1. Sally lives for two periods, t = 1, 2. In each period she decides whether or not to eat a cheeseburger, c1 = 0 or 1 and c2 = 0 or 1. Her initial consumption of a cheeseburger, co, is exogenous. Sally's true utility is u(c1, $1) + u(C2, $2) - (2 + c1) (1 + c2) Sally's state is equal to her consumption in the previous period, St = Ct-1. Therefore, her true utility is u(C1, Co) + u(C2, C1) - (2 + c1) (1 + c2). u(1, 1) -3 u(1, 0) 5 u(0, 1) 3 u (0, 0) -5 a. If Sally does not eat a cheeseburger initially, co = 0, what is her optimal consumption plan? b. What is her optimal consumption plan if she does eat a cheeseburger initially, co = 1? Now we assume Sally is projection biased so that her perceived utility is u(C1, Co) + au(C2, Co) + (1 - a)u(c2, C1) - (2 + C1) (1 + C2) c. If Sally is fully projection biased, a = 1, and she does not eat a cheeseburger initially, co = 0, what is her consumption plan? d. What is her consumption plan if she is fully projection biased, a = 1, and she does eat a cheeseburger initially, co = 1? e. Explain the intuition for why your results for parts a and c are similar or different. f. Explain the intuition for why your results for parts b and d are similar or different