Calculating percentage change. Using average or endpoint values?

Question

I have always been taught that when I need to find the percentage change of a value I should do

$$ ΔX = \frac{X_{new}-X_{old}}{X_{old}} * 100\% $$

Yesterday however I was reading on price elasticity of demand and I came across the following

$$ η = \frac{\%ΔQ}{\%ΔP} = \frac{\frac{ΔQ}{Q_{A}}}{\frac{ΔP}{P_{A}}} $$

Where $Q_{A}$ is the average quantity $\frac{Q_{1}+Q_{2}}{2}$ and similarly for $P_{A}$

I searched a bit on Google but everything I found concerned the Elasticity.
My question is: When calculating percentage change, should I use the average value to divide or one of the end points? Is using the average an economics/elasticity thing or is it a valid alternative?
Thank you

Answer 1

I don't know from where your old knowledge comes from, but are you sure about it? Try an example where you know the answer, that is always the best. I guess that you are missing the point that for elasticity you have two variables, one depending on the other. In the first formula you have only $X$; so you have only the change in $X$ in percents.

Here is the definition of elasticity:

http://en.wikipedia.org/wiki/Output_elasticity

So your elasticity should be:

$$ \frac{d Q}{d P} \cdot \frac{P}{Q} $$

This seems to be the second formula.

Answer 2

The elasticity $\eta$ that you have found is the arc elasticity