Intuition - Why does elasticity vary along a curve? Source: p 96, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw


  Even though the slope of a linear demand curve is constant, the elasticity is not.
  This is true because the slope is the ratio of changes in the two variables, whereas
  the elasticity is the ratio of percentage changes in the two variables.
  
  [Source:] Elasticity along a straight line demand curve varies from zero at the quantity axis to infinity at the price axis. ... At the midpoint ... elasticity is equal to one, or unit elastic.


Please explain the above intuitively? I ask NOT for a formal proof.
Think of it this way. A yacht costs $\$0.01$. How much do you demand? Then double the price. Now how many would you demand?

Then consider something closer to a market price. Something in 6 or 7 figures I guess. If you've got some money, you might buy one at the market price. But then if that price doubles, wouldn't that affect your demand a lot more than the 1 to 2 pennies change?

Simply put, as you go up the demand curve, the same percentage change in price is a much bigger absolute movement in price.