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 have the following utility function (U) U= W^.05 W is the consumer's wealth as represented by the value of the car. What premium should No-State offer for full-coverage insurance?