Question

A firm has the following cost and marginal cost​ functions: Upper C left parenthesis q right parenthesis equals 64 plus q squared and MC equals 2 q. What is the minimum efficient​ scale? The minimum efficient scale LOADING... occurs at nothing units of output ​(enter your response as a whole number​).

Answer 1

Answer: Minimum efficient​ scale is 8 units.

Explanation:

Given that,

Cost function: C(q) = 64 + $q^{2}$

Marginal cost function: MC = 2q

Average cost: AC = $\frac{C(q)}{q}$

                             = $\frac{64 + q^{2}}{q}$

                             = $\frac{64}{q} + q$

The minimum efficient scale is at a point where MC = AC

2q =  $\frac{64}{q} + q$

$q^{2} = 64\\q = \sqrt{64} \\q = 8$

Therefore, minimum efficient​ scale is 8 units.