ora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x). a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation? c) What is the maximum that Leora would be willing to pay for a full insurance policy? d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.
Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).
a) What is the expected income? What is Leora’s expected utility (you may leave in log form)?
b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?
c) What is the maximum that Leora would be willing to pay for a full insurance policy?
d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.
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