Needing help on question C.

An author receives a royalty based on 1/2 of the revenue generated by the sale of her book.1 Assume that the book's inverse demand is given by: P = 100 - Q. It costs the publisher $10 to produce an additional copy of the book.

a. Given the royalty plan, discuss the conflict that this arrangement creates between the author and the publisher about the amount to produce. Ignore issues related with the promotion of the book in your answer. Your explanation should read like a textbook. All illustrations should be hand-drawn. Include an illustration. The numbers associated with profit maximization are not important here.

b. As a consumer, whose interests would you like served - the interests of the publisher or the author? Explain.

Explanation:

Demand, i.e. P = 100 - Q is similar for both author and publisher.

Publisher

Publisher's total cost, C = 25Q + 200 + 0.1Q = 25.1Q + 200

Revenue = P x Q = 100Q - Q²

Marginal revenue, MR = dTR / dQ = 100 - 2Q

Marginal cost for publisher = 25.1

Equating MR to MC gives:

100 - 2Q = 25.1

2Q = 74.9

Q = 37.45

P = 100 - Q = $62.55

Author

For the author, MR = 100 - 2Q

But author incurs no cost in receiving the royalty payment, so MC = 0

Thus,

100 - 2Q = 0

Q = 50

P = 100 - 50 = $50

The publisher's optimal quantity Q (37.45) is less than the author's optimal quantity Q(50) and is sold at a higher price ($62.55) compared to the author's optimal price($50). Therefore, the publisher would love less quantity to be sold at a higher price while the author prefers more quantity sold at any price because he/she incurs $0 marginal cost.

c. Consider the case where the book is sold only as an electronic book, where the marginal cost of production equals $0. What is the effect of this change in production on your answers to parts a and b? Please assist with an illustration.