Question

You are a producer in a constant-cost perfectly competitive
industry. Your long-run total, marginal, and average costs are
given by *TC* = 2*Q*² + 128, *MC* =
4*Q*, and *ATC* = 2*Q*+ (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 = 2*Q*+ (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.**

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