A large corporation collected data on the reasons both middle managers and senior man- agers leave the company. Some managers eventually retire, but others leave the company prior to retirement for personal reasons including more attractive positions with other firms. Assume that the following matrix of one-year transition probabilities applies with the four states of the Markov process being retirement, leaves prior to retirement for per- sonal reasons, stays as a middle manager, stays as a senior manager.
|
Retirement
|
Leaves- Personal
|
Middle Manager
|
Senior Manager
|
|
Retirement
|
1.00
|
0.00
|
0.00
|
0.00
|
|
Leaves-Personal
|
0.00
|
1.00
|
0.00
|
0.00
|
|
Middle Manager
|
0.03
|
0.07
|
0.80
|
0.10
|
|
Senior Manager
|
0.08
|
0.01
|
0.03
|
0.88
|
a. What states are considered absorbing states? Why?
b. Interpret the transition probabilities for the middle managers.
c. Interpret the transition probabilities for the senior managers.
d. What percentage of the current middle managers will eventually retire from the company? What percentage will leave the company for personal reasons?
e. The company currently has 920 managers: 640 middle managers and 280 senior managers. How many of these managers will eventually retire from the company? How many will leave the company for personal reasons?