Please help me with this exercise. Thank you.

Consider an individual who lives for three periods and whose preferences are represented by the utility function: U (cl, 02,03) 2 log (cl) + 6 [310g (Cg) + )32 log (C3)]. Suppose this individual has access to a perfect capital market. That is, he can borrow or lend unlimited amounts at the going interest rate, which is given by (1 + 7'). Let wt denote the consumer's income in period t =1, 2, 3. You may assume that: w1+w2+w3=1. In this problem, the parameter 6 is an additional discount factor that is applied to every future period. 1. Set up and solve this individual's utility maximization problem under the assumption that ,8 = 1, (1+ 1') = 1, and 6 = 1. Find consumption in each of the three periods. Does the consumer smooth consumption completely? If not, explain why not. 2. Consider now the same problem but assume that 6