QUESTION 2 OPTIONAL There are two equally likely states of the world. In state 1, your endowment of wealth will be 12; in state 2, it will be 3. You are an expected utility maximizer with a utility function of the form u(w) = vw where w denotes your final wealth. You can buy and sell state-contingent claims to wealth at prices 1/3 for one unit of state-1 wealth and and 2/3 for one unit of state-2 wealth. (a) Write down the expression for your expected utility. (b) Write down the budget constraint for your choices of final wealth quan- tities wi and we in the two states. (c) Work out the optimal choices of wi and w2. (d) Would your results in (i iii) above change if you exhibited logarith- mic utility of wealth instead? What argument would you give for the difference in the results of the two cases if any? Total for Question 2: 20 marks QUESTION 2 OPTIONAL There are two equally likely states of the world. In state 1, your endowment of wealth will be 12; in state 2, it will be 3. You are an expected utility maximizer with a utility function of the form u(w) = vw where w denotes your final wealth. You can buy and sell state-contingent claims to wealth at prices 1/3 for one unit of state-1 wealth and and 2/3 for one unit of state-2 wealth. (a) Write down the expression for your expected utility. (b) Write down the budget constraint for your choices of final wealth quan- tities wi and we in the two states. (c) Work out the optimal choices of wi and w2. (d) Would your results in (i iii) above change if you exhibited logarith- mic utility of wealth instead? What argument would you give for the difference in the results of the two cases if any? Total for Question 2: 20 marks