Information for questions 21 and 22: A worker in a firm can choose one of two effort levels, e € {1, 2}. • If the worker chooses low effort, e = 1, then the firm generates a revenue of 9 with probability pi = 1/6. With probability 1 – P = 5/6, the firm's revenue is just 0. • If the worker chooses high effort, e = 2, then the firm generates a revenue of 9 with probability p2 = 5/6. With probability 1 – p2 = 1/6, the firm's revenue is just 0. The firm offers a constant wage (that is, there is no bonus for performance). The utility of worker if be accents the joh offer given the chosen offort lovel end the wege is

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Chapter1: Making Economics Decisions
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Information for questions 21 and 22: A worker in a firm can choose one of two
effort levels, e E {1,2}.
• If the worker chooses low effort, e = 1, then the firm generates a revenue of 9 with
probability p1 = 1/6. With probability 1– P1 = 5/6, the firm's revenue is just 0.
• If the worker chooses high effort, e = 2, then the firm generates a revenue of 9
with probability p2 = 5/6. With probability 1 – P2 = 1/6, the firm's revenue is
just 0.
The firm offers a constant wage (that is, there is no bonus for performance). The utility
of a worker if he accepts the job offer, given the chosen effort level and the wage, is
U(e, w) = 2w – e?. There is the option of not accepting the job, which gives the worker
a utility level of 0. The firm maximizes expected profits (that is, it is risk neutral)
21. Suppose that the firm can observe the effort chosen by the worker and specify a desired
level of effort in the contract (such that, if the worker accepts the job but does not put
in the required effort level, the worker earns no income). Calculate the wage offered
divided by the expected revenue of the firm.
(a) 4/3
(b) 4/15
(c) 1/15
(d) 8/15
(e) 1/3
Solution: b
22. Suppose now that the firm CANNOT observe the effort chosen by the worker. Calculate
the wage offered divided by the expected revenue of the firm.
(a) 1/3
11
(b) 4/15
(c) 1/15
(d) 4/3
(e) The firm does not try to hire the worker in this case.
Solution: a
Transcribed Image Text:Information for questions 21 and 22: A worker in a firm can choose one of two effort levels, e E {1,2}. • If the worker chooses low effort, e = 1, then the firm generates a revenue of 9 with probability p1 = 1/6. With probability 1– P1 = 5/6, the firm's revenue is just 0. • If the worker chooses high effort, e = 2, then the firm generates a revenue of 9 with probability p2 = 5/6. With probability 1 – P2 = 1/6, the firm's revenue is just 0. The firm offers a constant wage (that is, there is no bonus for performance). The utility of a worker if he accepts the job offer, given the chosen effort level and the wage, is U(e, w) = 2w – e?. There is the option of not accepting the job, which gives the worker a utility level of 0. The firm maximizes expected profits (that is, it is risk neutral) 21. Suppose that the firm can observe the effort chosen by the worker and specify a desired level of effort in the contract (such that, if the worker accepts the job but does not put in the required effort level, the worker earns no income). Calculate the wage offered divided by the expected revenue of the firm. (a) 4/3 (b) 4/15 (c) 1/15 (d) 8/15 (e) 1/3 Solution: b 22. Suppose now that the firm CANNOT observe the effort chosen by the worker. Calculate the wage offered divided by the expected revenue of the firm. (a) 1/3 11 (b) 4/15 (c) 1/15 (d) 4/3 (e) The firm does not try to hire the worker in this case. Solution: a
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