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# finalansw - EC 206 Microeconomics II Final Examination May...

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EC 206 Microeconomics II: Final Examination May 4, 2007 (Professor Glenn C. Loury) Answers 1. { 50 points } (A Principal-Agent Problem) The value of the project is the maximal net surplus that can be realized by exerting costly effort which raises the chance of success. Thus, the value K is given by: K = Max e o { p ( e ) V e } , which implies p ( e ) V = 1 = V d de ( e a + e ) = aV ( a + e ) 2 . That is, that the marginal cost of effort [=1] equals its marginal benefit of effort [= p ( e ) V ]. Solving for the first-best effort level, e , we have: e = ( aV ) 1 2 a. And, substituting, we find that the value of the project is: K = p ( e ) V e = V ( ( aV ) 1 2 a ( aV ) 1 2 ) [( aV ) 1 2 a ] = V + a 2( aV ) 1 2 = [ V 1 2 a 1 2 ] 2 . The manager is assumed to be risk-neutral, with a utility function as follows: u ( w, e ) = w e. Moreover, the manager’s outside option is zero ( u 0 = 0). 1. a. When the manager’s effort is observed, the agent can be exactly compensated for the cost of the principal’s desired level of effort: w ( e ) = e . If any different level of effort earns zero, then the agent will have an incentive to accept this contract and to exert the desired level of effort: w ( e ) = e and w ( e ) = 0 , e negationslash = e . (a) When the project’s outcome is observed but not the manager’s effort, and if the agent is risk neutral, then perfect effort incentives can be maintained by transfering ownership of the project from the principal to the agent for a price equal to the value of the project, K . The contract ( w 0 , w 1 ) which accomplishes this transfer causes the agent’s compensation to vary directly and fully with variations in output: w 1 = V K and w 0 = K . This contract also is just acceptable to the agent, and the principal’s net return, K , is independent of the outcome. This transfer is leads to efficiency only because the agent and principal are both

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finalansw - EC 206 Microeconomics II Final Examination May...

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