Question
========
Consider the following inverse demand function:
$p(x) = 50 - 0.5 \cdot x$
for the price $p$ given the demanded quantity $x$.
What is the price elastiticy of demand at a price of
$p = 5$?


Solution
========
First, we obtain the demand function by inverting the
inverse demand function:
$x = D(p) = (50 - p)/0.5 = 100 - 2 \cdot p$.

Then, at $p = 5$ the price elasticity of demand is
$$
\frac{D'(p)}{D(p)} p = \frac{-2}{90} 5 = -0.111111.
$$


Meta-information
================
extype: num
exsolution: -0.111
extol: 0.01
exname: price elasticity of demand
