Mu$$strame c$$mo resolver Probabilities, Risk, & Value of Information: Job Recruiting & Candidate Quality Probabilities, Risk, & Value of Information: Job Recruiting & Candidate Quality

Suppose GoldMorgan Global Capital Advisors is interviewing five candidates for an open investment banking analyst role. Four of

the five candidates are equally skilled with Excel and valuation techniques, but one candidate has absolutely no clue how to do

anything related to basic finance. The posted starting salary is $$100,000$ for this role. Due to new labor regulations, after hiring an

analyst the bank cannot legally reduce this salary or terminate the employee for one year. The value of a skilled employee for the

bank is $$300,000$ in annual revenue and the value of a clueless employee is $$20,000$ in annual revenue. The bank tests candidates

on their valuation and Excel skills as a part of the interview process, but when interviews are conducted remotely it is impossible

to determine anything indicative of candidate quality because the clueless candidate can cheat on the test when taken remotely.

Any on$-$site interview conducted in the bank$$s office always has exactly a $90\%$ accuracy rate for correctly identifying whether a

candidate is skilled or clueless, independently and regardless of interviewed candidate$$s type. All candidates have income$/$leisure

preferences heavily skewed towards work so all of them would be happy to accept the $$100,000$ offer and the bank is aware of this.

a$)$ How much should a risk$-$neutral bank be willing to pay for one randomly chosen candidate to come into the office

for an on$-$site interview instead of conducting that interview remotely? Very briefly $($qualitatively$)$ explain whether

or not this answer would change if the bank was risk$-$averse instead, as most of them are in the real world.

b$)$ How much should a risk$-$neutral bank be willing to pay to bring a second randomly chosen candidate into the office

for an on$-$site interview instead of conducting that interview remotely?

c$)$ How much higher of a salary should the bank be willing to offer to the first candidate who voluntarily chooses to

come into the office for an on$-$site interview?

d$)$ Suppose the bank invites all five candidates to come into the office for an interview, with zero costs from this for

anyone involved. Will all five of them attend? Is this situation better or worse for the bank?

Suppose the bank makes an initial offer to one of the candidates. Before day one of employment, the bank is able to incur a cost of

$R to rescind this offer and make a new offer to one of the other four candidates instead. It can only do this one time. An

investigative employment screening firm contacts the bank offering to sell a $$background check$$ report on one of the other four

candidates which proves with $100\%$ accuracy whether that person is skilled or clueless.

e$)$ If the background check candidate is selected randomly from the four who did not get an offer and the bank is riskneutral, how much would this bank be willing to pay for this report?

f$)$ Would a risk$-$averse bank be more, less, or equally willing to pay for this report?

g$)$ If the investigative firm knows with $100\%$ certainty that one of the four candidates who did not get an offer is a

skilled type, now what is the risk$-$neutral bank$$s willingness to pay for this piece of information?