Question

The town of Scoville has 2,200 family units. For simplicity, we will take each family unit to be one person. Each person is an expected utility maximizer with the "square root" Bernoulli utility function: u(x)=√x. There are two types of inhabitants: 200 have a wealth of $700,000, and they have houses worth $300,000 each (the total wealth includes the house); the remaining 2,000 people have a wealth of $150,000 each, and they have houses worth $100,000 (and the total wealth again includes the house). For any house, there is a 1% chance that it would have a fire in any given year. If there is a fire, the loss to the inhabitant would be 80% of the value of the house.

Please answer the questions in enough detail for me to see exactly how you got to your answer. Submit both your answers and how you found them. You may use Excel to find your answers. If you do so, please attach the relevant file.

Suppose that there is one insurance company in Scoville. They offer insurance to everyone in town, and the policy they offer would pay the full amount of the loss to the policy holder in case of a fire.

How much would they be able to charge for insurance to the wealthier inhabitants?

How much would they be able to charge for insurance to the less wealthy inhabitants?

What would be the expected loss in any given year that the insurance company would have to pay out?

How much would be the expected profit of the insurance company?

Answer 1

Answer a) when full insurance is covered , such that in case if loss, the insurance company fully compensate for the loss .thus it is called actuarially fair insurance.

Thus total charge for insurance, is loss*loss probability

For wealthier people , value of house = 300,000

Loss = .8* 300,000 = 240,000

Thus charge = 240,000*.01 = 2400 $

answer b)

charged by less wealthy inhabitant = .01*80,000

= 800 $

as value of house = 100,000

Loss = .8*100,000 = 80,000

Answer 3)expected loss equals expected payment  

= Probability of loss *( total payment to all wealthy +total payment to all less wealthy)

= .1 * ( 200*240,000 + 2200* 80,000)

= $ 20800000

Answer 4)

Expected profit for insurance company in actuarially fair insurance equals zero.

Bcoz expected revenue equals expected loss in full insurance