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 studios 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?