1. Suppose that your wealth is $1,500,000. You buy a $900,000 house and invest the remainder in a risk-free asset paying an annual interest rate of 1.5%. There is a probability of 0.001 that your house will burn to the ground and its value will be reduced to zero. The real estate market is (uncharacteristically) stable, so if your house does not burn down, its value will still be $900,000 at the end of the year. a) Consider a fire insurance policy that pays you $900,000 at the end of the year if your house burns down. If you have log utility of end-of-year wealth, what is the most that you would be willing to pay for this insurance policy at the beginning of the year? (Remember to use natural logarithms in this and all other contexts where the word "log" is used in this course.) b) What is your relative risk aversion in the log case? How would your previous answer change if you had a higher relative risk aversion coefficient? c) Suppose other homeowners have a similar willingness to pay as you, in the log utility case. Does your answer in part a) tell you what insurance companies will charge for fire insurance? Why or why not