A person has a net asset of $1 million, including a $300,000 net equity of a house (market value of the house – mortgage). Specifically, the house has a market value of $600,000 including $400,000 for the structure and $200,000 for the land, and a mortgage of $300,000.  The person plans to buy $400,000 fire insurance for full coverage of the house. For simplicity, assume that each year the house has a 1% probability of being totally destroyed by fire and a 99%

probability of no damage occurring to the house. The person’s utility for money is approximately proportional to the quartic root of money with U($100,000,000)=1,000 and U($0)=0.

a. Draw the decision tree for the person’s decision of buying or not buying the insurance.

b. Determine the maximum insurance premium IP the person would be willing to pay.

c. What is the risk premium at the maximum IP?

Bonus Problem

Determine the maximum insurance premium the person would be willing to pay for a $300,000 insurance just to cover the mortgage.

(Hint: in this case, the house is under-insured. Inother words, with the $300,000 insurance, if the house is totally destroyed by fire, the person willsuffer a loss in the net asset because the insurance covers only the mortgage not the full net equity of the house, and the maximum insurance premium the person would be willing to pay will need to be determined through numerical iterations).