Depends on price and amount of scandal reported

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Third Problem 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, 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 2 the total cost of printing Q copies of the paper with S column inches of scandal is $10S + .10Q. 1. 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? 2. Remember that MR = P(1 + 1 ). 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 ? 3. If the Daily Calumny charges the profit-maximizing price and prints 100 column inches of scandal, how many copies would it sell? Write a general expression for the number of copies sold as a function of S. 4. 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. 5. 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?

Reference no: EM131118714

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