Consider the following two period model max log(Co) + Blog(cı) subject to C+01 = 90 C1 = (1 + r)a + yı where yo is const

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Consider The Following Two Period Model Max Log Co Blog Ci Subject To C 01 90 C1 1 R A Yi Where Yo Is Const 1 (59.88 KiB) Viewed 23 times

Consider the following two period model max log(Co) + Blog(cı) subject to C+01 = 90 C1 = (1 + r)a + yı where yo is constant, and yi can take 2 possible values {91, H , 91,L}, with probability {1,1 – }. Denote the expected value of yı as yı yi = 141,H + (1 - 7)41, L (math hint: dlog(2) du == 1.) (a) Suppose that y1, h = 41,1 = 71. Derive the solution to the optimal consumption in the first period co. (8 points) (b) Suppose y1,H > 41, 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)