An individual with current wealth of 10 at time t, investing over a single period, has a utility function U=100Wt+1-0.5Wt+12 where Wt+1 is wealth at t+1. She can hold either cash which pays zero interest or a share which has a price today of P and will have a price next period of 90 in state 1 with probability 0.5 and 120 in state 2 with probability 0.5 (the price includes any dividend owing). What is the optimal portfolio for this individual to hold? (15 marks) Use you solution in the problem above to explain the optimal portfolio selection when an individual's labour income varies across the two states of the world in the second period (10 marks)