Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 25

A number of additional conclusions can be drawn from the fact that the marginal revenue curve associated with a linear demand curve is also linear and has the same intercept and twice the slope of the original demand curve.
a. Show that the horizontal intercept of the marginal revenue curve (for a linear demand curve) is precisely half of the value of the demand curve s horizontal intercept.
b. Explain why the intercept discussed in part a shows the quantity that maximizes total revenue available from the demand curve.
c. Explain why the price elasticity of demand at this level of output is -1.
d. Illustrate the conclusions of parts a-c with a linear demand curve of the form Q = 96 - 2P.