Consider a policy maker who uses an instrument kt to control the path followed by some target

Question:

Consider a policy maker who uses an instrument kt to control the path followed by some target variable Yt. The policy maker has the following objective function

The environment imposes the following constraint on this policy maker:
Yt = 0.2kt + .6Yt ˆ’1
The initial Y0 is known to be 60.
(a) What is the best choice of kt for period t = 4?
(b) What is the best choice of kt for period t = 3?
(c) From these, can you iterate and find the best choice of kt for t = 1?
(d) Determine the value function Vt that gives the optimal payoff for t=1, 2, 3, 4.
(e) Plot the value function Vt and interpret it.