Indicate whether the statement is true or false, and justify your answer.In a Rothschild–Stiglitz model separating equilibrium, low-risk consumers of insurance are quantity constrained. They cannot buy as much insurance as they want because the insurance company is worried it will lose money on them.
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Indicate whether the statement is true or false, and justify your answer.
In a Rothschild–Stiglitz model separating equilibrium, low-risk consumers of insurance are quantity constrained. They cannot buy as much insurance as they want because the insurance company is worried it will lose money on them.
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- In the mid-1990s, the state of New Jersey revised its rules for the individual insurance market and began requiring that insurers charge the same premiums for the same coverage to all applicants. Assuming that insurers had previously used medical underwriting, which of the following is a predictable consequence of adverse selection? 1) Insurance becomes less attractive to the healthiest individuals, so fewer of them buy it 2) Insurers’ average costs of providing coverage increase because of a changing risk pool 3) The average age of those buying in the individual market goes up 4) All of the aboveLife 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.In class we talked about how the Arrow-Pratt coefficient of absolute risk aversion can be thought of as proportional to the insurance premium that an expected utility maximizer would be willing to pay to completely avoid a small, mean zero risk. Mathematically, we could write this insight the following way: E[u(w + ë)] = u(w – 7) where u is the agent's Bernoulli utility function, w is their wealth level, a is the insurance premium/willingness to pay to avoid č, and č is mean-zero risk (i.e. č is a random variable with E[ē] = 0). Prove that for small č, r(w) = -u"(w)/u'(w) is proportional to 7. What is the constant of proportionality for this relationship? [Hint: start by taking the second- order Taylor expansion of the equation above].
- Let W represents an individual’s annual earned income and U(W) = (W/10)0.5 is this individual’s von Neumann-Morgenstern utility index (or utility function) . This individual earned income is $49,000. This individual faces the prospect of a 20% chance of needing health care, with a price tag of $13,000. Assume this person is risk averse. Also assume that the insurance company has only claim costs and that administrative costs are $0. The maximum health insurance premium this individual is willing to pay is??Indicate whether the statement is true or false, and justify your answer.Private markets are powerless to combat adverse selection, so the only solution is a government-mandated insurance 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.
- Health insurance is normally seen as a good that is most valuable to sick people, since health expenditures are highest for the sick. Yet, in the basic insurance model discussed in this chapter, actuarially-fair health insurance is worth nothing to people who are certain to become sick (p = 1). Why does the standard model produce this result? How is this different from the way real-world insurance markets work?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 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?
- Multiple Choice Adverse selection describes a situation where an individual's demand for insurance is positively correlated with the individual's risk of loss. Adverse selection occurs when someone increases their exposure to risk when insured. This can happen, for example, when a person takes more risks because someone else bears the cost of those risks. The relationship between smoking status and mortality provides a good illustration for adverse selection, especially in the case in which a life insurance company did not vary its premiums according to smoking status of its customers. To counter the effects of adverse selection, insurers may offer premiums that are proportional to a customer's risk.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.Which of the following statements is FALSE regarding the concept of "adverse selection"? Multiple Choice Adverse selection describes a situation where an individual's demand for insurance is positively correlated with the individual's risk of loss. Adverse selection occurs when someone increases their exposure to risk when insured. This can happen, for example, when a person takes more risks because someone else bears the cost of those risks. The relationship between smoking status and mortality provides a good illustration for adverse selection, especially in the case in which a life insurance company did not vary its premiums according to smoking status of its customers. To counter the effects of adverse selection, insurers may offer premiums that are proportional to a customer's risk.