Story:

Your company wants to hire several new workers for its process improvement projects. The company has 2 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 3 categories: one third are very talented, one third are good, and one third are merely adequate. Any of these applicants could easily get a job elsewhere earning $48,000 annually. 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 $1,100 in overtime and stress. By comparison, each project costs $2,200 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 $7,000 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 3 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.

Questions:

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 and how to apply for a job. You will need to model, analyze, and interpret the situation to respond the companys questions below. For questions 1 and 2, you do not need any decision variables; you can either define 3 incentive compatibility conditions for each one, or analyze it informally using good logic. For question 3, you will need to define 1 decision variable and 3 incentive compatibility conditions (depending on your perspective, they might look like 3 participation conditions). For question 4, you will need to use some judgment, as there is more than one possible answer; be sure to briefly explain your reasoning.

1. Suppose your company offers to hire certified black belts as experts and everyone else as associates. Which categories of applicants would apply for each job type?

2. Suppose instead your company offers to hire certified green belts as experts and everyone else as associates. Which categories of applicants would apply for each job type?

3. Suppose instead your company requires applicants to have completed at least a certain number of projects before being hired as experts. Any other applicants will be hired as associates.

i. For what numbers of projects would no workers apply for expert jobs?

ii. For what numbers of projects would all workers apply for expert jobs?

iii. For what numbers of projects would only talented workers apply for expert jobs?

iv. For what numbers of projects would only good workers apply for expert jobs?

v. For what numbers of projects would only adequate workers apply for expert jobs?

vi. If the company wants talented and good workers to apply for expert jobs, while adequate workers apply for associate jobs, what is the best number of projects to require?

4. Briefly compare your results from the 3 options above, recommend one of them for your company, and explain the reason for your recommendation. Your answer should take about a paragraph.