Question

A producer supplies $100$ units of a good at a price of $Rs.20$ per unit. Price elasticity of supply is $2$. At what price will he supply $50$ units? Calculate.

Answer 1

Suppose the producer supplies $50$ units at $Rs.X$.
Given, $P=Rs.20;P_1=Rs.X;△P=Rs.(X-20)$
$Q=100units;Q_1=50units;△Q=Q_1-Q=(50-100)units=(-)50units$
$E_S=2$
Price elasticity of supply $\left(E_S\right)=\frac{P}{Q}\times \frac{△Q}{△P}$
$2=\frac{20}{100}\times \frac{-50}{X-20}$
$\Rightarrow 2=\frac{-10}{X-20}$
$\Rightarrow X-20=\frac{-10}{2}$
$\Rightarrow X-20=-5$
$\Rightarrow X=-5+20=15$
The producer will supply $50$ units at $Rs.15$.