Question 2 Consider an economy with only 2 individuals, Mr A and Mr B. They each live for 2 periods only. Their lifetime utility function is U (ch02) = 22(c1) + ,622(c2), 1 where subscript t, t = 1, 2, denotes period t. Further suppose that 22 (c1) = ln (c1) and 22 (C2) = 111(62) . Both Mr A and B can borrow and lend freely at a real interest rate of 2-". They are each endowed with 50 units of consumption goods in both the rst and second periods. (2') Show that 22' (ct) > 0 and 22\" (ct) 0. (22') Draw the rst period utility function 22 (c1). Does it matter that for values of cl from 0 to 1 that the utility function takes on negative values? Why? (2'2'2') Without any computation, tell me what Mr A and B's optimal consumption and savings choices (CI, 0;, sf, 3;) are. (iv) Explain the intuition for your result in part (222')