Note: The answer should be typed.

The first is for context, what I would like help on is question 5: EXERCISE C The household faces the following optimization problem max U = c) 1L(0)ente - ptat (1) [c(t) )=0 S.t. a(t) = r(t)a(t) + w(t) - c(t) - na(t), a(0) given (2) lima(t)e- Ju=o(r(v)-n)du > 0 (3) where n, 0, p are constant parameters, c is per capita consumption, a is per capita wealth, r is the real rate of interest, w is the real wage. . Question 5. Assume the real rate of interest, r, as well as the wage rate, w, are constant. We thus have a(t) = ra(t) + w - c(t) - na(t), a(0) given c (t) c (t ) o ( r - p ) 7Show that the level of consumption at time zero is given by c(0) = /(0) [a(0) + w(0)] where "(0) = w (t) e (r-n)tat and 1 el( )r-8+nt H(0) 0