Question

In 1990, the town of Ham Harbor had a more-or-less free market in taxi services. Any respectable firm could provide taxi service as long as the drivers and cabs satisfied certain safety standards. Let us suppose that the constant marginal cost per trip of a taxi ride is $5, and that the average taxi has a capacity of 20 trips per day. Let the demand function for taxi rides be given by D(P)1200 − 20P where demand is measured in rides per day, and price is measured in dollars. Assume that the industry is perfectly competitive. • What is the competitive equilibrium price per ride? What is the equilibrium number of rides per day? How many taxicabs will there be in equilibrium? • In 1995 costs had not changed, but the demand curve for taxicab rides had become D(P) = 1220 − 20P. If the taxi operated every day, what was the profit per taxicab license per year? • If the interest rate was 10% and costs, demand, and the number of licenses were expected to remain constant forever, what would be the market price of a taxicab license?

Answer 1

Constant marginal cost per trip of a taxi ride is $5, and the average taxi has a capacity of 20 trips per day. Let the demand function for taxi rides be given by D(P) = 1200 − 20P.

In the competitive equilibrium, the taxi drivers must be maximizing their profits which will be zero in equilibrium at the same time covering their costs. In competitive equilibrium, price must equal marginal cost. Thus, the competitive equilibrium price per ride is = $5.00

With a price of $5.00 the market demand for taxi rides is
D(p) = 1200 - 20p
= 1200 - 20*5 = 1,100

Hence, equilibrium number of rides per day is 1,100.

If each taxi can do 20 rides per day, then the equilibrium number of taxicabs is 1,100/20 = 55 taxicabs.

In 1995 costs had not changed, but the demand curve for taxicab rides had become D(P) = 1220 - 20P. The supply is fixed at 1100, the price that equilibrates supply and demand is found by solving

1,100 = 1,220 - 20p

20p = 1,220 - 1,100

20p = 120

p = 120/20 = $6 per ride

With the new demand, the license holders will be making $1.00 per ride profit. At 20 rides per day that is $20 per day profit and the profit per taxicab license per year is 365days*$20 =$7,300.

With interest rates of 10%, costs, demand, and the number of licenses were expected to remain constant forever, the market price of a taxicab license is $7,300/0.1 = $73,000.