Indicate whether the statement is true or false, and justify your answer.A consumer with declining marginal utility of income will never prefer actuarially fair, partial insurance to actuarially unfair, full insurance.
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Indicate whether the statement is true or false, and justify your answer.
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- Indicate whether the statement is true or false, and justify your answer.There are no possible utility functions in which a person is indifferent between actuarially fair, full insurance and actuarially fair, partial insurance.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.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).a. Draw a utility function in U–I space that fits this description.b. Explain the connection between U'' and risk aversion.c. True or false: this individual prefers no insurance to (IS, IH) to an actuarially fair, full contract.
- 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 insuranceScenario 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 placesSuppose 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
- 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 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)?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…
- Individuals will prefer to fully insure against a potential adverse event if A. individuals are risk-loving and insurance is priced at an actuarially fair rate. B. individuals are risk-averse and insurance is priced at an actuarially fair rate. C. individuals are risk-loving and insurance is priced above the actuarially fair rate. D. individuals are risk-averse and insurance is priced above the actuarially fair rate.Indicate whether the statement is true or false, and justify your answer.Under partial insurance, income in the sick state with insurance is higher than income in the healthy state.Indicate whether the statement is true or false, and justify your answer.In an actuarially fair insurance contract, the insurance premium equals the probability of sickness times the payout amount.