On Sundays people in Los Angeles consider taking a boat to Catalina Island to spend the day on the beach there. The utility that a person gets from visiting Catalina is 1 - [n/80] - p, where n is the number of visitors on the island and p is the price of round-trip transportation (by boat). (Note that a visitor obtains more satisfaction if there are fewer other visitors on the island.) The utility of staying home is zero.
Part A: In equilibrium, how many people visit the island on a given Sunday? (Your answer should depend on p.)
Part B: Suppose that the boat companies can transport people to and from the island at zero cost. If the boat transportation market is perfectly competitive, what is the equilibrium price p∗ and what is the number of visitors n∗?
Part C: Compute the total surplus in this market in the equilibrium of part (b).
Part D: How does an externality arise in this problem and is it positive or negative?
Part E: Now suppose that the demand for boat transportation is served by a monopoly firm. That is, a single firm sets the price p. What price will the monopolist set and how many people will visit the island?
Part F: Compute the total surplus for the outcome of part (e). Is the monopoly good or bad for the economy? Explain.