Consider an insurance company that offers a standard contract with the premium r=$300 and payout q=$500 to anyone who will purchase it. Alice has healthy-state income I_H=$700 and sick-state income I_S=$0. He has probability of illness p=0.6.Answer the following questions.If Alice purchases the insurance and stays healthy, her income will be $[C].If Alice purchases the insurance and ends up getting sick, her final income will be $[D].For Alice, the standard insurance contract is [E] (choose either fair or unfair) and [F] (choose either full or partial).

There is an insurance company and three customers, Alice, Bob and John. The timing is as follows.(1) The insurance company announces the premium and excess of a health insurance policy.(2) At Date 1, each customer decides whether to purchase the health insurance policy.(3) At Date 2, each customer will discover their health status, which is either G (healthy) or B (needing treatment inhospital).(4) Nothing happens if a customer is healthy. If a customer needs treatment in hospital, then they pay $10,000 if theydo not hold a health insurance or the excess of the policy if they do. They are cured after treatment in hospital.For simplicity, assume that the insurance company is a monopolist.Each customer has the following utility index: 𝑢(−𝑥1) + 11.02 𝑢(−𝑥2), where 𝑥𝑡 is the payment (either to the insurancecompany or to the hospital) at Date 𝑡 and 𝑢(−𝑥) = 40000√1 − (𝑥∕20000) − 40000. Table 1 summarizes each customer’sage and probability of remaining healthy.Name Age Probability of GAlice 25 99.5%Bob 25 98%John 60 95%(a) First, assume that the insurnace company offers the policy with premium $210 and excess $750. Who would like tobuy this policy? (You should find that Bob and John would like to buy the policy.)(b) David is also 25 years old and will remain healthy with probability 98% at Date 2. Unlike Bob, David’s utility indexis −𝑥1 + 11.02 (−𝑥2). Show that David does not want to buy the insurance policy in (a).(c) Note that David and Bob are equally healthy, what makes one buy the insurance policy and the other does not?(d) Next, assume that the insurance company offers the policy with premium $530 and excess $500. Who would like tobuy this policy?(e) From the insurance company’s perspective, describe the potential problem of selling only one of the two policies in(a) and (d)

Your utility function is u(c) = √c where c is consumption. Your income is W = $40, 000. With probability p = 0.05 you get sick and have medical expenses of δ = $30, 000. (a) What is your expected utility without insurance?

Matt applies for an income protection policy which has an indemnity value. In his application hereports that his previous year’s salary was $80,000 p.a. His application is approved and he accepts apolicy with a maximum insurance benefit of $5,000 per month. Matt falls ill and is unable to maintainhis work. He is forced to reduce his working hours and as a result his income falls to an average of$70,000 over the year. Eventually, he needs to stop working at which point he makes a claim for aninsurance payout. On what level of income will his claim benefit be calculated and how much will thebenefit be per month

Insurance: An insurance company sells a 1-year term life insurance policy to an 83-year-old man. The man pays a premium of $4700. If he dies within 1 year, the company will pay $82,000 to his beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 83-year-old man will be alive 1 year later is 0.9437. Let X be the profit made by the insurance company.Part: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Find the probability distribution.The probability distribution isx 82000 4700Px

Suppose now June can purchase insurance for the transport of her householde§ects at a price of q 2 (0; 1) per dollar of coverage. That is, if she chooses apolicy that covers a maximum of C in the event of a loss, she pays qC to theinsurance company and they agree to pay her in the event of a loss, the valueof her loss up to the agreed maximum cover of C. So, in particular, if she3takes out a policy with the maximum coverage of L, then she will be fullyinsured in the event of the truck crashing since her state-contingent wealthwill be M qL in the event the truck does not crash and M qL L + L =M qL in the event the truck crashes.(d) (5 points) Illustrate on your diagram from part (a) her state-contingentwealth bundles corresponding to the set of choices going from zero cov-erage (that is, C = 0) to full coverage (that is, C = L). [Hint: eachadditional dollar of coverage reduces Juneís wealth by q dollars in theevent the truck does not crash and increases it by q + 1 in the eventthe truck crashes.]