Question

Global Hubcap is a maker of automobile hubcaps that serves all global automakers from its headquarters on the shores of Lake Huron. Manufacturing supervisors are important employees at Global Hubcap. A supervisor’s most important responsibility is training shop-floor workers. This training is done each June, as the firm shifts production over to a new model year’s hubcap designs. At the end of the training period (June 30 each year), every manufacturing team must pass a skills assessment, which is a test designed to tell whether the supervisor’s training program was successful. Supervisors are expected to work hard during this training period. If the supervisor works hard to train his/her manufacturing team, then the team passes the test with probability 1. If the supervisor shirks this important responsibility, then it is still possible that the team passes the test. However, the poor training is likely to result in hard-to-identify defects in the firm’s products - even if the team passes the test. These defects are likely to result in quality problems for the firm down the road, as its hubcaps age. Global Hubcap fires a supervisor immediately if his/her team fails the skills test. Fired supervisors typically are able to hire on quickly as manufacturing workers with a local rival at a wage of $20 per hour. Any supervisor whose team passes the test will keep his or her job - at least until the following June 30 when another training period and test rolls around. Training and preparation for training is costly and difficult for supervisors. Supervisors will work hard at this important training task if and only if doing so results in annual compensation that is higher by at least $1040.

Question (a) John Smith is a long-time Global Hubcap supervisor, whose current hourly wage is W. He is currently 59 years old and has announced an intention to retire next June at age 60. Hence, the upcoming training period is expected to be his last. Suppose Smith decides to shirk his training responsibilities this year. Suppose further than if he shirks, the probability his team passes the test is 80%. Write an expression for Smith’s expected total compensation over the period from June 30, 2018 to June 30, 2019. (Hint: If Smith shirks, there is a 20% chance that he works for 52 weeks as manufacturing employee at a rival, making $20 per hour. There is an 80% chance he works those 52 weeks as a Global Hubcap supervisor, making W. Assume here a 40 hour work week, and ignore the time-value of money.)

Answer 1

If John Smith shirks,the probability that he works for 52 weeks and 40 hours per week as a manufacturing employee or Pr(M) in a rival firm is 20% or 0.2 and will earn $20 per hour meaning that his total compensation as a manufacturing employee=(52*20*40)=$41,600.

Now,the probability that Smith works at Global Hubcups for 52 weeks and 40 hours per week or Pr(G) is 80% or 0.8 and he will then earn hourly wage W in which case,his total compensation from working at Global Hubcups =(52*W*40)=2080W

Hence,Smith's expected total compensation from the period of June 30,2018 to June 30,2019 will be:-

E(TC)=Pr(M)*Total Compensation as a manufacturing employee+Pr(G)*Total Compensation as a Global Hubcup supervisor

={0.2*($41,600)}+{0.8*(2080W)}

=$8320+1664W

Hence,the above calculation done is an expression for John Smith's expected overall compensation from choosing both the options(manufacturing employee and Hubcups superviser) for the one year period concerned.However by knowing exact value of "W" or the hourly wage we can derive an exact value for the above expression.