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Consider the following Principal-agent moral hazard problem. The agent's utility function is 2/w – e;, where effort is either e, = 2e or e, = 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 p, = 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 x2 = 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 e2?

Consider the following Principal-agent moral hazard problem. The agent's utility function is 2/w – e;, where effort is either e, = 2e or e, = 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 p, = 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 x2 = 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 e2?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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