I have found the Markov Process to be

.5 .2 .3
.1 .7 .2
.4 .4 .2

that state 1 is Industry, that state 2 is Small Business, and that state 3 is Self-Employed.
How do you find the long-run distribution of people among these various types of employment?

Question

I have found the Markov Process to be 

.5     .2     .3
.1     .7     .2
.4      .4    .2

that state 1 is Industry, that state 2 is Small Business, and that state 3 is Self-Employed. 
How do you find the long-run distribution of people among these various types of employment?

zarkon · Answer

Find the eigenvector that corresponds to an eigenvalue of 1

anonymous · Answer

It's also $$\lim_{N \rightarrow \infty}P ^{N}$$
where P is that transition matrix. Here is an approximation that might be useful to you in checking your results.

0.28070181,  0.49122801,  0.22807019
0.28070172,  0.49122812,  0.22807017
0.28070177,  0.49122805,  0.22807018

I used the Python numpy library.

zarkon · Answer

$$\left[\frac{16}{57},\frac{28}{57},\frac{13}{57}\right]$$