Policy function calculation from value function iterations

We consider the following switching model:

for t=1,3,5,7,. . .

and

for t=2,4,6,8,. . .

We then consider the corresponding set of Bellman equation:

and

where value functions on the right hand side are switched. Here,

and .

In this case, the movement of capital soon gets into two-cycle process.

The points of two-cycle process are usually not steady-state points.

Behavior of capital

The corresponding behavior of consumption

Only two states lead to some cycle consisting of only two points.

They are usually not steady-state levels themselves.