We are going to have problems on the exam which give you a utility function for a person (U=2/I, or square root of I, etc), and their income with different probabilities. Like 40% chance of being fine and making $100 and 60% chance of getting hurt and paying $10 of it for medical bills or whatever. So the question will ask something like, what is the maxmium so and so would pay for insurance?

I know how to get the Expected Utility without insurance, I think. EU = pU(I not hurt) + (1-p) U(i if hurt). No problem. But it seems to me there are different ways to calculate how much one would be willing to spend to take away the risk, yet I always get different answers depending on how I do it.

Should I be making the max insurance cost = EU(no insurance) - U(insurance)? Or do I use the U(lost income * prob) ? An example worked out would be helpful!

Solution Preview

Expected Utility without insurance is
E(U) = pU(I high) + (1-p)*U(I low) = 40%*SQRT(100)+ 60% *SQRT(10) = ...

Solution Summary

Expected Utility without insurance is exemplified.

... So, the person's willingness to pay for insurance is going to be equal to his risk premium. First, we need to work out expected utility from earlier which is ...

...insurance =p*[(Wo+y)^(-1)-1]+(1-p)*[Wo^(-1)-1] The wealth will be Wo+y with probability p and Wo with probability 1-p. Expected utility with insurance =(Wo+yc ...

...Expected utility is the sum of utility in each outcome weighted by the probability. Insurance premium - the amount of money that individual has to pay no ...

... the person expects to earn $950000 over his remaining life time. With linear utility this means his expected utility is 950000. If he buys insurance he will be ...

... income levels, risk attitudes, etc.) would you expect to observe ... 0.15+0.25)40000 / 2 = 8000 Type 1 person's expected utility without insurance is : E(U1 ...

... the risk cover is L. Then the agent will choose the risk cover such that his expected utility is maximized. The wealth because of the insurance contract is as ...

... new insurance plan 11.907419 Incremental increase in utility 0.000015 Since the expected utility has increased, Pierre should buy the probabilistic insurance. ...

... his wealth will be w-0 = w and the probability is 1-p. Then the according utility is u(w) = 1 - exp(-à£w) The expected utility of not taking insurance is u(NI ...