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A firm has long-run total costs of C = 10Q -10Q2 - 0.5Q3. What is the...

A firm has long-run total costs of C = 10Q -10Q2 - 0.5Q3. What is the firm's minimum efficient scale?
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Answer #1

Minimum efficient scale is the smallest level of output where long run average cost(LRAC) curve is minimum. A long run average cost curve is minimum where long run marginal cost(LRMC) curve is equals to it. So

C = 10Q -10Q2 - 0.5Q3

LRMC= differentiation of C with respect to Q= 10-20Q-1.5Q2

LRAC= C/Q= 10-10Q-0.5Q2

LRMC=LRAC

10-20Q-1.5Q2= 10-10Q-0.5Q2

10-20Q-1.5Q2-(10-10Q-0.5Q2)=0

-10Q-Q2=0

Multiply -1 on both sides

Q2+10Q=0

Q(Q+10)=0

Q=0 or Q= -10

But quantity can not be negative so Q=0 is the level of output where minimum efficient scale arises.

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