solution

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.

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 all

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 = W0.5

W is the consumer’s wealth as represented by the value of the car.

What premium should No-State offer for full-coverage insurance?