macroeconomics problem set

1. Consider the following problem. subject to an initial kg and a law of motion kt+1 + Ct = FUt) + (1 6) It}. (a) Write down the Bellman equation. Now assume that u (c) = 1n (0) , FUc) = Aka where A > 0,a E (0,1),6 E (0,1) , and 6 = 1. (b) Let VB ('6) = 0 and derive V1(k),V2(k),Vn(k). (c) Derive V (k) by n > 00. ((1) Let's make a guess on the value function V(k)=Pln(k-)+Q and solve for P, Q by "guess and verify". Compare the result with (c)