My book (Goodwin's Microeconomics in Context, pg. 117) states the following about price-elasticity of demand:
Given two demand curves that go through a specific point on graphs with the same scale, the flatter demand curve will represent the relatively more elastic demand and the stepper one the relatively less elastic demand.
I have actually two questions about this:
1) Will the flatter demand curve be more elastic at any given point (for any given value of $p$) or just at the point that both curves pass through?
2) How can we show this mathematically using the definition of elasticity as $$\epsilon=\frac{dQ}{dp}\frac{p}{Q}$$?
Thanks very much in advance.