Problem: Seniority and Time-Based Pay
Michelle has just offered a job at Mullaney/Hunter Enterprises in the production line. Michelle expects to stay at this firm for at least 40 years, during this time her productivity, V, is given by the first column in the attached table. Michelle is faced with the option of choosing one of two wage profiles. The first profile, Wage I, is combined with a mandatory retirement clause: if she takes it, she must retire after 40 years (thus she gets a wage of zero after year 40). Note that year 40 is the date at which the value of her production equals the value of her leisure (denoted in dollar value by L). The second wage profile pays Michelle less in her younger years, but more in her older years. Because profile II offers her a relatively attractive wage after year 40 and does not contain a mandatory retirement clause, it induces her to work past year 40 (just one year, for simplicity). Using the attached table please answer the following questions.
a. Under both wage profiles, is Michelle overpaid (relative to her productivity) or underpaid when she is young? When she is old? At which wage does she change from being over/underpaid to the other in each wage profile?
b. Assuming the discount rate is zero, calculate the present value of Michelle's lifetime output, and of her lifetime wages received under both wage streams. Show that the form just breaks even on employing Michelle under both schemes.
c. Which wage structure will Michelle earn more in? What is the difference in total wages between wage profile I and wage profile II?
d. Which wage profile does Michelle prefer and WHY?
e. How much more would she have to be paid in the final year of the contract in profile II in order to be indifferent between the two wage structures? Why won't the firm agree to this new wage structure?
Attachment:- Data Q1.xls