Question

The price elasticity of demand of a good is $(-)\mathrm{0.5.}$ At a price of $Rs20$ per unit its demand is $300$ units. At what price will its demand increase by $10$ percent ?

Answer 1

We have,

$e_D=(-)0.5$

$P_1=20$

$P_2=?$

$Q_1=300$

We know that,

$\Delta Q=Q_2-Q_1$

$\Delta Q=330-300$

$\Delta Q=30$

Now,

$Q_2=10$

$Q_2=330$

So,

$ {{e} D =} \ dfrac {\ Delta P} {\ Delta Q}. \ dfrac {P} {Q} $

$\Rightarrow (-)0.5=\frac{30}{\Delta P}\times \frac{20}{300}$

$\Rightarrow (-)0.5\times 300\times \Delta P=600$

$\Rightarrow -150\Delta P=600$

$\Rightarrow \Delta P=\frac{600}{-150}$

$\Rightarrow \Delta P=-4$

So, new price will be $P+\Delta P$

$\Rightarrow 20-4=Rs.16$

Hence, this is the answer.