Rosa, who has a 10% chance of getting sick in the next year. If she gets...

Rosa, who has a 10% chance of getting sick in the next year. If she gets sick, her medical bills will amount to $1900. She has a wealth of $10,000. Suppose she has the utility function ?(?) = √ ?, where x is her net wealth at the end of the year.

6. Calculate Rosa’s risk premium. (a) $5 (b) $7 (c) $9 (d) $11 (e) None of the above

7. What is the most that Rosa is willing to pay for an insurance policy that fully covers against her loss? (a) $99 (b) $199 (c) $299 (d) $399 (e) None of the above.

8. 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 $396 for $1900 of coverage. Plan B has a deductible of $392, but charges a premium of just $199. Will Rosa purchase insurance and, if so, which plan? (a) Rosa prefers do not purchase any insurance (b) Rosa prefers to purchase plan A (c) Rosa prefers to purchase plan B (d) Rosa is indifferent between all three options (e) None of the above

Solutions

Expert Solution

6) Expected utility=Utility of( expected value- risk premium(RP) )

If don't get sick income would be 10,000 corresponding utility=√10000=100 ,when sick income would be 10000-1900=8100 and Utility=√8100=90

Expected value=0.9*10000+0.1*8100=9810

Expected Utility=0.9*100+0.1*90=99

Now ,using formula, 99=√(9810-RP) or 9801=9810-RP gives RP=9 Hence,Risk premium is $9 option (c) is correct

7) Ross expected utility as calculated earier is 0.9*100+0.1*90=99 Now corresponding value for utility of 99=99^2=9801 ,So Ross has the value of 9801 for expected utility hence maximum premium she would be willing to pay for full coverage =10000-9801=$199 hence option(b) $199 is correct

8) Since,As calculated in part (7) Ross was willing to pay maximum of $199 for full coverage She will not be willing to accept Plan A as the premium nis higher that $199 and Plan B since $199 is maximum she is willing to pay for full coverage not partial Hence,Option (a) Rosa prefer do not purchase any insurance is correct answer

Rahul Sunny answered 1 week ago

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