Let firms not have perfect information about the consumer's type; that is, they do not know if the consumer is a robust type or a frail type. Explain why a firm offering two insurance plans Omega1 and Omega3 is an equilibrium.
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Let firms not have perfect information about the consumer's type; that is, they do not know if the consumer is a robust type or a frail type. Explain why a firm offering two insurance plans Omega1 and Omega3 is an equilibrium.
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- Nathan's income in a typical year is 75,000. There is a 10 percent chance that Nathan will be seriously ill next year, incurring 15,000 in medical expenses. Samantha also earns 75,000 in a typical year. Her chance of becoming seriously ill next year and incurring ur 15,000 in medical expenses is 20 percent. a. Calculate the actuarially fair premium for full insurance for (i) Nathan and (ii) Samantha. b. Suppose that a private insurance firm cannot distinguish between Nathan and Samantha in terms of their risk and assumes the risk of being seriously ill in the general population is 10%. In this context, discuss the adverse selection problem the firm might face. c. Can a compulsory, government - run health insurance program avoid the problem of adverse selection? Explain why or why not.Explain how risk aversion makes a market for insurance possibleConsider the model of competitive insurance discussed in lectures (Topic 6.7). Peter is a risk averse individual with the utility function u(w) = w0.5. His current wealth is $300 and with probability 1/2 he will incur a loss of D = $240, but with probability 1/2 he will incur no loss. Ann has the same utility u(w) = w0.5 and current wealth $300 as Peter, but a different probability of loss: she will incur a loss of D = $240 with probability 0.1, and no loss with probability 0.9. As we showed in lectures, in the separating equilibrium Peter is offered actuarially fair full insurance contract, so his wealth is equal to $180, whether loss happens or not. Ann will be offered an insurance contract with the amount of insurance (approximately) equal to Group of answer choices 0 16 36 66 120 240
- 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?Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U’ > 0) and convex (U” > 0). Draw a utility function in U - I space that fits this description. Explain the connection between U” and risk aversion. True or false: this individual prefers no insurance to an actuarially fair, full contract. Be sure to explain your answer.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 partial
- Suppose the probability that Recall Scarlett is sued is .1 and her income is 1000. In the case, she is sued she will lose all of her income in the settlement. She may purchase malpractice insurance at a rate of $r per $1 of coverage. Finally assume that her utility of income is U($) = ($)^1/2. What is Scarlett’s demand curve for insurance (that is find her demand for insurance for all r ≥ .1)?Suppose that there is a 20% chance Malik is injured and earns $100,000, and an 80% chance he stays healthy and will earn $500,000. Suppose further that his utility function is the following (utility = square root of income) Malik is risk ____. He will prefer ____ (given the same expected income). a. lover; actuarially fair and full insurance to no insurance b. averse; no insurance to actuarially fair and full insurance c. neutral; he will be indifferent between actuarially fair and full insurance to no insurance d. lover; no insurance to actuarially fair and full insurance e. averse; actuarially fair and full insurance to no insuranceAn investor has a power utility function with a coefficient of relative risk aversion of 3. Compare the utility that the investor would receive from a certain income of £2 with that generated by a lottery having equally likely outcomes of £1 and £3. Calculate the certain level of income which, for an investor with preferences as above, would generate identical expected utility to the lottery described. How much of the original certain income of £2 the investor would be willing to pay to avoid the lottery? Detail the calculations and carefully explain your answer.
- Indicate whether the statement is true or false, and justify your answer.Risk-averse consumers always prefer insurance that is actuarially fair but not full to full insurance that is actuarially unfair – but the opposite is true for risk-loving consumers.Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 Suppose that insurance companies do not know specific probabilities of adverse events for Tess or Lex, but do know the average probability of an adverse event. If they assumed that both Tess and Lex purchase full insurance, what is the actuarially fair premium charged? Round to two decimal placesB 2 Consider a pool of potential consumers of insurance with a known probability of sickness, p=0.5. Also consider that there are many competitive insurance firms that operate in the same manor, with the same operating costs. A. In the IH/IS space, show a random endowment point, E, the zero-profit line (calculate the slope), a full insurance line and an indifference curve that contains point E. Show the set of feasible contracts and explain what conditions hold that make the contracts feasible. B. On your graph, label equilibrium point Z. Why is equilibrium at point Z?
