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Let W represent and individuals annual earned income and U(W) = (W/10)^0.5 is th

ID: 1201160 • Letter: L

Question

Let W represent and individuals annual earned income and U(W) = (W/10)^0.5 is this individual's Von Neumann-Mortgenstern 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 health insurance company has only claim costs and that administrative costs are $0. What is the maximum health insurance premium that this individual is willing to pay? Let W represent and individuals annual earned income and U(W) = (W/10)^0.5 is this individual's Von Neumann-Mortgenstern 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 health insurance company has only claim costs and that administrative costs are $0. What is the maximum health insurance premium that this individual is willing to pay?

Explanation / Answer

Utility when health care not needed(so W = 49,000) = U(W) = (W/10)^0.5 = (49,00)^0.5 = 70

Wealth in case of health care needed = 49,000 -13,000 = $36,000

Utility when health care needed(so W = 36,000) = U(W) = (W/10)^0.5 = (36,00)^0.5 = 60

Expected Utility = Probability of health care needed*Utility when health care needed + prob health care not neded*Utility when health care not needed

= 0.2*60 + 0.8*70

= 12 + 56

= 68

Wealth corresponding to u = 68

68 = (W/10)^0.5

68^2 = W/10

W = 46420

Risk premium = 49,000 - 46,420

= $2580

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