Question

A perfectly competitive firm’s total cost function is given
by: TC = 400+4Q^2 . The minimum point of average total cost (ATC)
is reached at Q=10. You also know that the market demand function
for this product is: QD=100-P. How many firms are in the market in
the long-run? (Hint: first you need to find the price in the
long-run)

Select one:

a. N=6

b. N=4

c. N=2

d. None of the above

Answer #1

In the long-run, equilibrium is achieved where

P = MC = ATC

At the minimum of ATC, ATC and MC both are equal

So we can say in the long-run, equilibrium is achieved at the minimum of ATC where

P = MC = ATC

Now in the above question P = MC = ATC at 10 units.

ATC = TC / Q

ATC = 400 + 4Q^{2} / Q

ATC = 400/Q + 4Q

P = ATC = 400/Q + 4Q

P = ATC = 400/(10) + 4(10)

P = 80

Now we will use this price in demand function to find the market demand

Q = 100 - P

Q = 100 - (80)

Q = 20

Number of Firms = Market Demand / Individual Demand

Number of Firms = 20 / 10

*Number of Firms = 2*

*Hence C is correct*

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