Answer
$E=0.4286$
$p=\$50$
Revenue: $p\times q=50\times (1000-10\times50)=25,000$
Work Step by Step
If the demand function is $q=1000-10p$ and $p=\$30$
The elasticity can be calculated as:
$E=-\frac{dq}{dp}\times\frac{p}{q}$
The derivative of the demand function is :$\frac{dq}{dp}=-10$
Therefore at the given price $E=-(-10)\times\frac{30}{1000-10\times30}=0.4286$
The maximum revenue is at the price, where $E=1$
$E=10\times\frac{p}{1000-10\times p}=1$
$20p=1000$
$p=\$50$
Here, the revenue is $p\times q=50\times (1000-10\times50)=25,000$
