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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.
Sometimes the consumer who is a risk-averse will choose full insurance to not full insurance even it is actuarially unfair (it is not full insurance but technically actuarially fair.
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Solved in 2 steps
- 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.A consumer with declining marginal utility of income will never prefer actuarially fair, partial insurance to actuarially unfair, full insurance.Indicate whether the statement is true or false, and justify your answer.When insurance is fair, in a sense, it is also free.
- The difference between the actuarily fair price for insurance and the price a risk-averse individual is willing to pay to fully insure is called a-insurance benefit b-risk aversion c-the risk premium d-risk profitDraw a graph with utility on the Y axis and income on the X axis for a risk averse person. Label the following points on the Y axis The expected value of utility while uninsured The expected value of utility with actuarially fair, full insurance The expected value of utility with actuarially far, partial insuranceConsider 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.
- Explain how risk aversion makes a market for insurance possibleIndividuals 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.. 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?
- Indicate whether the statement is true or false, and justify your answer.In the Rothschild–Stiglitz model, an individual who is offered a choice between full insurance and no insurance will always choose full insurance if they are risk-averse.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. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) √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.