Q. 9. Consider the following demand scenario:

Quantity | Probability |

2,000 | 3% |

2100 | 8% |

2200 | 15% |

2300 | 30% |

2400 | 17% |

2500 | 12% |

2600 | 10% |

2700 | 5% |

SUPPOSE THE MANUFACUTURER 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.

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 customer.
- The manufacturer produces the amount ordered by the distributor.
- Customer demand is observed.

Suppose the manufacturer sells to the distributor at $40/unit, how much will the distributor order? Wheat is the expected profit for the manufacturer and distributor?

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; 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

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).

Find a cost-sharing contract such that both the manufacturer and distributor enjoy a higher expected profit that that in (c)(i), and calculated their expected profits.

Q. 10. Using the data of Question 9, suppose the manufacturer has an inflated demand forecast as follows:

Quantity | Probability |

2200 | 5% |

2300 | 6% |

2400 | 10% |

2500 | 17% |

2600 | 30% |

2700 | 17% |

2800 | 12% |

2900 | 3% |

Suppose the manufacturer is make-to-order (timing of events as in 9(b)). Using your contracts in Question 9(b)(ii)., find the order quantity, and expected profits of the distributor and of the manufacturer. Compare your answers with 9(b)(ii).

Suppose the manufacturer is make-to-stock (timing of events as in 9(c)). Using your contracts in Question 9(c)(ii), find the production quantity, expected profits of the manufacturer and of the distributors. Compare your answers with 9(c)(ii)

If you are the distributor and you have the choice of revealing the true demand forecast or inflated demand forecast to the manufacturer, what will you do in each case? Explain.