A bank is in the process of hiring bankers. It has two types of applicants: Type D and Type E. Type E has higher productivity comparing to Type D. The applicants know their own productivity and which type they are, but the bank does not know; and it is quite difficult to use screening to distinguish the two types. The bank certainly wants to hire the E types since they are more productive. How can the bank construct a job offer that is attractive to the E types but not the D types?

Here is a bit more information: 1. Assuming that the bank can figure out what type that an employee is after observing him or her on the job for one year. However, the accuracy of the judgement is not perfect: ten percent of the time, the wrong decision is made. Thus, 10 percent of D types are promoted when they should not be, and 10 percent of E types are not.

2. Assuming that the bank knows that D types can earn $175,000 per year in other jobs, while E types can earn $200,000 per year in other jobs.

3. Also assume that if the applicants get hired and promoted, they will work for one year after promotion (this is really an assumption to keep things simpler...) (1) Examining the job offers below (all numbers are in $1,000), determine whether applicants will apply. Consider what are the more general conditions that W1 and W2 should meet to make the job offer attractive to E types but not D types?

Type D E W1 W2 Expected Pay Apply? Expected Pay Apply? Alternative Apply Alternative Apply $200 $200 $350 $378 $400 $400 180 225 350 400 160 250 350 400 140 275 350 400 120 300 350 400 100 325 350 400Type D W1 E W 2 Expected Pay Apply? Expected Pay Apply? Alternative Apply Alternative Apply $200 $200 $350 $378 yes $400 $400 yeso 180 225 350 360 yes 400 403 yes 160 250 350 343 no 400 405 yes 140 275 350 325 no 400 408 yes 120 300 350 308 no 400 410 yes 100 325 350 290 no 400 413 yes