The publisher of a book faces a demand curve for the book, P = 100 - Q, where Q is the number of books sold and P the price per copy of the book. The cost of producing the book (excluding the royalty payment) is given by, TC = 25Q + 200. The author of the book receives a royalty (r) of 10 percent, i.e., r = 0.1, for every book sold.
Is there a "conflict of interest" between the publisher who wants to maximize profit and the author who wants to receive as large an income as possible? Show and explain all your calculations. Be sure to determine the price charged by the publisher, number of copies sold, profit of the publisher and the income of the author. Explain why your conclusion does not depend on the specific demand and cost functions or the amount of the royalty.
(Hint: There is a "conflict of interest" if the optimal output and price from the perspective of the author are different from the optimal output and price from the perspective of the publisher. Note that the cost of production does not include the royalty paid by the publisher. For convenience, you may assume that 1 unit of Q represents 1000 copies of the book. It does not affect your calculations.)