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 = 15S^1/2P⁻³, where Q is the number of issues sold per day, Sis the number of column inches of scandal reported in the paper, and Pis 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 re-ported __________ ? Is the price elasticity constant over all prices _______________?

(b) Remember that MR = P(1 + 1/ε). 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) =  ____________.

(d) Assuming that the paper charges the profit-maximizing price, write an expression for profits as a function of Q and S. ______________. Using the solution for Q(S) that you found in the last section, substitute Q(S) for Q to write an expression for profits as a function of S alone ___________________.

(e) If the Daily Calumny charges its profit-maximizing price, and prints the profit-maximizing amount of scandal, how many column inches of scandal should it print? _____________. How many copies are sold ____________ and what is the amount of profit for the Daily Calumny if it maximizes its profits ___________?