Applications 2: Elasticity and inverse

Introduction: In this section we consider the elasticity of a function and the elasticity of its inverse.

Theorem: Consider the function $y(x)$ and its inverse function $x(y)$. Let $\epsilon^y$ denote the elasticity of the function $y(x)$ and $\epsilon^x$ denote the elasticity of the inverse function $x(y)$. Then $$\epsilon^x=\frac{1}{\epsilon^y}.$$