Question

Given the functions: ATC= x-6+(30/x) and AR =10+(15/x), where x represents output, find TC, TR, and the output level when net revenue is zero.

Answer 1

$ATC=\frac{TC}{Q}$

$AR=\frac{TR}{Q}$

Q=x

$TC=ATC\times Q$

$TR=ATR\times Q$

$TC=(x-6 + (\frac{30}{ x}))\times x=x^2-6x+30$

$TR= (10 + (\frac{15}{ x}))\times x=10x+15$

TR=TC=0

$(x^2-6x+30)-(10x+15)=0$

$x^2-16x+15=0$

x=1, x=15

x=15

TR=150+15=165

TC=225-90+30=165

x=1

TR=10+15=25

TC=1-6+30=25