Problem: Consider Jack has a property that worths $10,000. With probability 0.05 there will be a damage of $6,000 next month (hence afterthe damage the property's value is $4,000); with the remaining probability no damage would occur and the value of the property nextmonth is still $10,000. Jack can buy the following insurance to protect his property: For each unit of insurance that he buys, he pays$50 (namely the price or premium of insurance is $50 per unit) and will receive a reimbursement of $1,000 from the insurance companyif the damage occurs; if no damage occurs, the insurance company doesn't reimburse. Describe your answer and give examples.

Required:

(a) What's the expected monetary value of Jack's property next month if doesn't buy insurance?

(b) Suppose Jack buys x units of insurance. What's his expected monetary payoff next month?

(c) Suppose Jack has utility function over monetary payoff u(w) = 2√w. What's the optimal amount of insurance that Jack shouldbuy to protect his property? (The answer may not be integer, you may use a calculator to get the answer.)