Measurement of Price Elasticity — The Geometric (Point) Method

When elasticity is to be measured at a particular point on a straight-line demand curve, the geometric method (point method) is used. Extend the straight-line demand curve so that it touches both axes. At any point on the curve, elasticity equals the ratio of the lower segment of the curve (from the point down to the X-axis) to the upper segment (from the point up to the Y-axis):

On a straight-line demand curve AB (A on the price axis, B on the quantity axis) with a point R on it, the two segments RA (upper) and RB (lower) fix the elasticity at R:

This yields three neat results that hold on every straight-line demand curve:

• At the midpoint of the curve the lower and upper segments are equal, so $E_p = 1$ (unitary elastic).
• Above the midpoint (nearer the Y-axis) the lower segment is longer than the upper, so $E_p > 1$ (elastic). Elasticity approaches $\infty$ as the point nears the Y-axis.
• Below the midpoint (nearer the X-axis) the lower segment is shorter than the upper, so $E_p < 1$ (inelastic). Elasticity approaches $0$ as the point nears the X-axis.

So elasticity is not the same at every point of a straight-line demand curve even though its slope is constant — a vital caution against confusing slope with elasticity. …