Question

Rosa has a 10% chance of getting sick in the next year. If she gets sick, her medical bills will amount to $500. She has a wealth of $1,000. Suppose she has the utility function u(x) = x0.5, where x is her net wealth at the end of the year.
(a) Calculate Rosa’s risk premium.

(b) What is the most that Rosa is willing to pay for an insurance policy that fully covers against her loss?

(c) 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 $55 for $500 of coverage. Plan B has a deductible of $K, where K<500, but charges a premium of just $(55 – .1K). Suppose K =b $300. Will Rosa purchase insurance and, if so, which plan? Show this mathematically.

Answer 1

a) In layman's language, Risk Premium is the premium that an individual will get because of taking risks. As in this case, if Rosa is taking a risk of not getting Insured while there is a 10% chance of getting ill in the next year. If she does not get ill in the next year than what ever she saved by not paying the insurance premium is her risk premium.

If she takes a rsik of not paying the premium then she has a chance of losing out $500 & not getting anything financially from this loss while on the other side she has only 10% chance for this.

b) I think, Rosa is willing to pay $55 for her $500 coverage as if there are 10% chances of her getting ill & she is looking at the selective problems being covered in the Plan B then there is further risk enhancement that whatever problem is there with her might be or might not be covered under the insurance policy. so, It is better to go with an expensive but zero deductible plan.

c) Rosa, if takes a plan should go for Plan A which is charging $ 55 but there are zero deductible while Plan B $300 are deductibles & the charges are $ 25 (assuming what is given in the question.) for covering $ 200 (apart from the deductibles) .