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Moral Hazard Model

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Moral Hazard Model. Only Question #1. See attached file for full problem description.

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Solution Summary

The probabilities of low and high output are considered.

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Please see the attached file.

Question 1

Part a
In this case, the agent will be paid 10 if output is low and 15 if output is high. Let's see in which case the expected utility is higher:

Working hard (Cost = 10)
In this case, the expected utility is:

Shirking (Cost = 0)
In this case, the expected utility is:

Clearly, the agent will choose to shirk.

Part b
In order for the agent to work hard, the expected utility of working hard should be higher than the expected utility of shirking. Given s and b, the expected utility of working hard would be:

On the other hand, the expected utility of shirking would be:

Therefore, in order for the agent to work hard, the following constraint (the incentive constraint) must be satisfied:

Part c
Given that he works hard, he would only accept the contract if his expected utility is higher than his alternative utility, which we're told it's 50. Therefore, the participation constraint (PC) is:

Part d
Clearly, both constraints must hold with equality; otherwise, the principal could ...

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