Uncertainty and Insurance:

You own a house and have a utility function equal to

U=(1pf)ln(x1f2)+pln(x) in whichx1represents your total wealth in a state of nature in

which your house is still standing, andx2represents your total wealth in a state of nature in which your house has burned down. Assume all of your total wealth is related to the value of your house (and its property) in each state of nature. If your house is still standing, it is worth $2,500,000. If it burns down, it is worth $1,000,000 (land value).

The probability of a fire is pf= .02.

(a) (1pt) What is your current level of utility without fire insurance?

(b) (1pt) If the insurance company offers full coverage at a fair insurance premium, how much be your insurance premium be? (show work)

(c) (1pt) What is your level of utility with insurance?

(d) (2pts) Instead of the fair insurance premium, what is the highest price you would be willing to pay for the insurance policy?