Question

When the price of $X$ doubles, its quantity demanded falls by $60$ per cent. Calculate its price elasticity of demand. What should be the percentage change in price so that its quantity demanded doubles?

Answer 1

Given, percentage change in price $=100\%$
Percentage change in quantity demanded $=(-)60\%$

Elasticity of demand $\left(E_d\right)=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$

$=(-)\frac{60\%}{100\%}=0.6$.

Given, $E_d=0.6$ and $100\%$ increase in quantity demanded, change in price can be estimated as under:

Elasticity of demand $\left(E_d\right)=\frac{100\%}{\text{Percentage change in price}}=0.6$

Percentage change in price $=(-)\frac{100\%}{0.6}=(-)166.67$
Elasticity of demand $=0.6$
Percentage fall in price $=166.67\%$.
Note : Fall in price by more than $100\%$ refers to a peculiar situation. It just cannot happen as it would take us to the realm of 'negative price'. There seems to be some fallacy in framing this question.