$7.$ Individual Problems $19-6$

You need to hire some new employees to staff your startup venture. You know that potential employees are distributed throughout the population as follows, but you can't distinguish among them:

Employee Value

Probability

$$35,0000\mathrm{.}25$$$54,0000\mathrm{.}25$$$73,0000\mathrm{.}25$$$92,0000\mathrm{.}25$

The expected value of hiring one employee is

$.$

Suppose you set the salary of the position equal to the expected value of an employee. Assume that employees will not work for a salary below their employee value.

The expected value of an employee who would apply for the position, at this salary, is

$.$

Given this adverse selection, your most reasonable salary offer $($that ensures you do not lose money$)$ is$.$