Problem Set 4
Top Dollar Sales (TDS) is a national firm that sells automobile and life insurance. TDS employs 500 insurance agents. Each agent works somewhat independently to contact and service clients. However, TDS is organized into 100 different geographically regions. The average sales for a region is $1,000,000, with a standard deviation of $100,000. The manager of each geographical region has the autonomy to establish a compensation plan. The average annual compensation for an insurance agent is $60,000, with a standard deviation of $12,000.
Assume that TDS has hired you as a consultant. Your services are desired to help TDS make two critical decisions. The first decision concerns the compensation plan. Several insurance agents have recently quit TDS. In fact, the average annual turnover rate is 25% across regions, with a standard deviation of 15 %. This rate of turnover is problematic, as it costs the firm $60,000, on average, to replace an agent. During their exit interviews, several high performing agents suggested that compensation levels at TDS are too low. TDS is trying to decide if it will be beneficial to increase the wages it pays to agents.
Your research of the TDS geographic regions has determined that there is a correlation between level of compensation and sales, probably because higher compensation attracts and retains better people. (See our earlier problem set on selection utility and the role of Z in that formula.) After controlling for differences in regional opportunity (e.g., local economic conditions), you found a correlation coefficient of .28 between regional pay level and regional sales. (We will assume that adding sales does not have any substantial impact on costs, except for the impact on compensation costs.) You also found a correlation of -.30 between regional compensation level and regional agent turnover.
The second decision for which TDS seeks your recommendations relates to employee...