Question

When the price of commodity $A$ falls from $Rs.10$ to $Rs.5$ per unit, its quantity demanded doubles. Calculate its elasticity of demand. At what price will its quantity demanded fall by $50$ per cent?

Answer 1

Given, percentage change in quantity demanded $=100\%$
$P=Rs.10;P_1=Rs.5;△P=P_1-P=Rs.5-Rs.10=(-)Rs.5$
Percentage change in price $=\frac{△P}{P}\times 100=\frac{-5}{10}\times 100=(-)50\%$
Elasticity of demand $\left(E_d\right)=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$
$=(-)\frac{100\%}{-50\%}=2$
When quantity demanded falls by $50\%$.
$E_d=2$
Elasticity of demand $\left(E_d\right)=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$
$2=(-)\frac{-50\%}{\text{Percentage change in price}}$
Percentage change in price $=(-)\frac{-50\%}{2}=25\%$
When price of the commodity rises by $25\%$, new price $=Rs.10+Rs.2.5(25\%$ of $10)=Rs.12.5$
Elasticity of demand $=2$.
New price $=Rs.12.5$.