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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 eFort 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 eFort [=1] equals its marginal bene±t of eFort [= p ( e ) V ]. Solving for the ±rst-best eFort level, e , we have: e = ( aV ) 1 2 a. And, substituting, we ±nd 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 eFort is observed, the agent can be exactly compensated for the cost of the principal’s desired level of eFort: w ( e ) = e . If any diFerent level of eFort earns zero, then the agent will have an incentive to accept this contract and to exert the desired level of eFort: w ( e ) = e and w ( e ) = 0 ,e n = e . (a) When the project’s outcome is observed but not the manager’s eFort, and if the agent is risk neutral, then perfect eFort 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 e²ciency only because the agent and principal are both
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finalansw - EC 206 Microeconomics II Final Examination May...

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