Question

A consumer spends $\text{Rs.}200$ on a good priced at $\text{Rs.}5$ per unit. When the price falls by $20\%$, he continues to spend $\text{Rs.}200$. Find the price elasticity of demand by percentage method.

Answer 1

Initial price, $P_i=Rs.5$
Fall in price (by $20\%=5\times \frac{20}{100}=\text{Rs.}1$

New price, $P_f=\text{Rs.}5-\text{Rs.}1=\text{Rs.}4$
Given, $P_i=Rs.5$

$P_f=Rs.4$

$\Delta P=P_f-P_i=\text{Rs.}4-\text{Rs.}5=-1$

Initial Quantity, $Q_i=\frac{200}{5}=40\text{units}$

Final Quantity, $Q_f=\frac{200}{4}=50\text{units}$

$\Delta Q=Q_f-Q_i=(50-40)\text{units}=10\text{units}$

Price elasticity of demand, $E_d=-\frac{P}{Q}\times \frac{\Delta Q}{\Delta P}$
$=-\frac{5}{40}\times \frac{10}{-1}$
$=\frac{5}{4}=1.25$
Hence, Price elasticity of demand $=1.25$.