DVD retailers choose how many
copies of a movie to purchase from a studio and to stock. The retailers have
the right to return all unsold copies to the studio for a full refund, but the
retailer pays the shipping costs for returned copies. A small mom-and-pop
retailer will sell 1, 2, 3, or 4 copies with probabilities 0.2, 0.3, 0.3, and
0.2, respectively. Suppose that the retail market price of the DVD is $15 and
that the retailer must pay the studio $8 for each copy. The studio’s marginal
cost is $1. The retailer’s marginal profit is $7 for selling each copy, and the
studio’s marginal profit is $7 for each nonreturned copy sold to the retailer.
The cost of shipping each DVD back to the studio is $2. The studio and retailer
are risk neutral.
a. How many copies of the DVD
will the retailer order from the studio? What is the studio’s expected
profit-maximizing number of copies for the retailer to order?
b. Alternatively, suppose that
the studio pays the shipping costs to return unsold DVDs. How many copies would
the retailer order?
c. Does the number of copies the
retailer orders depend on which party pays the shipping costs? Why?