Question

A college senior must choose between two Choices: going for an MBA or taking a full-time entry-level-level position right after graduation. She thinks that she has 0.6 probability of completing the MBA in a year. If she completes the MBA, she believes that she has 0.1 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 job but with less seniority than what she would have if she had gone to work right after graduation. Once started at the entry-level 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-level 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 getting a management position

(2) Completing the MBA and getting a senior staff position

(3) Moving to junior staff without going to MBA and thus more seniority

(4) Moving to junior staff after failing the MBA

(5) Staying at entry level without going to MBA and thus more seniority

(6) Staying at entry level after failing the MBA

Using the simple decision tree for utility estimation, 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 0.35 probability yielding (1) and a 0.65 probability of yielding (6).

Outcome (4) and the lottery if the lottery has a 0.2 probability yielding (1) and a 0.8 probability of yielding (6).

Outcome (5) and the lottery if the lottery has a 0.1 probability yielding (1) and a 0.9 probability of yielding (6).

6a (10 points) By assigning a utility 0 to (6) and 100 to (1), find the utility for each of the four outcomes between (1) and (6).

6b (10 points) Draw a decision tree for her career decision and find her best Choice for the two-year period

Answer 1

Solution :

Outcome	Decision	Utility Score
Outcome 1	Completing the MBA and getting a management position	100
Outcome 2	Completing the MBA and getting a senior staff position	0.5*(100) + 0.5*(0) = 50
Outcome 3	Moving to junior staff without going to MBA and thus more seniority	0.4*(100) + 0.6*(0) = 40
Outcome 4	Moving to junior staff after failing the MBA	0.2*(100) + 0.8*(0) = 20
Outcome 5	Staying at entry level without going to MBA and thus more seniority	0.1*(100) + 0.9*(0) = 10
Outcome 6	Staying at entry level after failing the MBA	0

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