Question

Given a firms demand function Q-90+2P=0 and it's average cost function AC=Q²-8Q+57+2/Q. Find the level of output which maximises marginal cost.

Answer 1

Average cost function$=AC=Q^2-8Q+57+\frac{2}{Q}$

$TC=AC\times\ Q=Q^3-8Q^2+57Q+2$

$MC=\frac{dTC}{dQ}=3Q^2-16Q+57$

During the first order condition, $MC=0$

Therefore, $3Q^2-16Q+57=0$

Solving for $Q$ using the quadratic equation we get $Q=-4.68\ or \ 36.68$

36.68 will maximize Marginal Cost.