#### Answer

a. $200$ the demand is elastic
b. $0.5$ the demand is inelastic

#### Work Step by Step

a. $\frac{dp}{dq}=-2$
$E=\frac{-p}{q}.\frac{dp}{dq}=\frac{-p}{300-2p}(-2)=\frac{2p}{300-2p}$
Let p=100 to get $\frac{2(100)^{2}}{300-2(100)}=200$
Since $200\gt 1$ the demand is elastic, and a percentage change in price will result in a smaller percentage change in demand.
b. a. $\frac{dp}{dq}=-2$
$E=\frac{-p}{q}.\frac{dp}{dq}=\frac{-p}{300-2p}(-2)=\frac{2p}{300-2p}$
Let p=50 to get $\frac{2(50)}{300-2(50)}=0.5$
Since $0.5\lt1$ the demand is inelastic