Answer to Question #224772 in Macroeconomics for Tuji Yusuf

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

$a)\\ TVC=\frac{1}{3}q^3−2q^2+60q\\AVC=\frac{1}{3}q^2−2q+60\\ TC=\frac{q^3}{3}−2q^2+60q+100$

$MC=\frac{d}{dq}[\frac{q^3}{3}−2q^2+60q+100]$

$MC=\frac{1}{3}.\frac{d}{dq}[q^3]−2.\frac{d}{dq}[q^2]+60.\frac{d}{dq}[q]+\frac{d}{dq}[100]$

$\\MC=\frac{3q^2}{3}−(2×2q)+(60×1)+0\\MC=q^2−4q+60$