3) [25 marks] Intertemporal Model. Assume that a small open economy runs for 2 periods and has production, investment, and a representative consumer with: Lifetime utility function: U = In(C) + Bln(C) Production function: Y = K-75 where the initial capital stock is K = 500 Capital Stock in Period 2: K K +1, where I is period-1 investment Access to international credit markets at an interest rate r = 0.1XX, where XX are the last two digits of your student number. For example, if the last two digits of your student number are "49", the interest rate r = 0.149. B(1+r) = 1. Initial Net International Investment Position: B = 0. a. [3 marks] write down the maximization problem for the representative consumer b. [8 marks] Solve for the optimal investment level 1 for the economy in period 1. c. [2 marks] What is the optimal investment level 1 for the economy in period 2? d. [9 marks] Solve for optimal consumption levels for the economy in both periods. e. [3 marks] What is the current account balance of the economy in Period 1? What are total savings in the economy in Period 1?