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27 Jan 2019

A person with utility function U(w)= ln (w) has wealth of $12,000, and faces a 0.3 probability of losing $1,200. What is this person❝s expected utility? Does it make sense to insure against this loss at the cost of $300? What is the maximum amount this person will pay for this insurance?

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Collen Von
Collen VonLv2
28 Jan 2019

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Related questions

Mr. Fogg is planning an around-the-world trip. The utility from the trip is a function of how much he spends on it (Y) given by

U(Y)=log(Y)

a. If there is a 25 percent probability that Mr. Fogg will lose $1,000 of his cash on the trip, what is the trip's expected utility?

b. Suppose that Mr. Fogg can buy insurance against losing the $1,000 (say, by purchasing traveler's checks) at an actuarially fair premium of $250. Show that his utility is higher if he purchases this insurance than if he faces the chance of losing the $1,000 without insurance.

c. What is the maximum amount that Mr. Fogg would be willing to pay to insure his $1,000?

d. Suppose that people who buy insurance tend to become more careless with their cash than those who don’t, and assume that the probability of their losing $1,000 is 30 percent. What will be the actuarially fair insurance premium? Will Mr. Fogg buy insurance in this situation? (This is another example of the moral hazard problem in insurance theory.)

Let W represent 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's earned income is $49,000. This individual faces the prospect of a 20% chance of needing healthcare 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?

1，

Suppose Mary can have good health with probability 0.95 and bad health with probability 0.05. If Mary has a good health her wealth will be $90,000, if she has bad health her wealth will be $10,000 (after paying the health bill). Suppose that the utility of wealth comes from the following utility function: U(W)=W^0.5 Note: When the question is about utilities, report the answer with one decimal. When the question is about money, report integers (without comas for thousands). In both cases, round appropriately.

Find the maximum premium she is willing to pay for full insurance.

2，

Suppose Mary can have good health with probability 0.95 and bad health with probability 0.05. If Mary has a good health her wealth will be $90,000, if she has bad health her wealth will be $10,000 (after paying the health bill). Suppose that the utility of wealth comes from the following utility function: U(W)=W^0.5
Note: When the question is about utilities, report the answer with one decimal. When the question is about money, report integers (without comas for thousands). In both cases, round appropriately.

Find her expected utility if she paid the fair premium and has full insurance.

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