QUESTIDNS 2 to 0' ANALYEE DATA USING STATE. 1. For each of the following types of health insurance give a brief description, pointing out the key features, especially those that are lilrely to reduce health care comumption. [a] sea 01) EMU [c] eeo 2. Arnold behaves he faces health costs in the current year of either $10,000 with probability 0.? or costs of $20,000 with probability 0.3. [a] Find the mean and standard deviation of the costs that Prrnold faces. [th Give a definition of riskaversion. [c] If Arnold is risk-averse, will Arnold purchase an insurance policy that completely covers his losses if the annual premium of the policy is $5,000? Earplain your answer. 3.{a] The company that offered this insurance policy insures 2,500 people with exactly the same disuihution of health losses as that of Arnold. Calculate the variability that the insurance company faces in the average claim per individual insured. (Hint; use your answer in question 2 Part {all- (h) It can be shown that 05 percent of the time the average claim size will equal the expected average claim plus or minus 1.00 times the standard deviation of the average claim. Give this range for the insurance company considered in part [a]. [1:] Is the insurance company taking a large risk in selling this insurance policy? 4. An insurance company has determined that for a group of 10,000 people that it insures the expected loss per person covered is $5,000 per year. It sells the insurance policy for $0,000 per year. [a] What is the actuarially fair premium for this policy? (b) What is the loading factor for this insurance policy? {1:} Is the loading factor the same as the pmt the insurance company makes on the policy? Explain. 5- Martin's utility {U} depends on his income (w) in the following way. w 0 2 a, E 0 10 12 14 10 10 20 U[w]| 0 30 22 102 128 150 100 102 102 100 200 His usual job has income of 20, but he believes there is a 20% chance he'll lose his job and have an income of zero. Thus he has income of 20 [and utility of 200} with probability 0.80 and income of 0 units (and utility of 0] with probability 0.20. [a] Calculate Martin's expected utility. (Note: expected utility not expected income}. [1?] Plot Martin's utility as a function of income. [1:] Now suppose Martin could purchase insurance that fully replaced his income if he lost his job, so he is guaranteed income of 20 uru'ts in either state of the world. Show that the acmarially fair premium for this insurance policy is Li units