Why does the price elasticity of demand (PED) of a product change at different levels of production?

Price Elasticity of Demand (PED) is the responsiveness of demand to a change in a product's price. PED may be calculated using the formula (% Change in quantity demanded / % Change in price). PED differs at different levels of production. Imagine a demand curve on a simple price/quantity diagram, as price increases the quantity demanded decreases. The curve has a constant slope which is the ratio between price and quantity, the difference in demand from a unit change in price. However, the curve does not have a constant PED, the slope is the ratio of changes in the two variables, whereas the PED is the ratio of percentage changes in the two variables. To visualise this imagine the demand for a luxury car. If the car sold at £1 today and doubled to £2 tomorrow there is likely to still be a very large demand for the car, suggesting the price elasticity of demand for luxury cars is inelastic at this point (<1). However if the car already sold for £100,000 and doubled to £200,000 the change in demand is likely to be much more significant, suggesting the price elasticty of demand is elastic (>1) at this price/quantity equilibrium. There is a point on every demand curve where price elasticity of demand is unit elastic (=1).