Question

Jane arrives in New York where she will hire a car from AA Rentals for 24 hours. Her rental fee, which she has already payed, includes AA Rentals risk taker insurance policy. Under this policy, Jane will have to pay the first $2,000 if she causes an accident (and the rest will be covered by the insurance policy). Any accident, even a minor one, will result in at least $2,000 of repair costs. At the AA Rentals counter, Jane is offered to upgrade to AA Rentals ‘Hassle Free’ policy at a cost of $25. If she purchases the Hassel Free insurance policy, she will not have to pay anything if she has an accident. Based on her past driving record, Jane’s probability of have an accident during the rental period is 1/200. Janes value function is sqrt(​x/​2) for gains and -2√(|x|) for losses. Jane does not think she will have an accident What is the value to Jane of purchasing Hassel Free insurance? What is the value to Jane of not purchasing Hassel Free insurance? Should she purchase the Hassel Free policy?

Answer 1

Jane value function of she purchased the hassle free insurance is √(x/2)gain =[√(25/2)=3.5355]g gain.

But if jane will not purchase the hassle free insurance then the value will be 2√(|x|)lose = 2√(|25|)=10 lose.

It jane will purchase the hassle free insurance he will gain√(x/2)&if jane will not purchase the Hassel free insurance then he will have to suffer a loss of 2√(|x|) .

So it's better to purchase the Hassle free insurance.

I think jane should purchase the Hassel free insurance as the probability of accidents is only (1/200)i.e,0.5% And if accidents occur then jane will not have any lose but if she will not purchase the Hassel free insurance then in case accidents occur jane will have to pay $2000 and would have to bear a loss of 2√(|x|)or 10.