Economics HW6

Econ 6680: Homework #6

Due Tuesday, December 1

1. There are two workers: Alice and Benjamin. They are both going up for promotion which would increase their current salary by $10,000. Whether they get a promotion depends on both luck and their effort. High effort costs $3,000 and low effort costs 0. The likelihood of promotion for each worker is as follows:

A : 1

2 ∗ (luck) +

1

2 (effort)

B : 1

10 ∗ (luck) +

9

10 (effort)

Both Alice and Benjamin will be “lucky” with a 60% chance (i.e. the luck term in the equation is replaced by 60

100 ). The effort term depends on whether the worker exerts high effort (the

effort term in the equation is replaced by 80 100

) or low effort (the effort term in the equation is replaced by 40

100 ). Thus, increasing effort results in a higher likelihood of promotion.

(a) By how much is Alice’s likelihood of promotion increased by exerting high effort (instead of low effort)?

(b) By how much is Benjamin’s likelihood of promotion increased by exerting high effort (instead of low effort)?

(c) Given the cost of effort, what level of effort should Alice exert?

(d) Given the cost of effort, what level of effort should Benjamin exert?

Note that Alice and Benjamin are NOT competing against each other for promotion. Their likelihoods of promotion are unrelated.

2. A firm offers a worker the choice between a non-monetary benefit that costs the firm $2,000 and a salary increase of $2,000. The tax rate on salary is 15%. The worker is indifferent between this choice if the worker values the benefit at $X. What is the value of X?

3. Your firm is considering offering a new non-monetary benefit, but is not sure how much the employees would value this benefit. What method would you suggest to the firm to determine the value of the benefit to the employees? How would your method get around the incentive employees have to answer benefit value questions strategically?

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.

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Optional Extra Credit Problem (3 points): Please do not discuss this with class- mates. A worker has a current salary of $10,000. This worker is considering some additional training that includes both general and firm-specific human capital. The training costs $5,000. The worker could earn $16,000 at a different firm after the training (i.e. the worker has an outside offer of $16,000 af- ter training). The worker’s productivity after receiving the training is worth $19,000 to the worker’s current firm. The worker is somewhat loyal to the current firm and therefore switching firms would result in the worker experiencing an emotional cost of $1,500. If the worker switches firms, the worker’s current firm could immediately find a replacement worker that would have productivity worth $10,000 for a salary of $10,000.

1. If the worker’s current firm has a “matching offer” policy (where outside offers are matched), would the worker want to invest in the training?

2. If the worker’s current firm has a “no matching offer” policy (where outside offers are not matched), would the worker want to invest in the training?

3. If the worker’s current firm has no policy regarding matching offers, is it likely that the firm and the worker would be able to negotiate a salary that would be acceptable to both (if the worker invests in training)?

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