A publisher sells books to Borders at $12 each. The marginal production cost for the publisher is $1 per book. Borders prices the book to its customers at $24 and expects demand over the next two months to be normally distributed, with a mean of 20,000 and a standard deviation of 5,000. Borders places a single order with the publisher for delivery at the beginning of the two-month period. Currently, Borders discounts any unsold books at the end of two months down to $3, and any books that did not sell at full price sell at this price.
(a) How many books should Borders order? What is its expected profit? How many books does it expect to sell at a discount?
(b) What is the profit that the publisher makes given Borders' actions?
(c) A plan under discussion is for the publisher to refund Borders $5 per book that does not sell during the two-month period. As before, Borders will discount them to $3 and sell any that remain. Under this plan, how many books will Borders order?
What is the expected profit for Borders? How many books are expected to be unsold? What is the expected profit for the publisher? What should the publisher do?