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I know the equation for economic elasticity is:

$$\varepsilon = \frac{\%\,\Delta Y}{\%\,\Delta X}\frac{X}{Y} = \frac{\partial Y(X)}{\partial X}\frac{X}{Y} = \frac{\partial \log(Y)}{\partial \log(X)}$$

In fact, this is the generalization for any sensitive-analysis or elasticity for a given function; in this case $Y(X)$.

But, where does come it from? I mean, why is it the equation and no -for example- just the partial derivate of the given function?

Thanks in advance!

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up vote 1 down vote accepted

The elasticity gives you the percentage change of the dependent variable with respect to the percentage change of the independent variable. Elasticity by definition is dimensionless and I believe this is part of the motivation behind using this over the derivative like you mentioned.

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Ok, i understand, it is about dimensions (aka units of measurements). Thanks. Good point. – Diego Andrés Díaz Espinoza Aug 6 '13 at 20:31

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