Suppose that an author of popular science fiction novels is paid a royalty of a share of the revenue from sales, where the revenue is R = pq, p is the competitive market price for such novels, and q is the number of copies of this novel sold. The publisher’s cost of printing and distributing the book is C(q). Determine the output level that maximizes the publisher’s profit. Compare it to the outcome that maximizes the sum of the payment to the author plus the firm’s profit. Answer using both math and a graph.