2 a) Consider the expression by( 1- N) Linearize this around the steady state level of N , N. (20) iij Use your expression to write an expression for the percentage deviation of the term, 1- N, , from its steady state value. (10) b) Consider the difference equation X =.9X_+6, where s, is a random error term with mean 0. ij Show that the first three terms in the solution for X, take the form X, =6, 4.96,-1 +.816,-2 (20) Use the solution above to determine the first term in the expression for EX ,4 1 where E, denotes expectation as of time / . Note that all variables with a r-subscript are known at time r. (10)c) Suppose that a government must maximizes Nu(c(w),D)f(w)dw subject to the constraint N T(w)/(w) z E where A is the population size, a is a utility function, cis consumption , I is labour supply, w is the wage, 7(.) is some function indicating tax revenue, f is a wage density function, and E are constants. Give an economic interpretation for this problem. (40)