Question

In 2000, Catalina Island had a more-or-less free market in boat services. Any adult citizen could provide boat services as long as the drivers and the boats satisfy certain safety standards. Suppose that the marginal cost per trip of a boat ride is constant, where MC = $14 (the boats are fully depreciated and there are no fixed costs), and that each boat can operate 10 trips per day. 12 passengers can board a boat.

If the demand function for boat rides was Q_d = 1000 – 20P, where demand is measured in rides per day. Assume that the industry is perfectly competitive.

1. What is the competitive equilibrium price per ride?
2. What is the equilibrium number of rides per day? How many boats will there be in equilibrium?
3. In this competitive market, what is the aggregate profit?
4. In 2013, costs had not changed, but the demand curve for boat rides had become Q_d = 1148 – 22P. However, the number of boats has not changed. What was the equilibrium price of a ride in 2013?
5. In 2015, the government of Catalina Island created a boat licensing board and issued a license to each of the existing boats. The board stated that it would continue to adjust the boat fares so that the demand for rides equals the supply of rides, but no new licenses will be issued in the future. In effect, all profit would be turned over to the township for licenses. How much would a license cost?

Answer 1