Albert owns a very cute house. It is worth 100.000 dollars. The house is located in a beautifully area, but unfortunately there are frequent forest res. There is 50% chance that his house will burn down- If his house burns down, it losses 75% of its initial value. Albert is an expected utility maximieer. His utility function is given by trim} = {5, where :1: denotes his wealth. Denote by (rhea) Albert's state-contingent consumption bundle where I; is the amount of wealth in bad state and 3:2 is the amount of wealth in good state [no forest re]. Albert may purchase D dollars of insuranoe from an insurance company. The insurance contract costs '1' - D dollars, where y E [0, 1]. It is known that on the average the insurance company just breaks even on the contract. 1. Determine Albert's risk attitude. Draw his utility function in a diagram. 2. Determine Albert's eontingent wealth for the case where he buys an insurance contract. Determine Albert's contingent wealth without insuranoe. 3. In a diagram in which a" is on the horizontal son's and 1:3 on the vertical axis, draw Albert's budget line. Determine the slope of this budget line. 4. Write down the equation for Albert's expected utility fmrction. Calculate Albert's expected utility for the case where he purchases no insurance. 5. Determine the equation for the indifference curve that passes through Albert's state contingent wealth without insurance. Draw that indifference curve in the previous diagram. Determine Albert's marginal rate of substitution {MR3}. 0. Determine the expected prot for the company selling one insurance contract- Deter- mine the rate "r" at which the company offers an insurance contract. 7. Determine Albert's optimal contingent wealth (ET, 3:5). Illustrate your solution in the diagram. How much insurance 13' will Albert demand at optimum. What is Albert's expected utility at optimum