Answer to Question #194719 in Microeconomics for victoria

Question

Suppose that the marginal cost per trip of a ride is constant, MC = N$4, and that each taxi has a capacity of 20 trips per day. Let demand function for taxi rides be given by: D = 1200 – 20P, where demand measured in rides per day. Assume that the industry is perfectly competitive. (i) What is the competitive equilibrium price per ride? (5) (ii) What is the equilibrium number of rides per day? How many taxicab will there be in equilibrium? 

Answer 1

Solution:

i.). Find the inverse demand function:

D = 1200 – 20P

P = 60 – Q/20

In perfect competition: P = MC

60 – Q/20 = 4

Q = 80 – 60

Q = 20

Substitute to get the equilibrium price per ride:

P = 60 – $\frac{Q}{20}$

P = 60 – $\frac{20}{20}$

P = 60

Equilibrium price per ride = 60

 

ii). Equilibrium number of rides per day:

60 – $\frac{Q}{20}$ = 4

Q = 80 – 60

Q = 20

Equilibrium number of rides per day = 20

 

iii). How many taxicabs will there be in equilibrium?

Number of taxicabs = Market output / individual output

Market output: Q = 1200 – 20(4)

Q = 1200 – 80

Q = 1120

Number of taxicabs = $\frac{1120}{20}$ = 56

Number of taxicabs = 56 taxicabs