Please explain how to solve a,b,c,d,e step by step

R\\I'Q&"&m bability of fire is p = 0.02. There are Rajesh owns a house worth 200,000. The pro numerous companies that offer fire insurance at a premium 7 (0, 1) per insured sum K. Rajesh's utility can be represented by u (z) = In(z), where z is wealth. The value of the land in case there is a fire is A. (a) Show that the coefficient of relative risk aversion is constant for this particular utility function. (2 marks) (b) Write an expression for with respect to the insured sum. (2 marks) nd express the optimal /. Comment on how the f the land in case there is a fire, A. (6 marks) Rajesh's expected utility, and derive the first-order condition (c) Solve the optimisation problem a optimal K varies with the value o (d) Suppose there is an actuarially fair insurance contract. What is the optimal insurance if A = 50,000? (2 marks) ;e e o e s 0 S o T (Continued overleaf) e 2020 (e) Suppose now that the utility function is state-dependent. In the good state, the utility function is as before u (z) = In(xg), whereas in the bad state, it is u(zp) = 1\"&33), where 2 is wealth in the good state, and zp is wealth in the bad state. Derive the optimal insurance K under these assumptions, and comment on the difference between 'nsurance when utility is state-dependent relative to what it was above. (6 marks)