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.
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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.
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- 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.A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. Calculate the actuarially fair insurance premium. What would your expected utility be if you were to purchase the actuarially fair insurance premium? b. What is the most you would be willing to pay for insurance, given your utility function?The lecture mentions that diminishing marginal utility applies to the consumption of money as well as the consumption of certain food. Can you give another example where diminishing marginal utility applies? Can you think of any example where diminishing marginal utility does not apply? From utility theory, the demand for insurance depends on the level of risk aversion (i.e. how much you hate uncertainty), the cost of insurance (i.e. if it is within your willingness to pay), as well as wealth. Can you think of anything else that affects demand for insurance? One of the predictions of prospect theory is that we tend to be overly concerned with relatively small risk. Can you think of any example (besides those given in the lecture) that either speaks to this or is an exception?
- Suppose Diane's utility function is U=- Vincome . Diane earns an income of $102,400, but there is a 15% chance that she will get sick and have a $62,400 medical bill. The health insurance company, DenialCare, will offer her a health insurance policy to pay for her medical bills. What would an actuarially fair premium be and what is the maximum she would be willing to pay for the insurance?Anita bought a new scooter for $500. She is deciding whether she should insureher scooter against theft. She has recently read in the news that one out of 10 scooters arestolen in her town. She can buy scooter theft insurance at the price of 12 cents per $1 ofinsurance. How much insurance will Anita buy if her utility function is U(C) = 2C + 100?In the summer of 1984, Nicholai opened a small art gallery in the West Village and amassed a collection worth $2,60,000. An insurance company figured there was a 5% chance the collection would be destroyed and worth $0. Nicholai has utility u(x) = x0.5. If Nicholai purchases full insurance at a fair price, his expected utility would be ___. while if he declines the insurance he would face an expected utility of а. 1,487.5; 1,531.8 b. 1,487.5; 1,444.9 с. 1,571.6;B 1,531.8 d. 1,571.6; 1,444.9
- 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.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.Life insurance companies require applicants to submit to a physical examination as proof of insurability prior to issuing standard life insurance policies. In contrast, credit card companies offer their customers a type of insurance called “credit life insurance” that pays off the credit card balance if the cardholder dies. Would you expect insurance premiums to be higher (per dollar of death benefits) on standard life or credit life policies? Explain.
- 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 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