For a firm, let total cost be TC(Q) = 160+10Q² and marginal cost be MC(Q) = 20Q. What is the minimum efficient scale for this firm? A) 0 B) 2 C) 4 D) indeterminate

Question

Quizplus · Accepted Answer

The minimum efficient scale is the level of output at which the firm can produce at the lowest average total cost (ATC) possible in the long run. 
To find the minimum efficient scale, we need to find the level of output at which ATC is minimized. 
ATC(Q) = TC(Q) / Q 
= (160+10Q+1U1P12S1S1P0)/Q 
= 160/Q + 10 + 1/(QU1P12S1S1P0)
To minimize ATC, we differentiate it with respect to Q and set it equal to zero: 
dATC(Q)/dQ = -160/Q^2 + 1/(QU1P12S1S1P0)^2 = 0 
Solving for Q, we get: 
Q = sqrt(1/(10U1P12S1S1P0)) 
Plugging in the values we get Q = 3.16 
Therefore, the minimum efficient scale for this firm is 4 units (rounded up), since the output has to be a whole number.

For a Firm, Let Total Cost Be TC(Q) = 160+10Q2

For a Firm, Let Total Cost Be TC(Q) = 160+10Q²