Question

Due to $10$ per cent fall in the price of $X$, its demand rises from $100$ units to $120units$. How much percentage will its demand fall due to $10$ per cent rise in its price?

Answer 1

Given, percentage change in price $=(-)10\%$
$Q=100units;Q_1=120units;△Q=Q_1=Q=(120-100)units=20units$
Percentage change in quantity demanded $=\frac{△Q}{Q}\times 100=\frac{20}{100}\times 100=20\%$.
Elasticity of demand $\left(E_d\right)=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$
$=(-)\frac{20\%}{-10\%}=2$
When price rises by $10\%$:
$E_d=2$
Elasticity of demand $\left(E_d\right)=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$
$2=(-)\frac{\text{Percentage change in quantity demanded}}{10\%}$
Percentage change in quantity demanded $=(-)20\%$
Elasticity of demand $=2$.
Percentage fall in demand $=20\%$.