11.7 This problem concerns the relationship between demand and marginal revenue curves for a few functional forms.

a. Show that, for a linear demand curve, the marginal revenue curve bisects the distance between the vertical axis and the demand curve for any price.

b. Show that, for any linear demand curve, the vertical distance between the demand and marginal revenue curves is %1/b Æ q, where b (< 0) is the slope of the demand curve.

c. Show that, for a constant elasticity demand curve of the form q ¼ aPb

, the vertical distance between the demand and marginal revenue curves is a constant ratio of the height of the demand curve, with this constant depending on the price elasticity of demand.

d. Show that, for any downward-sloping demand curve, the vertical distance between the demand and marginal revenue curves at any point can be found by using a linear approximation to the demand curve at that point and applying the procedure described in part (b).

e. Graph the results of parts (a)–

(d) of this problem.