Exam 33: Externalities

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $4,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(28x - x²). If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁. If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

Marbella has 101 residents. All wear the same fancy clothes and each has the same utility function, u(m, b, B) = m + 24b - b² - , where m is the amount of macaroni (in kilograms) that he or she eats per day, b is the number of hours that he or she spends on the beach per day, and B is the total number of person-hours spent per day on the beach by other residents of Marbella. Each has an income of $10 per day and macaroni costs $1 per kilogram. The city council is considering a law that would limit the amount of time that any person can spend on the beach. How many hours per day should they allow in order to maximize the utility of a typical Marbellite?