Consider the market for Harry Potter e-books. Suppose Amazon has a monopoly on the distribution of e-books, through the dominance of its kindle format. J.K. Rowling, in turn has the monopoly rights to all versions of the Harry Potter books, via her copyright. Suppose Amazon and Rowling are trying to negotiate a deal where Harry Potter e-books will be available on Amazon. Suppose the total demand for Harry Potter e-books is given by: Q = 60-p

Where p is the price paid by consumers. Amazon's only cost to selling digital versions of the book is a royalty r (per book) that it must pay Rowling. Essentially, Amazon's marginal cost of the e-books is r. Rowling, in turn, has zero marginal cost (the books are already written).

(a) Assume Amazon and Rowling both act like independent profit-maximizers. What is the profit-maximizing price Amazon will set for the books? (Hint: Your results will be conditional on r).

(b) Given your answer to part (a), derive Rowling's profit-maximizing royalty rate (r). Use your result to find the market price of Harry Potter e-books charged to consumers. Calculate the profits of Amazon and Rowling.

(c) In reality, J.K. Rowling did not originally allow Harry Potter e-books to be sold on Amazon. Instead, she formed her own online bookstore called Pottermore, which sold her books. Assume Pottermore faces the same demand as Amazon, but has zero marginal cost like J.K. Rowling. What is the price charged to consumers from Pottermore? How many books are sold, and what is the profit of Pottermore?

(d) Verify that the vertical integrated company has higher profits than the joint profits of the Rowling and Amazon. Explain and discuss why setting up her own online store also benefits consumers