Policy function calculation from value function iterations

Today we consider the basic AK model and its Bellman equation:

where or and

We consider the following m-state model:

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.

.

where

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.

.

and

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.

.

Or we consider m x m probability matrix P whose row sums are all ones.

Each probability lies between 0 and 1.

There are only m policy functions and nothing more.

Notice that grid method is valid only for a single value function.

We had better compute each policy function separately.