Please answer the following questions and show your work:

Question 2: Consumer's utility is given by U(C, L.) = In(C.) - L. Suppose production is given by: f ( K . , L . ) = K q L -a Where ke, C, and Le are capital, consumption and labour at time t. Let B be the discount factor. The social planner chooses consumption, investment and labor in every period to maximize utility of the individual. There is no depreciation of capital. (5 marks) a) Write down the social planner's maximization problem b) Transform the social planner's maximization problem in bellman form () Derive the first order conditions (You do not need to solve it)