Question

Suppose there is free entry in the market for microphones. The demand for microphones is given by: QD= 176-7P. All firms that produce microphones have identical long run average total cost functions given by: ATC = 32/q + 4 + 2q.

Calculate the long run number of firms in this market.

Answer 1

The number of firms in the long run is 9.

Step-by-step explanation:

Demand function: QD = 176 - 7P

Average total cost functions: ATC = 32/q + 4 + 2q

The long-run price of a perfectly competitive market is equal to the minimum average total cost.

The output at minimum average total cost is found by differentiating ATC and equating to zero.

`(dATC)/(dq)=(-32)/(q^(2) )+2=0`

`q^(2)=(32)/(2)`

`q^(2)=16`

`q=√(16)`

q = 4

Price = ATC = (32/4) + 4 + (2 × 4)

= 8 + 4 + 8

= 20

The market quantity is

QD = 176 - 7P

Q = 176 - (7 × 20)

Q = 176 - 140

Q = 36

Number of firms = Q ÷ q

= 36 ÷ 4

= 9

Therefore, the number of firms in the long run is 9.