Question

When price of a commodity $X$ falls by $10$ per cent, its demand rises from $150$ units to $180$ units. Calculate its price elasticity of demand. How much should be the percentage fall in its price so that its demand rises from $150$ to $210$ units?

Answer 1

Given, percentage change in price $=(-)10\%$
$Q=150units;Q_1=180units;△Q=Q_1-Q=(180-150)units=30units$
Percentage change in quantity demanded $=\frac{△Q}{Q}\times 100$
$=\frac{30}{150}\times 100=20\%$
Price elasticity of demand $\left(E_d\right)=(-)\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$
$=(-)\frac{20\%}{-10\%}=2$
When demand rises from $150$ to $210$ units:
$E_d=2$
$Q=150units;Q_1=210units;△Q=Q_1-Q=(210-150)units=60units$
Percentage change in quantity demanded $=\frac{△Q}{Q}\times 100$
$=\frac{60}{150}\times 100=40\%$
Price elasticity of demand $\left(E_d\right)=(-)\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$
$2=(-)\frac{40\%}{\text{Percentage change in price}}$
Percentage change in price $=\frac{-40\%}{2}=20\%$
Price elasticity of demand $=2$.
Percentage fall in price $=20\%$.