USC is a strategy consulting firm that divides its consultants into three classes: Associates, Managers, and Partners. The firm has been stable in size for the last 20 years. There has been – and are expected to be- 200 Associates, 50 Managers, and 20 Partners in steady state.
The work environment at the firm is very competitive. After five years of working as an Associate, a consultant goes “either up or out”; that is, becomes a Manager, or is dismissed from the company. The number of Associates dismissed from the company, without being promoted to Manager, is traditionally about 30 per year.
Similarly, after several more years, a Manager either becomes a Partner, or is dismissed from the company. As a policy, the firm recruits new Iowa USC graduates as Associates; no hires are made at the Manager or Partner level. If a manager is promoted to Partner she/he remains as a Partner for 10 years on average, and then leaves the company. The diagram below traces the progression of personnel at USC.
a) On average, how many new MBAs does HKA need to hire every year to maintain the same number of Associates, Managers, and Partners?
b) What is the probability that an Associate will be promoted to Manager?
c) If an Associate is promoted to Manager, how many years does she/he serve as a Manager?