In Gomorrah, New Jersey, there is only one newspaper, the Daily Calumny. The demand for the paper depends on the price and the amount of scandal reported. The demand function is Q = 15S1/2P−3, where Q is the number of issues sold per day, S is the number of column inches of scandal reported in the paper, and P is the price. Scandals are not a scarce commodity in Gomorrah. However, it takes resources to write, edit, and print stories of scandal. The cost of reporting S units of scandal is $10S. These costs are independent of the number of papers sold. In addition it costs money to print and deliver the paper. These cost $.10 per copy and the cost per unit is independent of the amount of scandal reported in the paper. Therefore the total cost of printing Q copies of the paper with S column inches of scandal is $10S + .10Q.
(a) Calculate the price elasticity of demand for the Daily Calumny. ______. Does the price elasticity depend on the amount of scandal reported? ______. Is the price elasticity constant over all prices? ______.
(b) Remember that MR = P(1 + 1/ɛ). To maximize profits, the Daily Calumny will set marginal revenue equal to marginal cost. Solve for the profit-maximizing price for the Calumny to charge per newspaper. ______. When the newspaper charges this price, the difference between the price and the marginal cost of printing and delivering each newspaper is ______.
(c) If the Daily Calumny charges the profit-maximizing price and prints 100 column inches of scandal, how many copies would it sell? (Round to the nearest integer.) ______. Write a general expression for the number of copies sold as a function of S: Q(S) = _________.