Suppose your company wants to hire numerous new workers for its process improvement projects. The company has two process improvement job types: experts are paid $68,000 annually, and associates are paid $55,000 annually. From past hiring, you know that applicants for these jobs fall into three categories: one-third are very talented, one-third are good, and one-third are merely adequate. Talented workers could easily get a job elsewhere paying $48,000 annually; good workers could get paid $46,000; and adequate workers could get paid $44,000. Each applicant knows which category they fall into, but the company cannot easily tell them apart. Consequently, your company is thinking of specifying a prerequisite that applicants would need to satisfy.

Option one is to require applicants to have completed at least a certain number of improvement projects, as documented by previous employers. Completing each project costs a talented applicant $1,300 in overtime and stress. By comparison, each project costs $2,300 for a good applicant and $3,300 for an adequate applicant.

Option two is to require applicants to be professionally certified as a black belt in process improvement. To obtain a black belt, a talented applicant needs to spend time and effort equivalent to a $5,000 cost. Good applicants must work harder to get certified; their cost would be $14,000. Similarly, adequate applicants would face a cost of $21,000.

Option three is to require the less demanding green belt certification in process improvement. This would cost effort equal to $6,000 for a talented applicant, $11,000 for a good one, or $16,000 for an adequate one. Your task is to compare these three alternatives and recommend which one to use.

Although your company wants to hire the best applicants available for each job type, it also wants to minimize the potential costs or stresses on these applicants.

Treat this situation as a sequential-move game. The company moves first by specifying the prerequisites that applicants must meet. Applicants move second by choosing whether to apply for a job and which category to apply for.

1. Suppose your company wants to hire talented and good workers for expert jobs, while hiring adequate workers for associate jobs. To do this, it will require applicants to have completed at least a certain number of projects before being hired as experts. What is the best number of projects to require? (Hint: You will need a formal model with 1 DV, 3 PCs, and 3 ICCs.)