In class, we were able to demonstrate that slope and elasticity are not equivalent. We did so by showing that the elasticity changes along a demand function that has a constant slope.

For this question, do the reverse:

1. Sketch a demand function that has constant elasticity but variable slope.[You need not provide an equation, and the demand function need not be drawn to scale. However, make sure to label three points on the curve.]
2. Prove that your sketched curve has constant elasticity but variable slope.