Please Answer all parts of the question on paper and please show all work.

Question 1 (Consumer optimization problem in a two period model with investment) Suppose the utility function is given as: U = Cl + c'l' and the lifetime budget constraint is given as: I r _ r: (1 +T)c+(1+T)"=whwl+1r+wh w l H\" 1+?" 1+?" simplicity that the wage received by the consumer is the same in both periods such that w = w' . Here T and T' are consumption taxes. Assume for Answer the following questions: 1. Write down the problem of the consumer (Hint: Write down what the consumer is trying to maximize or minimize and what is the constraint) 2. Solve for the Optimal values of 6*, c\