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

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

Where $TC=AC×Q$

a) $AC=1.5Q+\frac{4}{Q}+46$

$TC=(1.5Q+\frac{4}{Q}+46)Q$

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

$MC=3Q+46$

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

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

$MC=5-6Q+6Q^2$