Question

In the demand function Q= P^0.4 , calculate price elasticity of demand and identify type of good

Answer 1

$Soln,$

Demand function $Q=P^{0.4}$

Price elasticity of demand$=\frac {p}{Q} \frac{dQ}{dP}$

$=\frac {dQ}{dP}=p^{0.4}$

$=\frac{dQ}{dP}=P^{-0.4-1}$

$E=\frac{P}{Q}\times\frac{dQ}{dP}$

$E=\frac{P}{P^{-0.4}}\times P^{-0.4-1}$

$=\frac{P}{P^{-0.4}}\times P^{-0.4}\times P^{-1}$

$=P\times P^{-1}=1$

$=PED=1$

This elasticity of demand is elastic, meaning as incomes increase there is also an increase in quantity demanded in the market. Hence it is a normal good.