Suppose that two economists write a textbook. Their publisher offers them royalties on sales of the book equal to $\alpha$ percent of the sales revenue. The economists are concerned. They believe that such a royalty system causes the publisher to sell less than the joint profit-

maximizing number of copies of the book. Demonstrate this reasoning. They believe that a royalty in the form of a lump-sum payment, $L$, or $\beta$ percent of profits does not cause the publisher to publish too few books.

Why do they agree to the $\alpha$ percent royalty? Hint: One explanation concerns asymmetric information on the part of the publisher concerning costs of publication.