Question: Problem 9: Consider the following demand scenario: Consider the following demand scenario: Quantity 2000 2100 2200 2300 2400 2000 2000 2200 Suppose the manufacturer produces

Problem 9: Consider the following demand scenario: Consider the following demand scenario: Quantity 2000 2100 2200 2300 2400 2000 2000 2200 Suppose the manufacturer produces at a cost of $20/unit. The distributor sells to end customers for $50funit during season and unsold units are sold for $10/unit after season. a) What is the system optimal production quantity and expected prot under global optimization? b) Suppose the manufacturer is make-to-order (i.e., the distributor must order before it receives demand from end customers). (i) Suppose the manufacturer sells to the distributor at $40funit, how much should the distributor order? What is the expected profit for the manufacturer? What is the expected profit for distributor? (ii) Find an option contract such that both the manufacturer and distributor enjoy a higher expected prot than (b)(i). What is the expected profit for the manufacturer and the distributor? c) Suppose the manufacturer is make-to-stock. (i.e., the manufacturer must decide how much to produce before the distributor sees the demand and places an order.) (i) Using the same wholesale price contract as part (b)(i), calculate the production level of the manufacturer. What are the expected prots for the manufacturer and for the 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 prot than that in (c)(i), and calculate their expected prots

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