Answer :
Answer:
The number of firms in the long run is 9.
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.
[tex]\frac{dATC}{dq}=\frac{-32}{q^{2} }+2=0[/tex]
[tex]q^{2}=\frac{32}{2}[/tex]
[tex]q^{2}=16[/tex]
[tex]q=\sqrt{16}[/tex]
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.