Answer
The price elasticity of demand is -.726, so the demand curve is inelastic.
Work Step by Step
Let $P_{1}$, $P_{2}$, $Q_{1}$, $Q_{2}$, $R_{1}$, and $R_{2}$ represent the prices, quantities, and total revenue before (1) and after (2) the price change respectively.
$P_{1}*Q_{1}=R_{1}$
$P_{2}*Q_{2}=R_{2}$
The quantity decreased 30%, and total revenue increased 15%.
$1.15*R_{1}=R_{2}$
$1.15*(Q_{1}*P_{1})=.7*P_{2}*Q_{2}$
$1.15*P_{1}*Q_{1}=.7*P_{2}*Q_{2}$
$1.15*P_{1}*Q_{1}/.7=.7*P_{2}*Q_{2}/.7$
$1.642*P_{1}*Q_{1}=P_{2}*Q_{2}$
We have adjusted for the change in quantities, so we can now say that $Q_{1}=Q_{2}$
$1.642*P_{1}=P_{2}$
$1.642*P_{1}/1.642=P_{2}/1.642$
$P_{1}=.609*P_{2}$
$Elasticity = \frac{(Q_{2}-Q_{1})/[(Q_{1}+Q_{2})/2]}{(P_{2}-P_{1})/[(P_{1}+P_{2})]}$
$Elasticity = \frac{(.7Q_{1}-Q_{1})/[(Q_{1}+.7Q_{1})/2]}{(P_{2}-.609P_{2})/[(P_{2}+.609P_{2})/2]}$
$Elasticity = \frac{(-.3Q_{1})/[(1.7Q_{1})/2]}{(.391P_{2})/[(1.609P_{2})/2]}$
$Elasticity = \frac{(-.3Q_{1})/(.85Q_{1}]}{(.391)/[(1.609)/2]}$
$Elasticity = \frac{(-.3Q_{1})/(.85Q_{1}]}{(.391)/[.8045]}$
$Elasticity = \frac{(-.3)/(.85)}{(.391)/(.8045)}$
$Elasticity = \frac{(-.3)/(.85)}{(.391)/(.8045)}$
$Elasticity = \frac{-.3529}{.486}$
$Elasticity = -.726$
