Question

Find the marginal cost functions for each of the following average cost functions. a) AC = 1.5Q + 4 + 46 𝑄 b) AC = 160 𝑄 + 5 - 3Q + 2Q2

Answer 1

Solutions

 $MC=\frac{dTC}{dQ}$

$TC = AC \times Q$

$a)AC = 1.5Q + 4 + 46Q$

Differentiate the AC function

$TC=1.5Q^{2}+4Q+46Q^{2}$

$MC=3Q+4+98Q$

$MC=101Q+4$

$b)AC=160Q+5-3Q+2Q^{2}$

$MC=\frac{dTC}{dQ}$

$TC=AC\times Q$

$TC=160Q^{2}+5Q-3Q^{2}+2Q^{3}$

$MC=320Q+5-6Q+6Q^{2}$

$MC=314Q+5+6Q^{2}$