Shooting Star Books is a small publishing company that specializes in science fiction books. Like most publishers, Shooting Star releases new books in hardcover form and later releases paperback versions of the books
The marginal cost of printing both types of books is $2 per book, and Shooting Star maximizes profits by practicing intertemporal price discrimination. The annual demand for recently released (hardcover) books is Q1 = 400 - 10P1 where quantity demanded is measured in thousands of books and price is measured in dollars per book. The annual demand for the paperback version of previously released books is Q2 = 800 - 40P2. a. What are the marginal revenue curves associated with the two demand curves for books? b. What are the profit maximizing prices for hardcover and paperback books? What are the quantities of books demanded at these prices for hardcover and paperback books? c. Suppose the market demand for paperback books shifts to Q2 = 150 - 100P2. How does this change affect the profit maximizing price and quantity in the paperback book market? Does this change affect the profit maximizing outcome in the hardcover book market?
a.
The price-dependent forms of the demand curves are P1 = 40 - 0.1Q1 and P2 = 20 - 0.025Q2, and the associated marginal revenue curves are MR1 = 40 - 0.2Q1 and MR2 = 20 - 0.05Q2.
b.
The profit maximizing output of hardcover books is found by solving MC = MR1, which provides
Q1 = (40 - 2 )/0.2 = 190 thousand books. Based on the demand curve for these books, the optimal price is P1 = 40 - 0.1(190 ) = $21 per book. The profit maximizing output of paperback books is then
Q2 = (20 - 2)/0.05 = 360 thousand books, and the optimal price of these books is
P2 = 20 - 0.025(360 ) = $11 per book.
c.
Based on this shift in the demand curve, the new marginal revenue curve is MR2 = 1.5 - 0.02Q2. Given that the marginal cost exceeds the maximum reservation price for paperback books, the company cannot profitably sell these books so that Q2 = 0. Further, the shift in demand for paperback books does not affect the optimal price and quantity outcomes in the hardcover book market.
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