Question

Suppose a person has the utility function U=x^.75 and makes $52,000. If he gets the flu, he will have to miss work for a week, costing him $1,000. His probability of getting the flu is 15%. Compare the following scenarios and rank his preferences over them:

1. His current situation
2. Participate in the company’s sick day program where $500 of his salary is withheld (regardless of whether he gets sick) but if he gets sick for a week he doesn’t loose any additional money.
3. Buy a flu shot for $75 which lowers his chance of getting the flu to 10%
4. Buy a premium flu shot for $100 which lowers his chance of getting the flu to 5%

Which makes him best off?

Group of answer choices

Situation 1

Situation 4

Situation 3

Situation 2

Answer 1

1)

Current situation=Situation 1

Expected utility=0.15*U(52000-1000)+(1-0..15)*U(52000)

Expected utility=0.15*(52000-1000)^0.75+(1-0.15)*(52000)^0.75=3436.05 utils

2)

Situation 2- Sick day program

Expected Utility=0.15*U(52000-500)+(1-0..15)*U(52000-500)

Expected utility=0.15*(52000-500)^0.75+(1-0..15)*(52000-500)^0.75=3418.66 utils

3)

Situation 3- buy a flu shot for $75

Expected Utility=0.10*U(52000-75-1000)+(1-0.1)*U(52000-75)

Expected Utility=0.10*(52000-75-1000)^0.75+(1-0.1)*(52000-75)^0.75=3434.81 utils

4)

Situation 4- buy a flu shot for $100

Expected Utility=0.05*U(52000-100-1000)+(1-0.0.05)*U(52000-100)

Expected Utility=0.05*(52000-100-1000)^0.75+(1-0.05)*(52000-100)^0.75=3436.06 utils

Expected utility is highest in case of situation 4. It will make him best off

Correct option is

Situation 4