Question

A consumer spends $Rs.1,500$ on a good priced at $Rs.10$ per unit. When price rises by $20$ per cent, the consumer continues to spend $Rs.1,500$ on the good. Calculate price elasticity of demand by percentage-change method.

Answer 1

Initial price (P) $=Rs.10$
Rise in price by $20$ per cent = $10\times \frac{20}{100}$ =Rs. 2
New price ($P_1$) $Rs.10+Rs.2=Rs.12$
Given, $P=Rs.10$; $P_1=Rs.12;$

$△P=P_1-P$=$Rs.12-Rs.10=Rs.2$
$Q=\frac{1,500}{10}=150units;Q_1=\frac{1,500}{12}=125units;$

$△Q=Q_1-Q=(125-150)units=(-)25units$
Price elasticity of demand $\left(E_d\right)=(-)\frac{P}{Q}\times \frac{△Q}{△P}$
$=(-)\frac{10}{150}\times \frac{-25}{2}=\frac{5}{6}=0.83$
Price elasticity of demand $=0.83$