The demand function for a very famous introductory economics textbook is P = 100 - 0.005Q. The publisher must pay $20 per book in printing and distribution costs and, in addition, she must pay the author a $20 royalty for each book sold.

A consultant says that the publisher and the author have the wrong agreement. He says the author and the publisher should tear up their original agreement, and instead enter a profit-sharing agreement. He recommends that the author gets 40% of the profit and the publisher gets 60%. (i) What price should the publisher set with this profit-sharing agreement, (ii) will the author and publisher prefer the profit-sharing agreement to their original agreement? (iii) which agreement will the students who buy the textbook prefer?