Policy function calculation from value function iterations

We consider the same basic AK model with technology change:

where

We set the following probability matrix:

whose row sums are all ones.

For example, we have probability p31 from state 1, p32 from state 2, p33 from state 3,

and p34 from state 4 when we are in state 3.

We can calculate which state we are in from the last point backward.

Behavior of capital

The corresponding behavior of consumption

where only a few number of states lead to some complex movement.