We consider the following m states model without labor as in 0827 and 0903:
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where
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with probability matrix:

We also consider the following m states model with labor as in 0828 and 0903:
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where

and
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and
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where both technology change parameter and form of leisure utility change according
to state. As done before, the probability matrix used here is considered backward and
it is different from transition matrix mentioned later.
The resulting state can be computed by the calculation of each policy function with
each state. We speed up each calculation by both error bounds and policy iterations.