How and why does price elasticity change along a demand curve?

Price elasticity of demand is defined as the proportional change in demand to a change in price. If the response in demand is more than proportional to the price change, demand is elastic. A less than proportional change in demand shows inelastic demand. 

However, along one demand curve, elasticity changes depending on the position on the demand curve. At the top end of the demand curve, an increase in price from say, 1 to 2, leads to a decrease in demand of say, 10 to 9. Although the units of change are identical, there is a 100% increase in price from 1 to 2, but a 10% decrease in demand from 10 to 9. By definition this shows inelastic demand as there only a 10% decrease in demand from a 100% increase in price.

At the lower end of the demand curve, an increase in price from say, 9 to 10, leads to a decrease in demand from say, 2 to 1. The price change is 1/9 so around 11%, but demand falls by 50% from 2 to 1. By definition this is elastic demand as the change in demand (50%) is more than proportional to the price change (11%).

This is an advanced evaluation of price elasticity, but would be impressive in an Oxbridge interview.