Elasticity

$E{L}_{x}f(x)=\frac{x}{f(x)}{f}^{\prime }(x)=\frac{\frac{df(x)}{f(x)}}{\frac{dx}{x}}$

Ratio of change in $f(x)$ to the percentage change in $x$ in %.

Marginal Changes … if we increase the price by 1%, the demand changes by x%.

The Derivative and the Elasticity share their sign.

Example

$D(P)=-10P+400$ $E{L}_{P}D(P)=\frac{P}{-10P+400}\ast (-10)=\frac{-10P}{-10P+400}$