Suppose now that the publisher in Exercise 2.6 faces a downward-sloping demand curve. The revenue is R(Q), and the publisher's cost of printing and distributing the book is C(Q). Compare the equilibria for the following compensation methods in which the author receives the same total compensation from each method:
a. The author is paid a lump sum, l.
b. The author is paid α share of the revenue.
c. The author receives a lump-sum payment and a share of the revenue.
Why do you think that authors are usually paid a share of the revenue?