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) = where 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 _{1 and 2 in the two states.}

(c) Work out the optimal choices of _{1 and 2.} (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?