Question

What is the relationship--if there is one--between the price elasticity of demand and the slope of the demand curve

Answer 1

People might think that there is a relation between price elasticity of demand and the slope of the demand curve, because the notion is that if the demand curve is steeper then the elasticity is lower and if the curve is flatter that means the price elasticity is high, which is a false notion. To analyze this look at the formula for Price elasticity of demand,

where the first term() is the reciprocal of the slope of the demand curve and the second term () is the ratio of price to quantity.

The slope of a demand curve, whether it is flat or steep, is based on absolute changes in price and quantity, which represents as    and,

The price elasticity of demand is concerned with relative changes in price and quantity and that represents as:

Therefore the slope of demand curve and the price elasticity of demand are different from each other, because

For example,

Two straight line demand curves originating from the same point. There are two straight line demand curves NM and NS in Figure below. At a glance, the curve NS is flatter than NM. Therefore, it appears that its price elasticity is higher than the other curve. But this is not a reality. If we draw a line PV passing through these curves and touching the vertical axis at point P, the elasticity at point T on the NM curve according to the point formula is:

and, elasticity at point V on the NS curve is:

Thus the elasticity is equal at both points T and V but slope does not.