An individual's Bernoulli utility function is u(w) = √w, and the individual has initial wealth 100. The individual might develop a health problem, which would reduce his or her wealth to 0. The individual might be "healthy" or "unhealthy." A healthy person develops the health problem with probability q = 0.3, while an unhealthy person develops the health problem with probability qH = 0.7. The probability that the individual in question is healthy is 1/2. An individual knows whether he or she is healthy, but an insurer does not. Without insurance, a healthy person's wealth is 100 with probability 0.7 and 0 with probability 0.3. Without insurance, an unhealthy person's wealth is 100 with probability 0.3 and 0 with probability 0.7. Insurers only offer "full insurance." That is, if the adverse event occurs, they will pay back 100, restoring the individual's full wealth. Insurers set a price for this policy that is "actuarially fair." Insurance company makes no money on average. Therefore (1) if insurers expect that only healthy people buy, then the price is PL = 30 (i.e., PL -0.3(100) = 0), (2) if insurers believe only unhealthy people buy, then the price is
An individual's Bernoulli utility function is u(w) = √w, and the individual has initial wealth 100. The individual might develop a health problem, which would reduce his or her wealth to 0. The individual might be "healthy" or "unhealthy." A healthy person develops the health problem with probability q = 0.3, while an unhealthy person develops the health problem with probability qH = 0.7. The probability that the individual in question is healthy is 1/2. An individual knows whether he or she is healthy, but an insurer does not. Without insurance, a healthy person's wealth is 100 with probability 0.7 and 0 with probability 0.3. Without insurance, an unhealthy person's wealth is 100 with probability 0.3 and 0 with probability 0.7. Insurers only offer "full insurance." That is, if the adverse event occurs, they will pay back 100, restoring the individual's full wealth. Insurers set a price for this policy that is "actuarially fair." Insurance company makes no money on average. Therefore (1) if insurers expect that only healthy people buy, then the price is PL = 30 (i.e., PL -0.3(100) = 0), (2) if insurers believe only unhealthy people buy, then the price is
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.1P
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VIEWStep 2: a) Examine if a unhealthy individual buy the insurance
VIEWStep 3: b) Examine if a healthy individual buy the insurance
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VIEWStep 5: d) Examine if a unhealthy individual buy the insurance
VIEWStep 6: e) Examine if a healthy individual buy the insurance
VIEWStep 7: f) State if the expectation is consistent
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