Supply contracts:

9a. What is the system optimal production quantity and expected profit under global optimization?

9b. Suppose the manufacturer is make-to-order; that is, the timing of events is as follows: The distributor orders before it receives demand from end customers. The manufacturer produces the amount ordered by the distributor. Customer demand is observed. i. Suppose the manufacturer sells to the distributor at $40/unit, how much will the distributor order? What is the expected profit for the manufacturer and distributor? ii. Find an option contract such that both the manufacturer and distributor enjoy a higher expected profit than (b)(i). What is the expected profit for the manufacturer and the distributor? c. Suppose the manufacturer is make-to-stock;

9.c. Suppose the manufacturer is make-to-stock; that is, the timing of events is as follows: The manufacturer produces a certain amount. The distributor observes demand. The distributor orders from the manufacturer. i. Using the same wholesale price contract as part (b)(i), calculate the production/ inventory level of the manufacturer. What is the expected profit for the manufacturer and distributor? Compare your results with part (b)(i). ii. Find a cost-sharing contract such that both the manufacturer and distributor enjoy a higher expected profit that that in (c)(i) and calculate their expected profits.

9. *Consider the following demand scenario*: Quantity Probability 2,000 3% 2,100 8% 2,200 15% 2,300 30% 2,400 17% 2,500 12% 2,600 10% 2,700 5% Page 133 Suppose the manufacturer produces at a cost of $20/unit. The distributor sells to end customers for $50/unit during season, unsold units are sold for $10/unit after season