Question

One particularly difficult aspect of analyzing the likely effectiveness of a new benefits program lies in knowing how many people will take advantage of each "sub-program" (e.g., health insurance, tuition reimbursement, on-site child care, etc.). With current data, you can estimate the inflow and outflow from only two benefits sub-programs: health insurance and tuition reimbursement.

A quick extrapolation from historical data shows that - in any given year - you expect to add 110 employees to the health insurance sub-program and 560 to the tuition benefit sub-program. In any given year, you expect to lose 3% of enrollees from the health insurance sub-program and 23% of enrollees from the tuition benefit sub-program.

a) What is the long-term equilibrium enrollment in the tuition reimbursement sub-program?

b) You believe that the ideal number of employees in the health insurance sub-program is 8,000. Assuming that you can alter the number of employees that enter the health insurance sub-program each year, but not the percentage of health insurance enrollees you lose, how many new employees would you need to add each year to yield a long-term equilibrium of 8,000? Assume here that you must add the same number of employees each year.

c) If the number of annual additions to each sub-program were reduced by 10 (that is, resulting in 100 new employees for health insurance and 550 new employees for tuition reimbursement), which sub-program's long-term equilibrium would be more greatly affected?