Question

During the Enlightenment, the City of Calgary 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) = 1100 − 20p, where demand is measured in rides per day, and price is
measured in dollars. Assume that the industry is perfectly competitive.
(a) What is the competitive equilibrium price per ride? What is the equilibrium number of rides
per day? What is the minimum number of taxi cabs in equilibrium?
(b) During the Calgary Stampede (The Greatest Outdoor Show on Earth), the influx of tourists
raises the demand for taxi rides to D(p) = 1500 − 20p. Find the following magnitudes,
based on the assumption that for these 10 days in July, the number of taxicabs is fixed and
equal to the minimum number found in part (a): equilibrium price; equilibrium number of
rides per day; profit per cab.

Answer 1

Answer a

Since the market is perfectly competitive, the Price at Equilibrium will be equal to Marginal cost.

Hence Competitive Equilibrium Price per ride = $5

Hence Equilibrium No. of Rides will be demand at $5 price,D(P) = 1100- 20P = 1100 - 20*5 = 1100-100=1000

Hence Equilibrium No. of Rides = 1000

One Taxi can take 20 rides, minimum no. of taxi = Total Rides/ No. of Rides by one taxi = 1000/20 = 50

Hence No. of Taxi = 50

Answer b

Since No. of Cab is fixed at 50, no. of Rides will be fixed at 1000 as calculated above

At Equilibrium, this will be the demanded ride, Hence D(P) = 1000.

Hence Price at Equilibrium can be calculated as D(P) = 1500-20P

or, 1000 = 1500-20P

or, 20P = 1500-1000

P = 500/20 = 25

Hence Equilibrium Price = $25

Since supply is fixed Equilibrium No. of Rides per day will be same as above i.e 1000

No. of Rides per Cab is 20, Marginal cost is $5, Equilibrium Price is $25

Profit per ride = 25-5 = $20

Hence Profit per cab = Profit per ride * No. of Ride = 20*20 = $400