A firm’s board of directors wants to maximize its profits. If the firm’s manager puts in a high effort, the firm gets a high profit of 9 with probability 80%, but if the manager puts in a low effort, the firm gets a low profit of 4 with probability 80%.   The utility functions of both the board of directors and the manager are identical and are simply u(b)=b. High effort for the manager costs 2. The manager has an outside wage of 1.                 Calculate the optimal wage schedule under high and low realized profits.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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  1. A firm’s board of directors wants to maximize its profits. If the firm’s manager puts in a high effort, the firm gets a high profit of 9 with probability 80%, but if the manager puts in a low effort, the firm gets a low profit of 4 with probability 80%.

 

The utility functions of both the board of directors and the manager are identical and are simply u(b)=b. High effort for the manager costs 2. The manager has an outside wage of 1.

 

              Calculate the optimal wage schedule under high and low realized profits.

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