1. Transition Matrices

2. Solve for x and y.

3. An Example
A small community has a workforce of 1800 people, with 1680
employed and 120 unemployed. During the course of one year, 10% of
the employed workers will lose their jobs and 60% of the unemployed
will find jobs.
The "Initial State Matrix" The "Transition Diagram"
E U
S =
E U
E U
S =

4. The "Transition Matrix"
E U
E
T = U
E U
T = E
U

5. Predicting the future ...
A small community has a workforce of 1800 people, with 1680 employed
and 120 unemployed. During the course of one year, 10% of the
employed workers will lose their jobs and 60% of the unemployed will
find jobs.
After 1 Year
S0T = S1
After 2 years
S0T2 = S2
After 5 Years
S0T5 = S5

6. Predicting the future ...
A small community has a workforce of 1800 people, with 1680 employed
and 120 unemployed. During the course of one year, 10% of the
employed workers will lose their jobs and 60% of the unemployed will
find jobs.
After 1 Year
S0T = S1
After 2 years
S0T2 = S2
After 5 Years
S0T5 = S5

7. After 50 years
S0T50 = S50
Demonstrate stabilization ...

8. Exercise 6
Questions 1 ­ 5