econ question 4

Econ 6680: Homework #4

Solutions

1. Pat and Allen.

(a) Let’s compare expected revenue in each case. High effort: 0.5(6)+0.5(2)=4. Low effort: 2. Revenue increases by 2 if high effort is exerted. The cost of that high effort is only 1. Thus high effort is the efficient level of effort (it is worth more than it costs).

(b) Let ws be the wage for a successful project and wu be the wage for an unsuccessful project. Now let’s write out the individually rational (IR) constraint and the incentive compatibility (IC) constraint.

0.5(ws − 1)α + 0.5(wu − 1)α ≥ 1 (1) 0.5(ws − 1)α + 0.5(wu − 1)α ≥ wαu (2)

We assume the constraints bind. Subtract (2) from (1) to get 0 = 1 − wαu , which implies that wu = 1. Plugging this into (1) yields 0.5(ws−1)α = 1. We can solve for ws = 2

1 α +1.

This is the wage structure that would induce high effort.

(c) Expected profit: 0.5(2 − 1) + 0.5(6 − 2 1 α − 1) = 3 − 2

1−α α .

2. The firm must also be concerned about how the employee divides effort between the two tasks.

3. Numeral, Inc. performance evaluation. It is likely that the team of software engineers will be evaluated based on a combination of quantitative and subjective measures. For example, certain targets for programs created, features added to programs, or bugs removed could be set in addition to having managers (and/or peers and/or subordinates) write reviews. The combination of quantitative and subjective measures may provide a more well-rounded picture of the employee. The subjective part of the review can help balance the quantitative targets to make sure that the employee does not focus too much on simply meeting the targets while ignoring other aspects of the job that matter (like communicating with team members). The subjective measure also allows for flexibility in how the employee is ultimately evaluated. Specific measures should be chosen to reflect what is most valuable to the firm. This applies to both quantitative and subjective measures. For example, with subjective measures the firm should state ahead of time what “softer” skills will be evaluated (such as leadership). Including a subjective measure may make the evaluations costly enough that they only make sense to do every quarter, twice a year, or even annually. Answers would likely change in the situation of a start-up. What matters to a start-up may be different from what matters to an established firm and this should be reflected in what is measured by the performance evaluations. It may also be necessary for more frequent evaluations though likely less formal ones.

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Note: There are a number of potentially correct answers. The answer should be supported by economic logic. Please refer to our class discussion on this question.

Extra Credit Answers:

1. No. Chloe should be on Xavier’s team.

2. No. Frank should be on Xavier’s team.

3. Yes.

Please let me know if you find any errors in these solutions.

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