Question

A perfectly competitive firm’s total cost function is given by: TC = 200+2Q² . You also know that the market demand function for this product is: Q^D=100-P. How many firms are in the market in the long-run?

Select one:

a. N=10

b. N=8

c. N=6

d. None of the above

Answer 1

In the long-run price, marginal cost and average total cost all are equal.

P = ATC = MC

Total Cost

TC = 200 + 2Q2

Marginal Cost

MC = dTC / dQ

MC = 4Q

Average Total Cost

ATC = TC / Q

ATC = 200/Q + 2Q

Equating both MC and ATC

200/Q + 2Q = 4Q

Q = 10

To find the price we will use this quantity in any of the above two equations

P = MC = 4Q

P = MC = 4(10)

P = 40

To find the market demand we will use this price in demand equation.

Q = 100 - P

Q = 100 - 40

Q = 60

Number of Firms = Market Demand / Individual Demand

Number of Firms = 60 / 10

Number of Firms = 6