In 2000, the town of Brother's Bay in Door County Wisconsin 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 = $5, and that each boat has a capacity of 20 trips per day.
If the demand function for boat rides was Qd = 1200 - 20P, where demand is measured in rides per day. Assume that the industry is perfectly competitive.
A. What is the competitive equilibrium price per ride?
B. What is the equilibrium number of rides per day? How many boats will there be in equilibrium?
C. In this competitive market, what is the aggregate profit?
D. In 2005, the town board of Brother's Bay 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 many licenses would be sold?
E. In 2010, costs had not changed, but the demand curve for boat rides had become Qd = 1220 - 20P. What was the equilibrium price of a ride in 2010?
F. In 2010, how much money would each current boat license owner be willing to pay to prevent any new licenses from being issued?
MC = 5
Boat cap = 20
Qd = 1200 -20P
P = 60 - .05Qd
MR = 60 - .05 Qd
a) Equilibrium Price is = to MC of $5
b) Set MC = P
5 = 60 - .05Qd
-55 = -.05Qd
Qd = ...
The Solution mathematically determines equilibrium points for a boat services industry.