Value function iterations with transition matrix

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

where and

for j=1,2,. . .,m.

We consider the following m x m transition matrix

where row sums are all ones. Here,

at probability of pij.

That is, we consider

.

.

.

or

in vector notation.

The resulting m policy functions are usually different from what we calculate

independently given .

The resulting policy functions depend on transition matrix as well.

The case with

The case with

where each policy function corresponds to what is calculated by independent

computation for each when row sums are also all ones. Usually they are different.