Elasticity of a function

In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output) at point a is defined as

or equivalently

It is thus the ratio of the relative (percentage) change in the function's output ${\displaystyle f(x)}$ with respect to the relative change in its input ${\displaystyle x}$, for infinitesimal changes from a point ${\displaystyle (a,f(a))}$. Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument. Generalisations to multi-input-multi-output cases also exist in the literature.

The elasticity of a function is a constant ${\displaystyle \alpha }$ if and only if the function has the form ${\displaystyle f(x)=Cx^{\alpha }}$ for a constant ${\displaystyle C>0}$.

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