20. The effort level E of an employee cannot be observed by the employer but it is known that it

leads to the employer’s additional profit of 8E with probability 0.2 and to zero additional profit

with the complementary probability.

a. Discuss the type of interaction, described in this question, and the resulting problems

from the managerial point of view.

b. Design a wage-bonus package (w,b) for this employee, which maximizes the expected

additional profit of the employer, if the expected utility function of the employee takes

the form u = w + b*1.6E – E*E – 0.2. Note that the bonus b specifies the proportion of

the additional profit that accrues to the employer. The wage w is paid independently of

the amount of the additional profit.

c. Given the optimal wage-bonus package, compute this employees’ effort, expected payoff

and employer’s profit.

d. Draw a game tree for the employer-employee game in parts a-c.

leads to the employer’s additional profit of 8E with probability 0.2 and to zero additional profit

with the complementary probability.

a. Discuss the type of interaction, described in this question, and the resulting problems

from the managerial point of view.

b. Design a wage-bonus package (w,b) for this employee, which maximizes the expected

additional profit of the employer, if the expected utility function of the employee takes

the form u = w + b*1.6E – E*E – 0.2. Note that the bonus b specifies the proportion of

the additional profit that accrues to the employer. The wage w is paid independently of

the amount of the additional profit.

c. Given the optimal wage-bonus package, compute this employees’ effort, expected payoff

and employer’s profit.

d. Draw a game tree for the employer-employee game in parts a-c.

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