Question

In: Economics

For questions 8-10 assume that Rosa has a 10% chance of getting sick in the next...

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

Solutions

Expert Solution

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

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.

Rahul Sunny answered 1 year ago

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