Laurel and Hardy have written a new managerial economics textbook, for which they receive royalty payments of 15 percent of total revenue from book sales. Because their royalty is tied to revenues, not profits, they want the publisher to set the price so that total revenue is maximized. However, the publisher’s objective is to maximize profits. If total gross revenue (before royalties are deducted) can be expressed as
TR = 10000Q – 2Q2
and the total cost function is
TC = 1,000,000 + 200Q + 2Q2
a. Determine the output rate that will maximize the total gross revenue. At this level of output, calculate how much gross revenue results for the publisher, the publisher’s net revenue (gross minus royalties), the publisher’s profit, and the amount of royalties received by Laurel and Hardy. Be sure you have found a maximum for revenues.
b. Determine the output rate that would maximize profits for the publisher. Using this output rate, how much would gross revenues be? What will net revenues be? What will profits be? What will royalty payments be for Laurel and Hardy under this solution?
c. Determine output, gross revenues, net revenues, and profits if the publisher grants Laurel and Hardy a fixed royalty of $1,500,000, but zero percent of revenues.