Labor Economics

Econ 6680: Homework #4

Due Tuesday, November 17

1. *Suppose Pat manages a large computer software company and Allen is a talented program designer. Pat would like to hire Allen to develop a new software package. If Allen works for Pat, Allen must choose whether or not to expend high effort or low effort on the job. At the end of the work cycle (say, 1 year), Pat will learn whether the project is successful or not. A successful project yields revenue of 6 for the firm, whereas the revenue is 2 if the project is unsuccessful. Success depends on Allen’s effort as well as on a random factor. If Allen expends high effort, then success will be achieved with probability 0.5; if Allen expends low effort, then the project is unsuccessful for sure. The cost of high effort for Allen is 1. Compensation can be contingent on the project outcome, but not Allen’s effort. Allen’s utility function is u(x) = xα (x should include net compensation; in other words wage minus cost of effort). Assume Allen is risk averse (so 0 < α < 1) and Pat is risk neutral. Allen’s reservation wage is 1.

(a) What is the efficient level of effort (high or low)?

(b) What is the wage structure that would induce Allen to expend a high level of effort? Note that your answer will be in terms of α.

(c) What is Pat’s expected profit with this contract? Note that your answer will be in terms of α.

* Adapted from Strategy by Watson.

2. A worker has agreed to take a job with a firm. The job requires the worker to perform two tasks, task A and task B (i.e. to multitask). Each task requires effort from the worker in order to produce any output (i.e. if the worker spends all effort on task A no task B is produced). Effort is costly to the worker. Both task A and task B are valuable to the firm. The firm knows that it must provide incentives for the worker to multitask. The firm agrees to pay the worker α per unit of task A and β per unit of task B. The employment contract cannot be based on worker effort (assume it is unobservable). In developing the compensation plan, the firm must consider what actions the worker is incentivized to take. In particular, the firm should be concerned about the level of effort the worker chooses. In the case of multitasking, the firm should also be concerned about an additional choice the worker makes about effort. What is this additional choice related to effort? In other words, in the worker’s maximization problem he/she we be maximizing over the choice of the level of effort and what other variable related to effort? Note that you do not need to solve or set-up the maximization problem to answer this question.

3. Imagine you are the manager in charge of performance evaluations for software company Numeral, Inc. You must design performance evaluations for a team of software engineers. Will

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Table 1: Employee Productivities for Extra Credit Question Employee Productivity on Team X Productivity on Team Y Alice 7 9 Bernard 10 8 Chloe 13 12 Daniel 9 11 Elle 8 10 Frank 14 13

you evaluate their performance based on quantitative or subjective measures? Why? What specific measures will you use (and why)? How frequently will performance be evaluated and why? Would your answers change if Numeral, Inc. was a start-up compared to an established firm?

Please turn in your homework at the beginning of lecture. You may discuss problems with class- mates, but must turn in individual homework solutions. Please list classmates that you worked with on this homework.

Optional Extra Credit Problem (3 points): Please do not discuss this with class- mates. Imagine two team managers: Xavier and Yolanda. They must divide a pool of employees between their two teams. Team members and their productivity on each team are shown in Table 1.

1. If alternating draws are used to divide the employees with Xavier picking first, is the outcome efficient?

2. If alternating draws are used to divide the employees with Yolanda picking first, is the outcome efficient?

3. If bidding is used to divide employees, is the outcome efficient?

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