Question

If two demand curve cross each other at a particular point, will the price elasticity of demand be equal at the point of intersection?

Answer 1

This is a more complicated question than usually thought. The price elasticity is defined as:

%change in Qd/%change in P = [(change in Qd)/Qd]/[(change in P)/P]

= [(change in Qd)/change in P) times (P/Qd)

The first term is the slope of the demand curve (actually the inverse of the slope, since economists incorrectly labeled the axes long ago) while the second term is “where you are” in the P-Q space. Critically, knowing the slope alone is insufficient to to know the elasticity, because it depends on “where you are.” If however, two demand curves cross each other, at the point of crossing the flatter demand curve is the more elastic (because “where you are” is the same!). Further clarifying, if a linear demand curve is rotated outward, the flatter slope compared to before the rotation does not effect elasticity at any price, because “where you are” is changing in proportion to the slope—a graph is instructive here).