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Ques 5a. (10 points) Set your utility for $0 to be 0 and $1 million to be 100. Use the simple decision tree used in determining the utility for money, where the lottery has a prize of $1 million if you win and $0 if you lose, to determine your utility for $500,000 and $200,000. Use these 4 utilities to draw your utility curve for money.
Ques 6(20 points) A college senior must choose between two alternatives: going for an MBA or taking a full-time entry position right after graduation. She thinks that she has 0.7 probability of completing the MBA. In a year If she completes the MBA, she believes that she has 0.6 probability of getting a manager position; otherwise, she will get a senior staff position. Should she fails the MBA, she will have to take the entry position but with less seniority than what she would have if she had gone to work right after graduation. Once started at the entry position for a year, she believes that she has a 50-50 chance of moving up to a junior staff position versus staying at the entry position. Her preferences for the possible outcomes of her choice at the end of two years are listed in decreasing order below:
(1) Completing the MBA and get a management position
(2) Completing the MBA and get a senior staff position
(3) Moving from entry position to staff without going to MBA and thus more seniority
(4) Moving from entry position to staff after not being able to complete the MBA
(5) Staying at entry position without going to MBA and thus having more seniority
(6) Staying at entry position after not being able to complete the MBA
Through self-questioning, she has found that she would be indifferent between:
Outcome (2) and a lottery with a 50-50 chance of yielding the best outcome (1) and the worst outcome (6).
Outcome (3) and the lottery if the lottery has a 0.4 probability yielding (1).
Outcome (4) and the lottery if the lottery has a 0.2 probability yielding (1).
Outcome (5) and the lottery if the lottery has a 0.1 probability yielding (1).
With a utility 0 for (6) and 100 for (1), find her best alternative for a two-year period
Ques 7 A person has a total net asset of $1 million, including a $200,000 net equity of a house, which is the market value of the house (structure and land values) – mortgage. Specifically, the house has a market value of $500,000, a structure value of $400,000, a land value of $100,000, and a mortgage of $300,000. The person plans to buy $400,000 fire insurance for full coverage of the house. For simplicity, assume that each year the house has a 1% probability of being totally destroyed by fire and a 99% probability of no damage occurring to the house. Furthermore, the person’s utility for money is approximately proportional to the cubic root of money and U($1000,000)=10 and U($0)=0.
B1.(5 points) Draw the decision tree for the insured about buying or not buying the fire insurance.
B2.(10 points) Determine the maximum insurance premium IP the person would be willing to pay.
B3. (5 points) What is the risk premium at the maximum IP?
Bonus Problem (20 points). Determine the maximum insurance premium the person would be willing to pay for a $300,000 insurance just to cover the mortgage (Hint: in this case, even insured, if the house is destroyed, the person will suffer a loss in net asset in addition to paying for the insurance premium, and the highest insurance premium needs to be determined through numerical iteration).
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