Question

A consumer buys $100$ units of $Good-Y$ at $Rs.5$ per unit. The price elasticity of demand for the good is $2$. At what price will he be willing to buy $140$ units of $Good-Y$?

Answer 1

Suppose consumer buys $140$ units at price $Rs.X$ per unit.
Price elasticity of demand $\left(E_d\right)=(-)\frac{P}{Q}\times \frac{△Q}{△P}$
Here, $P=Rs.5;P_1=Rs.X;△P=P_1-P=Rs.(X-5)$
$Q=100units;Q_1=140units;△Q=Q_1-Q=(140-100)units=40units$
$E_d=2$
Price elasticity of demand $\left(E_d\right)=(-)\frac{P}{Q}\times \frac{△Q}{△P}$
$2=(-)\frac{5}{100}\times \frac{40}{(X-5)}=(-)\frac{2}{X-5}$
$2\times (X-5)=-2$ or $2X-10=-2$
$2X=-2+10=8$
$X=4$
The consumer will purchase $140$ units of Good-Y at the price of $Rs.4$.