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Expected Utility without insurance

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.