Consider the following demand scenario:

Quantity Probability

2000 3%

2100 8%

2200 15%

2300 30%

2400 17%

2500 12%

2600 10%

2700 5%

Suppose the manufacturer produces at a cost of $20/unit. The distributor sells to endcustomers for $50/unit during season and unsold units are sold for $10/unit afterseason.

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

b) 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 orderd by the distributor.

Customer demand is observed.

(i) Suppose the manufacturer sells to the distributor at $40/unit, how muchshould the distributor order? What is the expected profit for themanufacturer? What is the expected profit for distributor?

(ii) Find an option contract such that both the manufacturer and distributorenjoy a higher expected profit than (b)(i). What is the expected profit for themanufacturer and the distributor?

c) Suppose the manufacturer is make-to-stock. (i.e., the manufacturer must decidehow 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 theproduction level of the manufacturer. What are the expected profits for themanufacturer and for the distributor? Compare your results with part (b)(i).

(ii) Find a cost sharing contract such that both the manufacturer and distributorenjoy a higher expected profit than that in (c)(i), and calculate theirexpected profits.