So, elasticity, say the price elasticity of demand, is: $$\text{elasticity}=\frac{\text{% change in demand}}{\text{% change in price}}$$ So an elasticity of one corresponds to situations where a 1% increase in prices led to a 1% decrease in demand. E.g. if a price movement from \$2.00 to \$2.02 per unit led to demand changing from 100 million to 99 million units, elasticity would be -1.
My question is: why does it make sense to equate percentage increases and percentage decreases in this way? In what sense are an increase of 1% and a decrease of 1% equivalent (as is implied by the term 'unit elastic')?
I guess my scepticism comes from personal finance examples - e.g. when an item's sale price has been reduced to 95% of its original price, in order to work out the original price, you'd have to divide by 0.95, not multiply by 1.05. But, on some level, aren't we doing the opposite here (i.e. equating multiplying by 0.95 with multiplying by 1.05)?
Thanks!