Consider a representative household with no population growth choosing {C(t), K (t)}3' to maximize +00 C t _ 19 ~/0 exp(pt)%dt, (P,0, '7) 6 Rio: subject to initial condition K (0) = K0 and capital law of motion K(t) = AK(t) C(t), AK.J 7 6 1a).). (a) Write down the expression of currentvalue Hamiltonian EKG, K, n). (1 points) (b) Write down the three rst order conditions derived directly from the current-value Hamiltonian. (3 points) (c) Write down the equation describing how consumption growth rate depends on consumption level. (2 points) (d) Solve for C(t) as an expression of 0(0). (2 points) (9) Conjecture that K (t) = no + H4005) with unknown parameters. Solve for K (t) in terms of 0(0). (3 points) (f) Find the solution of C(12) and K (t) in terms of Kg. (3 points) (g) Prove that the saving rate 3(t) is strictly increasing in time t and has a limit as t > +00. (1 points) (h) Find the range of p that satises transversality condition. (1 points) (i) Let 9 = 1. Suppose a developed economy has reached a roughly stable saving rate 20% and per capita GDP growth rate 2%. What are the values of parameter A and p? (2 points) (j) Let K0 2 1. Find the range of 7 at. the growth rate of per capita GDP g(t)