100g + 100. It does not change the price at which F can sell fishing trips.

Is it socially optimal for G to take the steps to reduce runoff? What are the socially optimal values of g and f, and resulting net benefits/profits?