annual earned income and U(W) = (W/10)0.5 is this individual’s von Neumann-Morgenstern utility index (or utility function) . This individual earned income is
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Let W represents an individual’s annual earned income and U(W) = (W/10)0.5 is this individual’s von Neumann-Morgenstern utility index (or utility function) . This individual earned income is $49,000. This individual faces the prospect of a 20% chance of needing health care, with a price tag of $13,000. Assume this person is risk averse. Also assume that the insurance company has only claim costs and that administrative costs are $0. The maximum health insurance premium this individual is willing to pay is??
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- Suppose that a person's utility function is the square root of wealth. Suppose the person earns $100,000 per year. He or she has an illness with a probability of 0.2, and the cost of the treatment is $30,000. Would the person pay $6,000 for insurance? Why or why not? What is the most this person would pay to be insured (hint: equate expected utility to utility with certainty)? Suppose their utility function changed to wealth squared (hint: are they now risk averse?). Would they pay $6,000 for insurance? Why or why not?Suppose a company offers a standard insurance contract with a premium (r) of $2,000 and a payout (q) of $10,000. Suppose that Adelia earns a healthy state income of $70,000, a sick state income of $50,000, and has a 20% chance of becoming ill. For Adelia, this insurance contract would be: A. actuarially fair and partial B. actuarially fair and full C. actuarially unfair and full D. actuarially unfair and partialQuestion 5 Suppose that there is a 10% chance Ja'Marr is sick and earns $10,000, and a 90% chance he is healthy and will earn $70,000. Suppose further that his utility function is the following (utility = square root of income) U (I) = VIncome Ja'Marr's utility from expected income is , and his expected utility of his income is 264.58; 100 248.12; 252.98 100; 265.58 252.98; 248.12
- 4. An individual's Bernoulli utility function is u(w) = Vw, and the individual has initial wealth 100. The individual might develop a health problem, which would reduce his or her wealth to 0. The individual might be "healthy" or "unhealthy." A healthy person develops the health problem with probability qL = 0.3, while an unhealthy person develops the health problem with probability qH = 0.7. The probability that the individual in question is healthy is 1/2. An individual knows whether he or she is healthy, but an insurer does not. Without insurance, a healthy person's wealth is 100 with probability 0.7 and 0 with probability 0.3. Without insurance, an unhealthy person's wealth is 100 with probability 0.3 and 0 with probability 0.7. Insurers only offer "full insurance." That is, if the adverse event occurs, they will pay back 100, restoring the individual's full wealth. Insurers set a price for this policy that is "actuarially fair." Insurance company makes no money on average.…Suppose an individual earns income $600 when they are sick, and $1000 when they are healthy. Suppose this individual is sick with probability p = 0.5 and has a utility function over income, I, of U(I) = ln(I). Is this individual risk-averse, risk neutral or risk-loving? Suppose she is able to purchase insurance at any amount from at an actuarially fair price. Fully describe the amount she would purchase (payout, premium and final outcomes). Verify that she is better off with the contract in part b, as opposed to being uninsured. Suppose insurance company A offers a payout q = $400 (when she is sick) at a premium of r = $220 and insurance company B offers a payout of $200 at a premium of $100. Company A's contract is: Actuarially fair or unfair? Is it full or partial insurance? Company B's contract is: Actuarially fair or unfair? Is it full or partial insurance? Which contract does this individual prefer? Suppose contract A is unfair, but offers full coverage at price . Contract B…Suppose in a given state's new insurance marketplace, with community rating and no restrictions on who can buy at the community rate, the risk pool (distribution of expected health costs) is as follows: 30% of eligible enrollees' expected health costs = $1,000 (per year)65% of eligible enrollees' expected health costs = $2,0005% of eligible enrollees' expected health costs = $10,000 Now suppose one insurer, and one insurer only, were allowed to offer any premium it wanted to any potential buyer and to exclude those it did not want to cover? What premium would they likely charge and who would they sell to and who would they exclude? What would happen to the other insurers? Does this help you see why the ACA was written to apply to all insurers?
