On estimating elasticity from a change in price

Elasticity of demand is defined at a given Price and Quantity by taking an infinitesimal change. But in real life you cannot measure the effects of a small change, so we are presented with discrete changes. If the elasticity is not constant (most demand curves get more elastic as you raise price as consumers find more substitutes) then the elasticity after the price change may be different from the elasticity before the change. Using the percentage change from the midpoint, is a way of dealing with this: Instead of elas=((Q1-Q0)/Q0)/((P1-P0)/P0) we use elas=((Q1-Q0)/midpointQ)/((P1-P0)/midpointP); where midpointP=(P1+P2)/2, and midpointQ=(Q1+Q2)/2, and you get the formula in our favorite textbook.