Horsehead, Massachusetts lies on a bay inhabited by lobsters. The town council issues permits for trapping lobsters and is trying to determine how many permits to issue. Assume that is costs $2,000 to operate a lobster boat and that if there are x boats in the bay, total revenue per month will be T R(x) = 1000(10x − x^2).
(a) Graph the marginal revenue and marginal cost curves for operating a boat.
(b) Suppose permits were free. How many boats would trap lobsters in the bay? Is this equilibrium efficient? Explain the source of inefficiency in terms of the divergence between private benefits and social contribution from trapping.
(c) Suppose the council wants to maximize profits (as a measure of welfare). What number of boats maximizes profits?
(d) Suppose the council wants to restrict the number of boats to that which maximizes profits. How much should be charged for each permit in order to implement this level of trapping?