No-state insurance Company has made the following estimate of auto damage for se

Question

No-state insurance Company has made the following estimate of auto damage for several groups of potential customers who own cars worth $10,000. there are an equal number of customers in each group. No-state is risk-neutral.

Group A, B, C Initial Value of Car: $10,000, $10,000, $10,000 Probability of Accident that devalues car to $5,000: .2, .3, .4

State regulation mandates that every customer must pay the same premium regardless of his or her group, and this premium must be sufficient to cover al expected claims from those who purchase insurance from No-state. There are no additional costs to the company other than paying off claims. All consumers hav ethe following utility function (U) U= W^.05 W is the consumer's wealth as represented by the value of the car. What premium hsould No-State offer for full-coverage insurance?

Explanation / Answer

Wealth in case of no accident = $10,000

Utility in case of no accident = (10,000)^0.05 = 1.58

Wealth in case of an accident = $5,000

Utility  in case of accident = (5000)^0.05 = 1.530

Expected utility of type A = 0.2*1.53 + 0.8*1.58

Expected utility of type B = 0.3*1.53 + 0.7*1.58

Expected utility of type C = 0.4*1.53 + 0.6*1.58

Expected utility of all type = EU of A + EU of B = EU of C/3

= (1.377 + 3.318)/3

= 1.565

Wealth for U = 1.565 = (1.565)^20 = 7767.59

So, Pemium for No-state = 10,000 - 7767.59 = 2232.4

If you don't understand any thing then comment , I'ill revert back onthe same. :)

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