Question

1. A publisher sells books to Barnes & Noble at $40 each. The marginal production cost for the publisher is $20 per book. Barnes & Noble prices the book to its customers at $50 and expects demand over the next two months to have the following scenarios:

Quantity Probability

2000 3%

2100 8%

2200 15%

2300 30%

2400 17%

2500. 12%

2600 10%

2700 5%

Barnes & Noble places a single order with the publisher for delivery at the beginning of the two‐ month period. Currently, Barnes & Noble discounts any unsold books at the end of two months down to $10, and any books that did not sell at full price sell at this price.

a). How many books should Barnes & Noble order? What is its expected profit? What is the publisher’s expected profit?

b). If the publisher and Barnes & Noble were integrated, what is the system optimal production quantity and expected profit under global optimization?

c). Find a coordinating buy‐back contract such that the sum of publisher’s and Barnes & Noble’s expected profit equal to your answer in b). Please show how the coordinating buy‐back contract allocates the profit between the publisher and Barnes & Noble.

Answer 1

Answer a:

Quantity	Probability	Expected quantity to be purchased (Quantity x probability)
2000	3%	2000*0.30 = 60
2100	8%	168
2200	15%	330
2300	30%	690
2400	17%	408
2500	12%	300
2600	10%	260
2700	5%	135
	Total	2351

Barnes & Noble should order 2351 number of books.

The profit, Barnes & Noble earns per book is = 50 - 40 = 10

Totalexpected profit = 2351 * 10 = 23510

The profit, publisher earns per book is = 40 - 20 = 20

Total expected profit = 2351 * 20 = 47020

Answer b:

If the publisher and Barnes&Noble were integrated, the system optimal production quantity would be = 2351.

The expected profit under global optimization = 50 - 20 = 30 per book

Total profit = 2351 * 30 = 70530