Answer
a. E=0.5 the demand is inelastic;
b. E= 8 the demand is elastic
Work Step by Step
a. $\frac{dp}{dq}=-0.4p$
$E=\frac{-p}{q}.\frac{dp}{dq}=\frac{-p}{400-0.2p^{2}}(-0.4p)=\frac{0.4p^{2}}{400-0.2p^{2}}$
Let p=20 to get $\frac{0.4(20)^{2}}{400-0.2(20)^{2}}=0.5$
Since $0.5 \lt 1$ the demand is inelastic, and a percentage change in price will result in a smaller percentage change in demand.
b. a. $\frac{dp}{dq}=-0.4p$
$E=\frac{-p}{q}.\frac{dp}{dq}=\frac{-p}{400-0.2p^{2}}(-0.4p)=\frac{0.4p^{2}}{400-0.2p^{2}}$
Let p=40 to get $\frac{0.4(40)^{2}}{400-0.2(40)^{2}}=8$
Since $8\gt1$ the demand is elastic, and a percentage change in price will result in a smaller percentage change in demand.
