Question

A producer supplies $80$ units of a good at a price of $Rs10$ per unit. Price elasticity of supply is $4$. How much will he supply at $Rs9$ per unit ?

Answer 1

Given:
$Q_0=80$ units
$P_0=Rs.10$
$E_s=4$
$P_1=Rs.9$
$Q_1=?$
$\Delta P=P_1-P_0$
$\Delta P=9-10=-1$
$\Delta Q=Q_1-Q_0$
$\Delta Q=Q_1-80$
We know, $E_s=\frac{\Delta Q}{\Delta P}\times \frac{P_0}{Q_0}$
$4=\frac{Q_1-80}{-1}\times \frac{10}{80}$
$4=\frac{Q_1-80}{-8}$
$-32=Q_1-80$
$Q_1=48$ units
Thus, producer will supply $48$ units of good at $Rs.9$ per unit.