Uncertainty and willingness to pay for insurance. Utility = (Wealth)1/3 Prob(flood) = .04 Prob(no flood) = .96 Total wealth if flood = $100,000. Total Wealth if no flood = $800,000. Find: (i) expected value, (ii) expected utility, (iii) certainty equivalent
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- Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function 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. 1. Suppose the actuarially fair premium charge is 2600, Calculate Tess’ expected utility with full insurance if she is charged the premium. Round to two decimal places. 2. What is the premium that private insurance companies will charge for full insurance? Round to two decimal places. 3.Assume the social welfare function is the sum of the Tess’ and Lex’s utility functions. Select the correct statement regarding the explanation for what has happened in the private market and the role of social insurance. a.Adverse section has lead to market failure. The government could improve social welfare by…. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = square root x. There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?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 insurance
- Assume that the probability of having an accident in a year is 0.08. Suppose that your yearly income is 50,000 TRY and in case of an accident your income drops to 15,000 TRY. Your utility function is U(?) = ln (?) where C is consumption. a) What is your expected utility at the end of the year without insurance?b) Calculate an actuarially fair insurance premium for the full insurance. c) What would your expected utility be if you purchase a full insurance with actuarially fair premium? Will you buy this insurance, why or why not?Abigail is a consumer whose utility is a function of her total wealth W. u(W ) = log W. Suppose that Abigail begins with initial wealth of A = 100 but will suffer a serious illness with probability π = 0.15 which will require extensive treatment costing L = 80. To hedge against this risk, Abigail considers buying a health insurance policy. She may buy as much insurance I as she wishes at a cost of p per dollar of coverage, so her payoffs in each state are Healthy Ill Probability 0.85 0.15 No Insurance 100 20 Claim 0 I Premium −pI −pI a) Show that Abigail is risk averse. b) Suppose that the insurance premiums are actuarially fair so that p = 0. Find Abigail’s expected wealth E[W ] and expected utility E[u(W )] as functions of how much insurance she buys I. c) How much insurance should Abigail buy?Abigail is a consumer whose utility is a function of her total wealth W. u(W ) = log W. Suppose that Abigail begins with initial wealth of A = 100 but will suffer a serious illness with probability π = 0.15 which will require extensive treatment costing L = 80. To hedge against this risk, Abigail considers buying a health insurance policy. She may buy as much insurance I as she wishes at a cost of p per dollar of coverage, so her payoffs in each state are Healthy Ill Probability 0.85 0.15 No Insurance 100 20 Claim 0 I Premium −pI −pI a) Now suppose that the insurance company raises premiums to p = 0.2 so that they are no longer actuarially fair. Find Abigail’s expected wealth E[W ] and expected utility E[u(W )]. b) How much insurance should Abigail buy now?
- Assume that you will earn $90,000 next year. The probability of having an accident in a year is 0.05 and your income will be $22,500 in that case. Your utility function is U(C)= C1/2 where C is consumption. a) What is your expected utility at the end of the year without insurance?b) Calculate an actuarially fair insurance premium for the full insurance. c) What would your expected utility be if you purchase a full insurance with actuarially fair premium? Will you buy this insurance, why or why not?Indicate whether the statement is true, false, or unclear, and justify your answer.Ex post risk is typically much lower than ex ante risk because uncertainty is largely eliminated by the purchase of an insurance contract.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?
- 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.If a risk‐neutral individual owns a home worth $200,000 and there is a three percent chance the home will be destroyed by fire in the next year, then we know that:a) He is willing to pay much more than $6,000 for full cover.b) He is willing to pay much less than $6,000 for full cover.c) He is willing to pay at most $6,000 for full cover.d) None of the above are correct.e) All of the above are correct.. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.