- Do you think Canada's universal health care program can alleviate problems caused by moral hazard and adverse selection in the private insurance markets? Why or why not? John's utility curve over total wealth is given by U(W) =VW (i.e. square root of W). Suppose that he has a 50% chance of being healthy. If he is healthy, he gets all his wealth-$10,000. If he becomes sick, he only has $3,600 remaining after medical expenditures. Calculate John's wealth and utility when he does and does not get sick, his expected utility, expected wealth, and his expected loss. Now he has the option of buying health insurance Calculate the maximum amount John would be willing to pay to fully insure against the cost of the sickness. How much is the actuarially fair and risk premium? Suppose that society consists of large, equal numbers of identical male and identical female consumers. Male consumers are similar to John; female consumers differ only in that they face a 25% probability of being sick, but…Consider the following example. A risk-neutral worker can choose high or low effort. The worker's outside option is 0. The manager cannot observe the worker's action, but the manager can observe the realized revenue for the firm (either $100 or $200). The probability of each revenue depends on the worker's effort: Low effort: cost of effort : $0 probability of low revenue ($100): 75% probability of high revenue ($200) : 25% High effort: cost of effort : $11 probability of low revenue ($100): 25% probability of high revenue ($200) : 75% The manager offers a contract which gives the worker a flat wage of $10 and a bonus of $20 if revenue is high. Given this payment scheme, the worker will put in ✓effort. The contract (is/is not) ✓incentive compatible. The firm's expected profit is $ The firm is considering an investment that would increase worker morale. By making work more enjoyable, the program would reduce the worker's cost of effort from $11 to $9. If it costs the firm $20 to…and you have a 10% chance of getting sick. Your income when sick is $0 and your income when healthy is $100. 1. Assume your utility over income is U=T ¥ 1. Graph your utility and income with income on the x-axis and utility on the y-axis. Show your income/utility when healthy and sick on the graph. 2. calculate your expected income. Show on graph. 3. calculate your expected utility. Show on graph. 1. Now you are offerred health insurance by Prof. Grossman's Totally Full and Fair Insurance Company. For a premium of $20, you will get a payout of $50 if you get sick. 1. Is the insurance company's name accurate (is this actuarially fair and full)? 2. What is the expected payout from this insurance? 3. What is the Income when sick and income when healthy under insurance? Show on your graph 4. What is the expected income and expected utility under this insurance? Show each on your graph 5. Propose a full and fair insurance given your 10% chance of getting sick and your healthy and sick…
- Suppose in a given state's new insurance marketplace, with community rating and no restrictions on who can buy at the community rate, the risk pool (distribution of expected health costs) is as follows: 30% of eligible enrollees' expected health costs = $1,000 (per year)65% of eligible enrollees' expected health costs = $2,0005% of eligible enrollees' expected health costs = $10,000 What would the pure community premium rate for this risk pool be? (assume zero loading costs for simplicity in this problem)An individual with the utility function given by u(y) = -e-0.5y, and gross disposable income y = 10 faces the probability p 0.3 of getting ill with health care expenditures L = 3. 1. [M] Find optimal insurance coverage if there are no loading factor and full knowledge? 2. [M] Depict this optimal choice. 3. [M] How does it depend on gross income Y?An individual has the utility function U(I) = I^(1/2), where I is their net income. (Note that I to the exponent/power of 1/2 is the same as the square root of I.) The individual starts with $1600 in income. The individual has a 20% probability of being very sick, 30% probability of being slightly sick, and 50% probability of being healthy. If the individual is sick, they lose net income because they need to pay healthcare costs. The healthcare costs are $1600 if they are very sick, $700 if they are slightly sick, and $0 if they are healthy. Please use this information for the following parts of this question unless otherwise specified. What is the individual's expected utility? Suppose a health insurance company offers the individual a full insurance contract. What is the actuarially fair, full insurance premium for this individual? What is the individual's expected utility if they purchase a full insurance contract at the actuarially fair, full insurance premium?