The author of a science fiction novel is paid a royalty of share of the revenue

The author of a science fiction novel is paid a royalty of β share of the revenue from sales, where the revenue is R = pq, p is the competitive market price for novels, and q is the number of copies of this book sold. The publisher’s cost of printing and distributing the book is C(q). Determine the equilibrium, and 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. M