Question

Imagine a perfectly competitive industry in which the industry demand function is P = 1550 – 0.5Q, and each firm’s total cost function is C = 2q² + 10q + 3500. For simplicity, assume that the long run average cost function has its minimum at the same point as the short run average cost function. At the long run equilibrium, how many firms will exist?

Answer 1

P= 1550–0.5Q

C= 2q2+10q+3500

Marginal Cost= 4q+10

Average Cost= 2q+10+3500/q

In the long run, Price Charged by each firm= Marginal Cost of each firm= Average Cost of each firm

4q+10= 2q+10+3500/q

4q2+10q= 2q2+10q+3500

2q2= 3500

q= 41.83

Price Charged by each firm= Marginal Cost of each firm= Average Cost of each firm= 4×41.83+10= $177.33

P= 1550–0.5Q

177.33= 1500–0.5Q

Q= 2745.34

Let there be n number of firms in the long run

nq= Q

n×41.83=2745.34

n= 66

In the long run, 66 firms will exist.