Question

# 2. Suppose a representative firm producing in a perfectly competitive industry has the following cost function:...

2. Suppose a representative firm producing in a perfectly competitive industry has the following cost function: C(q) = q2 + 8q + 36 a. Solve for the firm’s average cost function. b. At what level of q is average cost minimized (i.e. what is the minimum efficient scale for the firm)? What is the value of average cost at this level of q? c. Suppose all firms in this industry are identical and the demand function for this industry is as follows: Qd = 400 – 2P Solve for the long run equilibrium price and quantity in this industry. d. How many firms will operate at this long-run equilibrium?

a) Given, C = Q2 + 8Q + 36

thus, ATC = TC/Q = Q + 8 + 36/Q

b) Taking the first derivative of ATC w.r.t. Q and putting it equal to zero (first order condution).

1 - 36/Q2 = 0

we get: Q = 6

Taking the second derivative, we get: 1 + 72/Q3 > 0

Thus, ATC is minimized.

ATC (at Q = 6) = 20

c) Given demand, Qd = 400 - 2P

Eqquilibrium is attained where Demand = supply.

Thus, 200 - Q = 2Q + 8

whcih gives Q = 64 and P = 168

d) In the long run, firms will continue to operate as long as P = ATC

Thus, 168 = Q + 8 + 36/Q

whcih gives Q = 160.

Thus, 160 firms will operate in the long run.