Suppose a representative consumer faces the objective function: max EX B'U (C +s) where c, denotes consumption, a, denotes interest S=0 earning wealth, and x, is income in period t. and period utility function U(CH) = Cuts -7 Cuts; @ > 0 is a parameter and a budget constraint of the form: "c; = (1+r)a + E.> i=0 1+r 1=0 1+r Assume that (1 + r) B = 1 a) Use the Euler equation derived under problem 5 and the lifetime budget constraint in order to show how actual consumption depends on lifetime wealth. b) Derive the growth rate of consumption Ac, = c, -C,-1 c) What does consumption grow/shrink, i.e., when Ac, # 0