Problem 16-15 (Algorithmic) A large corporation collected data on the reasons both middle managers and senior managers 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 personal reasons, stays as a middle manager, and stays as a senior manager.

a. What states are considered absorbing states? Why?

1. Interpret the transition probabilities for the middle managers. Probability of retirement =____ Probability of leaving (personal) = ____ Probability of staying middle manager = ____ Probability of promotion to senior manager = ____
2. Interpret the transition probabilities for the senior managers. Probability of retirement = ____ Probability of leaving (personal) =____ Probability of staying middle manager = ____ Probability of promotion to senior manager = ____
3. What percentage of the current middle managers will eventually retire from the company? What percentage will leave the company for personal reasons? If required, round your answers to one decimal place. Retire from the company = ____ % Leave the company for personal reasons = ____ %
4. The company currently has 940 managers: 670 middle managers and 270 senior managers. How many of these managers will eventually retire from the company? How many will leave the company for personal reasons? If required, round your answers to one decimal place. Retire from the company =____ % Leave the company for personal reasons = ____ %

Leaves- Middle Senior Retirement Personal Manager Manager Retirement 1.00 0.00 0.00 0.00 Leaves-Personal 0.00 1.00 0.00 0.00 0.02 0.08 0.80 0.10 Middle Manager Senior Manager 0.08 0.02 0.04 0.86