Question 3: Consumption Smoothing (28 points) Consider the following two period model max log(co) + Blog(ci) subject to Co + a1 = yo C = (1+r)ai + yi where yo is constant, and y1 can take 2 possible values {y1,#, 31,2), with probability {n, 1 - x}. Denote the expected value of y1 as y1 91 = Ty1,# + (1 - 7)91,L (math hint: dog(@) = 1.) (a) Suppose that y1,# = 31,1 = 71. Derive the solution to the optimal consumption in the first period co. (8 points) (b) Suppose 31,# > 91,L. Derive the Euler condition. Use the budget constraint to write the Euler condition with only co as unknown. (10 points) (c) Show that co in part (b) is smaller that that in part (a). Briefly explain why under uncertainty case, the consumer consumes less in first period. (10 points)