A worker can choose high (H) or low (L) effort. If the worker chooses high effor

Question

A worker can choose high (H) or low (L) effort. If the worker chooses high effort, she incurs a personal cost of 2. In this case, output is high with probability one. If the worker chooses low effort, she incurs a personal cost of 0. In this case, output is high with probability 1 and low with probability 1 .

When output is high, the firm receives revenue of and zero otherwise.
a. Under complete information, what is the lowest bonus for high effort that the firm can

pay to induce the worker to exert high effort? (1 mark)
b. When there is complete information, under what condition on would the firm find

it worthwhile to pay this bonus? (2 marks)
c. When output is observable, but effort is NOT, what is the lowest bonus for high output

that the firm can pay to induce the worker to exert high effort? (3 marks)
d. Under what condition on would the firm find it worthwhile to pay this bonus under

asymmetric information? (3 marks)
e. Briefly, and in words, explain why a higher bonus has to be paid to induce high effort

under asymmetric information. (2 marks)

Explanation / Answer

a. Lowest Bonus = 2

As personal cost to put hogh efforts is 2, so worker will only put high efforts if he gets atleast equal to the personal cost incured to put high efforts, hence minimum bonus is 2.

b. >= 2

As revenue in case of low effort is 0, so reveune in high effort should be atleast equal to cost incurred to induce worker put high effort,

c. Since only output is observable

Benefit ( Bonus - personal cost) should be higher in case of high effort then low effort to induce worker to put high effort.

B - 2 > 0.5*2 + 0.5*0 - 0

B - 2 >= 1

B >= 3

d.

So,    >= 2

Cost put in to induce high effort.

e.

Since under assymetric information, agent cann't see the worker's action , so worker has an incentive to put low effort and earn the wage for high output as agwnt can only see the output,

hence agent should provide the wage which is higher then the given case and hence higher then in case of complete information where wages were provided according to personal cost or reservation utility of the worker.

If you don;t understand anything then comment, I'ill revert back on the same. )

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