Question

Given the cost function TC = 9q^2 + 2q + 8100. (i)Find marigibal cost (MC) and average cost (AC) as function of q. (ii) Show that MC<AC, AC is falling, and MC>AC, AC is rising.

Answer 1

(i) Marginal cost is MC = TC'(q) = 18q + 2, and average cost is AC = TC/q = 9q + 2 + 8100/q.

(ii) If MC < AC, then AC is falling until MC = AC, so:

18q + 2 = 9q + 2 + 8100/q,

$9q^2 - 8100 = 0,$

(3q - 90)(3q + 90) = 0,

The only suitable root is: q = 30.

MC > AC if q > 30, so AC starts to rise after this point.