A company searches for a new employee. Employees are either superb, meh, or grotty. The company values a superb employee at 8, a meh employee at 4 and a grotty employee at -4. There are two different types of interviews: In a thorough interview the company learns the worker’s type, in a superficial interview the company only learns whether the worker is grotty or not. 

Suppose there are 25% superb, 50% meh and 25% grotty employees. 

a) What is the expected value of an employee? 

b) Suppose the value of not hiring is -2. How much is the company willing to pay for the two types of interviews? 

c) Now suppose the company must hire an employee. There are two candidates. The company has to first decide whether or not to interview the first candidate. The company then decides whether or not to hire the first candidate. If the company has not yet hired the company decides whether or not to interview the second candidate. The company finally hires the second candidate if it did not hire the first candidate. Suppose a thorough interview costs 3 while a superficial interview costs only 2.5. What is the company’s optimal plan of action?