Please help me with this question

llitureistlon 1 Assume that an oil company called Texas Petroleum {TF'} has got oil rigs in the Gulf of Mexico. In normal conditions, TP is expected to make 40,000 prots per period. However, due to the effects of climate change, there is a concrete possibility that each period a violent hurricane hits TP's oil rigs resulting in a reduction in prots to 4,000 {which correspond to a loss of 30,000}. Experts estimate that the probability of this happening each period is given by p30. Assume that TP is an expected-utility maximiser with per-period expected utility function uEsU,n~U,p}=p log{rru)+ [1 p) logtw), where an; denotes TP's prots when the hurricane hits, TIN\" denotes TP's prots when the hurricane does not hit, and fog denotes the natural logarithm. Assume that each period TP has the opportunity to purchase insurance that pays Ex in the state of the world in which the hurricane hits, by paying an insurance premium of 103. a} Write down TP's contingent prot bundle when (i) TP does not insure at all and {ii} TP purchases x units of insurance. What are TP's attitudes towards risk? b} Assume that the probability p that the hurricane hits is 1i3. Derive TP's optimal choice under uncertainty. How much insurance does TP purchase? How much is the insurance premium? What is TF'*s contingent prot bundle at the optimum? c} For what values of the probability p, will TP decide not to fully insure? For wl'iat values of the probability p will TP decide not to insure at all? d} Assume that TP is risk neutral and resume the assumption that p=1f3. Derive TP's optimal choice under uncertainty. e} Suppose that TP has got Leontief preferences {also called perfect complements) over contingent prot bundles. How does TF'*s optimal choice change as a Jnction of the probability p that the hurricane hits? In answering the above, make sure to fully explain your reasoning