Question

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
$70,000	0.1
$83,000	0.1
$96,000	0.1
$109,000	0.1
$122,000	0.1
$135,000	0.1
$148,000	0.1
$161,000	0.1
$174,000	0.1
$187,000	0.1

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 ($70,000, $109,000, $96,000, $83,000) .

Answer 1

The expected value of an employee who would apply for the position is

E(X) = X1P1 + X2P2 + X3P3 + ..............+ XnPn

= (70000 x 0.1) + (83000 x 0.1) + (96000 x 0.1) + (109000 x 0.1) + (122000 x 0.1) + (135000 x 0.1) + (148000 x 0.1) +

(161000 x 0.1) + (174000 x 0.1) + (187000 x 0.1)

= $128500

Based on the expected value, you would not offer a salary of more than $128500.

so we offer salaries less than expected value $70,000, $83,000, $96,000, $109,000 and $122,000.