Question

Suppose that every year the city of New York auctions off a limited number of medallions that give cab drivers an exclusive right to taxi in the city for one year. After receiving the medallion the cab driver is essentially a monopolist facing an inverse demand function p = 20 - 1.4Q. The total cost function for each cab driver can be summarized as C(Q) = 3Q + F. Where F represents the cost of the medallion or annual fixed cost. What would each taxi medallion have to cost in the long run for this to be a case of monopolistic competition.

Hint: Write your answer to two decimal places.

Answer 1

In monopolistic competition, equilibrium occurs where MC=MR

TR= (20-1.4Q)*Q=20Q-1.4Q^2= 20Q-2.8Q^2

C(Q) = 3Q + F.

MR=dTR/dQ= 20-2.8Q

MC=dTC/dQ= 3

MC=MR

3=20-2.8Q

Q=6.07

In the long run Monopolistic competitive firms earn normal profit

Profit=TR-TC=0

TR=TC (Put Q= 6.07 to find the value of F)

20(6.07)-2.8(6.07)^2= 3(6.07) + F

121.4- 103.16= 18.12+F

F=0.12