In: Economics
For questions 8-10 assume that Rosa has a 10% chance of getting sick in the next year. If she gets sick, her medical bills will amount to $3600. She has a wealth of $10,000. Suppose she has the utility function u(x) = px, where x is her net wealth at the end of the year.
8. What is Rosa’s risk premium? (a) 0 (b) 16 (c) 36 (d) 56 (e) None of the above
9. What is the most that Rosa is willing to pay for an insurance policy that fully covers against her loss? (a) 0 (b) 196 (c) 396 (d) 596 (e) None of the above
10. Some insurance policies have deductibles. A deductible is an amount of a claim not covered by insurance. It’s a fixed portion of the medical bills that the insured person must pay in order to make a claim to their insurer. Suppose Rosa’s insurance company provides two plans. Plan A has zero deductibles (good!) but charges a high premium (bad!). Specifically, Plan A charges $591 for full coverage. Plan B has a deductible of $197, but charges a premium of just $199. Will Rosa purchase insurance and, if so, which plan? (a) Rosa will not purchase any insurance (b) Rosa will purchase plan A (c) Rosa will purchase plan B (d) Rosa is indifferent between plan A and plan B. She can purchase either of them. (e) None of the above
It is given that Rosa's utility is x.5
Her wealth at the end of year would be
If she gets sick=10000-3600=6400
If she does not get sick=10000
8. Expected utility= Probability of sick*wealth if sick+ probability of not sick*wealth if not sick
Expected wealth=.1*6400+.9*10000
=640+9000
=9640
Now we need to calculate certainty equivalent CE
U(CE)=CE.5=EU
EU is .9*10000.5+.1*6400.5
EU=98
Since CE=EU2,
CE=982=9604
So,
Risk premium=Expected wealth-CE
=9640-9604
=36
9.
Max Rosa will be willing to pay will be
Initial wealth-CR
=10000-9604
=396
10.
For plan A, EU=(10000-591).5
=97
For plan B
Wealth when not sick=10000-199=9801
Wealth when sick=10000-199-197=9604
So,
EU=.9*9801.5+.1*9604.5
EU=98.9
Since EU(Plan B)>EU(Plan A), Rosa will take plan B.