Here’s another way to identify the point of unit elasticity when the demand function is a straight line.
(a) Suppose the demand function has the form q = mp + b, where m < 0 and b > 0. Find the points where the line intersects the p and q axes.
(b) Find the midpoint of the two intercepts found in part (a).
(c) Show that the elasticity equals 1 at the point found in part (b). In other words, the point of unit elasticity is midway between the two intercepts of a straight line demand function.