Question

Price elasticity of supply of a good is $2$. A producer supplies $100$ units of a good at a price of $Rs.20$ per unit. At what price will he supply $80$ units?

Answer 1

Suppose the producer supplies $80$ units at $Rs.X$.
Given, $P=Rs.20;P_1=Rs.X;△P=Rs.(X-20)$
$Q=100units;Q_1=80units;△Q=Q_1-Q=(80-100)units=(-)20units$
$E_S=2$
Price elasticity of supply $\left(E_S\right)=\frac{P}{Q}\times \frac{△Q}{△P}$
$2=\frac{20}{100}\times \frac{-20}{X-20}$
$\Rightarrow 2=\frac{-4}{X-20}$
$\Rightarrow -2=X-20$
$\Rightarrow X=20-2=18$.