Question

You are a hiring manager, and you are designing a job posting for your next hire. The contract that you offer features:

• 1 year probationary period
• 10 extra years (Offered conditional on good performance during probationary period)
• Opt or Out

The likelihood that a good candidate will get retained after the probationary period is 80%, while the probability that a bad candidate will get offered retention is 5%.
A good candidate has a per-year outside option of $100'000; a bad candidate has a per-year outside option of $70'000.

Which of the following three options allows for an effective screening of candidates?

Option 1
w₁= $120'000
w₂=w₃=...=w₁₁=$185'000

Option 2
w₁= $70'000
w₂=w₃=...=w₁₁=$120'000

Option 3
w₁= $120'000
w₂=w₃=...=w₁₁=$70'000

Answer 1

we have from option 1 ,you are paying $120,000 in the first year and $185,000 in the next ten years, this is more than what both good and bad candidates are getting outside. So both will apply . This is not an effective screening method.

now from option 2 ,$70,000 for first year and $120,000 further on. At $70,000 good candidates will refrain from applying but seeing that they are getting more than outside in coming years they will apply. Bad candidates at $70,000 will apply as it is equal to the wage paid outside but since they have a low probability of getting retained they will refrain from applying and continue job outside.

we have from option 3, The first year wages are $120,000 which is higher what both good candidates ($100,000) and bad candidates ($70,000) are getting outside.
The next 10 year wages are $70,000 which is lower than what good candidates are getting outside so they will refrain from applying . So only bad candidates will apply. This is not an effective method.

so option 2 is best

required option is 2.