# Decision and risk analysis assignment

**Problem 1 (10 Points)**

We covered a lot of material in this class – from general viewpoints about decision making and risk management, to specific frameworks and tools. While most of the examples used were “textbook-like” and greatly simplified, I hope that you will find opportunities to apply the material/techniques/tools of this class in your professional life.

So, please describe a few examples about how this class can help you to confront important decision situations in your professional life. Also: why do you think these frameworks and techniques are not used more often?

**Problem 2 (10 points)**

During the course I talked about Thaler’s encounter with 23 executives. He asked them whether they would be willing to take a deal that gives them a 50% chance of making $2 Million and a 50% chance of losing $1 Million. Only three of the 23 executives were willing to take this deal. However, the CEO of the company was shocked by this because he didn’t look at these 23 deals in isolation but as a portfolio of 23 deals.

- What is the expected profit/loss of the 23 deals taken together?
*(5 Points)* - What is the probability of a loss taken the 23 deals together?
*(5 Points)* **Problem 3 (10 Points)**- To analyze the best location of a new library in Eugene, Oregon, the overall utility of each of four proposed locations was calculated using a multi-attribute utility model. One important feature of this study was that cost were
__not__included in this model because the analysts who conducted the study thought it would be better to leave the final “big” tradeoff between the overall utility and total cost to the decision maker. The graph below summarizes the overall utilities and cost for each of the four proposed locations. - If the decision maker would be willing to spend $1,000,000 for each additional “utility point”, which alternative should (s)he choose? What if (s)he is only willing to spend $100,000 for a one-unit increase in overall utility?

**HINT:**no calculations are required. You can actually figure out the answers by drawing lines in the above graph J

**Problem 4 (10 points)**

As you know, utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Steven Smith.

x |
u(x) |

-$400 | 0 |

-$365 | 10 |

-$320 | 20 |

-$270 | 30 |

-$200 | 40 |

-$110 | 50 |

$0 | 60 |

$130 | 70 |

$300 | 80 |

$600 | 90 |

$800 | 95 |

$1,100 | 100 |

Use these utilities to answer the following questions.

- a) What is the
__monetary__certainty equivalent for the following gamble: gain $130 with probability 0.4, lose $320 with probability 0.6? (*5 points)*

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- b) What is the risk premium in a)? Explain the concept of a risk premium in addition to calculating its value for a).
*(5 points)*

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**Problem 5(20 Points)**

- a) The marketing department of a soft drink company wishes to determine the maximum expected payoff from introducing a new crystal-clear drink. What decision, in terms of choosing the best investment level, should the marketing department make using the payoff table below? Assume that the probability that the market share is less than 1% is 0.2, that the probability that market share is between 1 and 4% is 0.5, and that the probability that market share is at least 4% is 0.3. Assume that the marketing department is risk neutral.
*(10 points)*

Market Share |
|||

Investment Level |
< 1% | 1%-4% | ³ 4% |

Low | 300,000 | 400,000 | 500,000 |

High | -400,000 | 300,000 | 3,000,000 |

- b) What is the maximum amount of money the company should be willing to spend to get more information about the market share?
*(10 Points)*

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