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