(12 pts) Suppose there are two periods t = 1, 2 and two possible states 3,; e {H , L} with probability 0.4 and 0.6, respectively. At period one, Ann decides her period-two consumption 02 6 {0,1,2}. If she consumes 0, her utility will be {10, 50} for the two states, if she consumes 1, her utility will be {30, 30}, and if she consumes 2, her utility will be {60,10}. (a) (2pts) If Ann is rational, what is the optimal c2? (b) (6pts) If Ann has projection bias (I = 0.7, calculate her utility in period two when 31 = H, L. What is her choice of 62 conditional on each state in period one? (c) (4pts) Find the maximal projection bias of\" such that as long as a S (1*, Ann's choice of (:2 is always the same as her rational choice