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Consider the following Principal-agent moral hazard problem. The agent's utility function is 2vw – e;, where effort is either e, = 2e or ez = e for some parameter e>0. The agent has a reservation utility ū = 10. If the agent uses high effort e, the probability of state 2 is p1 = 0.2 and if low effort e, is used the probability of state 2 is p2 = 0.6. The principal, who is risk neutral, earns x, = 200 in state 1 and x, = 50 in state 2. Work out the optimal contracts for low and high effort as a function of the parameter e. For which values of e does the principal prefer e, and for which values of e does the principal prefer e,?

Consider the following Principal-agent moral hazard problem. The agent's utility function is 2vw – e;, where effort is either e, = 2e or ez = e for some parameter e>0. The agent has a reservation utility ū = 10. If the agent uses high effort e, the probability of state 2 is p1 = 0.2 and if low effort e, is used the probability of state 2 is p2 = 0.6. The principal, who is risk neutral, earns x, = 200 in state 1 and x, = 50 in state 2. Work out the optimal contracts for low and high effort as a function of the parameter e. For which values of e does the principal prefer e, and for which values of e does the principal prefer e,?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider the following Principal-agent moral hazard problem. The agent's utility function is 2vw – e;, where effort is either e, = 2e or ez = e for some parameter e>0. The agent has a reservation utility ū = 10. If the agent uses high effort e, the probability of state 2 is p1 = 0.2 and if low effort e, is used the probability of state 2 is p2 = 0.6. The principal, who is risk neutral, earns x, = 200 in state 1 and x, = 50 in state 2. Work out the optimal contracts for low and high effort as a function of the parameter e. For which values of e does the principal prefer e, and for which values of e does the principal prefer e,?
Transcribed Image Text:Consider the following Principal-agent moral hazard problem. The agent's utility function is 2vw – e;, where effort is either e, = 2e or ez = e for some parameter e>0. The agent has a reservation utility ū = 10. If the agent uses high effort e, the probability of state 2 is p1 = 0.2 and if low effort e, is used the probability of state 2 is p2 = 0.6. The principal, who is risk neutral, earns x, = 200 in state 1 and x, = 50 in state 2. Work out the optimal contracts for low and high effort as a function of the parameter e. For which values of e does the principal prefer e, and for which values of e does the principal prefer e,?
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