Answer to Question #229619 in Microeconomics for aman

Question

Given a short run cost function as T C =1 /Q 3 (3 is under subscript ) - 2Q 2(2 is under subscript ) +60Q+100 , find the minimum value of AVC and MC

Answer 1

$TC=\frac{1}{3}Q^3-2Q^2+60Q+100$

$TVC=\frac{1}{3}Q^3-2Q^2+60Q$

To find the minimum value of MC,

$MC=\frac{dC}{dQ}\:$

$MC=Q^2-4Q+60$

$\frac{dMC}{dQ}=2Q-4=0$

$Q=\frac{4}{2}$

$Q=2$

To find the minimum value of AVC,

$AVC=\frac{TVC}{Q}=\frac{\frac{1}{3}Q^3-2Q^2+60Q}{Q}$

$AVC=\frac{1}{3}\:Q^2-2Q+60$

$\frac{dAVC\:}{dQ}=\frac{2}{3}Q-2=0$

$\frac{2}{3}Q=2$

$Q=3$