# Economics 301 Final Examination Final 2016

Personnel Economics Final 2016: Part I Northern Illinois UniversityDepartment of EconomicsPart IPart I is worth 40% of your final grade.Due: November 22 at 9:30 am. Instructions1. The test consists of two questions. 2. Do not work with another person or persons on any examination. Remember the Code ofConduct as outlined in the syllabus. 3. To answer both problems, open an Excel file. Put your answer to question 1 in Sheet 1and your answer to question 2 in Sheet 2. Type your verbal answers to the parts of eachquestion in the cells below each spreadsheet. 4. Name your excel file as: Lastname_Firstname, where Lastname is YOUR last nameand Firstname is YOUR first name. 5. Hand-in a hard copy of your answers at the beginning of the in-class exam. 6. E-mail your spreadsheet to: niuecon301@gmail.com 1 Personnel Economics 1. Final 2016: Part I Serena has just started a job at Android Consulting, Inc. She will stay there forexactly 12 years unless she is fired for shirking her duties. Her productivity (in thousandsof dollars) in each year she stays at Android is given in column (1) of the spreadsheetprovided.The only incentive system used by Android is to dismiss employees who are discoveredshirking their duties. Shirking gives Serena an instant boost of utility worth 100(thousand) dollars to her. (Set your spreadsheet up so you can change the value of thislater). If Serena shirks, she gets this utility boost, but is immediately detected and fired.She then works at another, alternative job, where her wages are given by the column (2)of the spreadsheet that is provided.Android, Inc. is choosing between two wage profiles it might offer Serena. They aregiven by the columns labeled “wage I” and “wage II” in the spreadsheet. There is nodiscounting, and there is no chance Serena will leave Android, Inc. for any reason otherthan dismissal. a.) Verify that both wage profiles I and II pay Serena the same total amount over hertwelve years there. Verify that, over the same period, the firm would just break even onemploying Serena under either profile if she didn’t shirk. What is her lifetimeproductivity if she doesn’t shirk?b.) In columns 5 and 6, calculate the remaining present value of wages Serena has still toreceive from Android, Inc. under the wage profiles I and II respectively.c.) In column 7, calculate the remaining present value of wages Serena would receive if sheworked at her alternative job for the rest of her 12-year career.d.) In columns 8 and 9, calculate Serena’s net gains to shirking in each year of her careerwith Android, separately for wage profiles I and II. Will both profiles prevent shirkingthroughout Serena’s career? Why or why not?e.) Using your spreadsheet, change the instantaneous benefit of shirking from 100 to a highernumber. Experiment to find the highest value of shirking for which wage profile IIprevents shirking throughout Serena’s career. 2 Personnel Economics Final 2016: Part I Three agents (agents 1, 2 and 3) are competing for a promotion. The winner gets paid ? +S, the two “losers” get paid ?. All three agents are risk neutral and have disutility of effortgiven by Ei2/2, i = 1,2,3. The probability that agent 1 wins the promotion is given by: 2. Prob(1 wins) = 1/3 + ?(E1 – [(E2 + E3)/2])In other words, 1’s chances of winning are a linear function of the difference betweenhis/her effort and the average effort level of the other two agents. The same formulaapplies to the other two agents. As we did in class, think of ? as a measure of theprecision with which the firm is able to measure the workers’ relative performance.Note: ?[Prob*S]/?E1 = ?S and ?[E12/2]/?E1 = E1 a.) If all three agents exert the same effort, what is the probability that agent 1 will win?b.) Write down the formula for the expected utility of agent 1. Find his/her utilitymaximizing effort as a function of the prize spread, S, and ?.c.) In the blank spreadsheet that is provided for this question, think of the various values of Sas different possible prize spreads the firm is considering. Enter a value of 0.2 for ?(alpha) in cell B5. Then, in column 2, fill in the (common) effort level that all threeagents will choose for each value of S.d.) Assume neither agent is paid to show up for work (? = 0). Using the definition of utility(and the fact that all three agents work equally hard) fill in the agents’ common utilitylevel in this situation in column 3.e.) Suppose that, to get each agent to take this job, he/she must attain an expected utilitylevel of 10. Enter this information into cell B8. Next, in column 4, compute the level of ?for each agent that just induces them to take this job.f.) Suppose the firm chooses the levels of ? given by part (e) above. Let the expectedvalue of each agent’s output be given by 10E (where E is the agent’s effort). Nowcompute the firm’s expected output per worker in column 5, and its expected profits perworker in column 6. What is the profit-maximizing prize spread and the maximized levelof profits? g.) Now reduce alpha to .1, cutting in half the precision of the firm’s measurementtechnology, i.e. doubling the amount of “noise” in its performance evaluation system.What is now the profit-maximizing prize spread? Is the firm worse off than in part (f)?Are workers worse off than in part (f)? Why or why not? 3 Personnel Economics Final 2016