Question

When price of a good rises from $Rs.8$ per unit to $Rs.10$ per unit, producer supplies $40$ units more. Price elasticity of supply is $2$. What is the quantity supplied before the price change? Calculate.

Answer 1

Suppose the producer initially supplies $X$ units at $Rs.8$.
Given, $P=Rs.8;P_1=Rs.10;△P=P_1-P=Rs.10-Rs.8=Rs.2$
$Q=Xunits;Q_1=(X+40)units;△Q=40units$
$E_S=2$
Price elasticity of supply $\left(E_S\right)=\frac{P}{Q}\times \frac{△Q}{△P}$
$2=\frac{8}{X}\times \frac{40}{2}$
$\Rightarrow 2=\frac{160}{X}$
$\Rightarrow 2X=160$
$\Rightarrow X=\frac{160}{2}=80$
Before the price change, quantity supplied $=80units$.