assignmentnine

assignmentnine - Economics 206 Spring 2007(Prof G Loury...

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Economics 206 Spring 2007 (Prof. G. Loury) Assignment 8: The Principal-Agent Problem (1) A principal needs to contract with an agent to get a risky project done. The project can either succeed or fail. If it succeeds it generates output with gross value V> 0 . If it fails, it’s output is worth 0 . The probability of success depends on the e f ort exerted by the agent. Let e 0 denote the agent’s e f ort, and let p ( e ) (0 , 1) be the probability of success given level of e f ort e . Assume that p ( e ) is strictly increasing, strictly concave, and satis f es: p (0) = 0 ; p 0 ( e ) →∞ as e 0 ; p 0 ( e ) 0 as e →∞ ,and p ( e ) 1 as e →∞ .E f ort of the agent is assumed not to be observable by the principal. A contract is simply a pair of numbers ( w 0 ,w 1 ) specifying what the principal pays the agent in the event of the project’s success ( w 1 ) or failure ( w 0 ). The principal is risk π neutral and seeks to maximize the expected payo f from the project, net of payments to the agent. The agent’s preferences are given by:
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assignmentnine - Economics 206 Spring 2007(Prof G Loury...

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