2. Consider Jack has a property that worths $10,000. With probability 0.05 there

Question

2. 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.

(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) = 2w. 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.)

Explanation / Answer

a) Expected monetary value of property = 0.05*4000+0.95*10000 = $9700

b) Expected monetary payoff for 0 unit of insurance = 0.05*1000 + 0.95*0 = 50 So Expected monetary payoff for x units = 50x

c) Optimal amount of insurance will be the one which will maximize the utility.

w=50x

So we see that utility is maximum when he buys 6 units of insurance.

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