please explain and show work, thank you!

Problem 2 Jaime owns a very cute house. It is worth 160 (thousand) dollars. The house is located in a beautiful 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. Jaime is an expected utility maximizer. His utility function is given by u(c) = , where c denotes his wealth. Denote by (chm) Jaime's state-contingent consumption bundle, where cl is the amount of wealth in bad state and c2 is the amount of wealth in good state (i.e., no forest re). Jaime may purchase K (thousand) dollars of insurance from an insurance company. The insur ance contracts costs 7K dollars, where 'y 6 [0,1]. It is known that on the average the insurance company just breaks even on the contract. . In a diagram in which c1 is on the horizontal axis and c2 on the vertical axis, draw Jaime's budget line. Determine the slope of this budget line. Label the endowment, which is the consumption Jaime has without insurance. . Write down the equation for Jaime's expected utility function. Calculate Jaime's expected utility for the case where he purchases no insurance. Calculate Jajme's expected utility for the case where he purchases the insurance. . Determine Jaime's marginal rate of substitution (MRS) using Jaime's expected utility func- tion (general utility function not specic to buying or not buying insurance). . Determine the expected prot for the company selling one insurance contract. Determine the rate 7* at which the company o'ers an insurance contract. . Determine J aime's optimal contingent wealth (Ci, d2"). Illustrate your solution in the diagram. How much insurance K * will Jaime demand at optimum. What is Jaime's expected utility at optimum