2. A consumer lives for two periods. Assume the following values apply: ), = 150, income received in period 1; 12 = 423, income received in period 2; r = 0.5, interest rate. The consumer maximizes his utility, given by the function, U(Cj, C2) = InC, + 0.8inC2, where C, and C2 represent consumption in periods 1 and 2, respectively. Given the values of /1, 12, and r, the consumer's lifetime budget constraint is (1.5) (150 - C,) + 423 - C2 = 0. a) Set up the Lagrangian function and use the first-order and second-order conditions to find the values of C and C2 that solve the consumer's problem. b) In view of your answer to part (a), how much does the consumer save or borrow in period 1, and how much interest does he receive or pay in period 2? c) What is the interpretation of the number 0.8 in the consumer's utility function? d) Now, if the consumer wishes to be a borrower in period 1, then the amount that he can borrow is limited to $50. Thus, C - 1,