Question

You are a producer in a constant-cost perfectly competitive industry. Your long-run total, marginal, and average costs are given by TC = 2Q² + 128, MC = 4Q, and ATC = 2Q+ (128/Q). What is the long-run equilibrium price?

Answer 1

the long run equilibrium price is at min ATC in a perfectly competitive industry. in other words, price equal to minimum ATC in the long run so that the firms earn zero economic profits in long run.

ATC = 2Q+ (128/Q)

to find minimum ATC we take first order derivative of the ATC function

dATC/dq = 2 - 128/Q^2 = 0

128/Q^2 = 2

Q^2 = 256

Q = +-16, the negative value will be ignored.so Q = 16

ATC at Q = 16, =2*16+ (128/16) = 40

so P = ATC = 40 in the long run

The long run equilibrium price is $40.