4.The publisher of a book faces a demand curve for the book, P = 100 - Q, where Qis the number of books sold and P the price per copy of the book. The cost of producingthe book (excluding the royalty payment)is given by, TC = 25Q + 200.The author ofthe 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 andthe author who wants to receive as large an income as possible? Show and explain allyour calculations. Be sure to determine the price charged by the publisher, number ofcopies sold, profit of the publisher and the income of the author. Explain why yourconclusion does not depend on the specific demand and cost functions or the amount ofthe royalty.

(Hint: There is a "conflict of interest" if the optimal output, price, profit and royalty from the perspective of the author are different from those 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.)

5.Perloff Brander (2^nd. edition) Ch.9, exercise 5.3.