Adverse Selection in the Labor Market (5 points)

An employer faces two types of employees. Regular workers are 80% of the population and generate $100,000 in productivity. Exceptional workers are 20% of the population, and generate $140,000 in productivity. Employees know their types, and have alternative employment opportunities yielding $80,000 for regular workers and $110,000 for exceptional workers. Employers don't know the employees' types, but they do know the value of their outside options, as well as the proportion of each type of worker in the population.

a)If the employer offers a salary equal to the weighted average productivity in the population, what will be the employer's per-employee profit? (multiple choice - 1 point)

a. - $20,000

b. - $8,000

c. $0

d. $4,000

e. $10,000

b)Suppose instead that the employer anticipates and protects itself from adverse selection. In this case, it would offer a salary of ________ and generate per-employee profits of ________ . (1 point)

Despite protecting itself from the consequences of adverse selection in part b), the employer recognizes that as a result of adverse selection, there is an unconsummated wealth-creating transaction available if it can screen the workers in a way that will reveal their types. They come up with the following hiring policy: Anyone who has passed a certain number, , of qualifying examinations will be regarded as an exceptional worker and will be paid $120,000. And anyone who has passed fewer than will be regarded as a regular worker and paid $90,000. Suppose that these examinations are tough and require a lot of studying, especially for the regular workers. Specifically, to pass each examination, exceptional workers face a studying cost valued at $1,000, while regular workers face a studying cost valued at $5,000.

c)For the policy to work, it needs to be incentive compatible. The number of examinations required () should be strict enough that the regular workers don't bother to meet it but not so strict as to discourage even the exceptional workers from attempting it. What is the minimum number of examinations required to ensure that the regular workers don't find it worth it to reach the requirement? What is the maximum number of examinations the firm can require beyond which the exceptional workers would just prefer the regular worker wage? (1 point)

d)Even if the incentive compatibility conditions are met, for the policy to work, the workers need to be willing to participate in the screening process at all instead of just taking their outside employment opportunities. For the regular workers, they're definitely willing to participate because they won't be taking the examinations, but will still be getting $90,000. What is the maximum number of examinations that the employer can require before the exceptional workers will take their outside employment opportunity? (1 point)

e)Propose one specific value of that would make this hiring policy a successful screen, thus allowing the employer to differentiate between the two different types of workers based on the actions of the workers? (1 point)