Policy function calculation from value function iterations

We consider the same basic AK model with technology change:

with probability 1/2

and

with probability 1/2.

That is,

with probability 1/2

and

with probability 1/2

where

and with depreciation

as in 0728. Today we set up stochastic simulation using these two policy functions.

The Behavior of capital k using two policy functions

where capital k moves around between two steady states almost forever.

Notice that the behavior will not lead to two steady-state levels straight

because the level of capital k in the previous time does not have to lie on

the same policy function.

Behavior of capital around two steady states

The corresponding behavior of consumption

Only two states lead to various types of fluctuations if we consider random process.