Econ808H3.02

Econ808H3.02 - The Ohio State University Department of...

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The Ohio State University Department of Economics Econ 808–Problem Set #3 due Thursday, May 2 Spring 2002 Levin and Peck Questions 1 and 2 relate to the principal-agent problem with hidden action presented in class and taken from Mas-Colell chapter 14B. Suppose the parameters are as follows: = 0, π ! [0,1], u f( π " e H ) = 1 for all π ,f ( π " e L ) = 2(1 - π ), There are two possible effort choices, e = e H or e = e L , where e H > e L . The project yields a random payoff, which depends on the effort choice, e, given by the density function f( π " e) over the support [0,1]. 1. Consider the first-best contract, in which effort is observable. Suppose the Bernoulli utility function is given by v(w,e) = log(w-g(e)), where g(e L ) = 1/4 and g(e H ) = 1/3. The contract specifies an effort level, e = e H or e = e L , and a wage profile w( π ) to solve: max ( ( )) ( ) log( ( ) ( )) ( ) . () w wf e d wg e f e d π ππ 0 1 0 1 0 −= subject to: (a) Derive the first order conditions that characterize the optimal wage profile for effort level e.
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Econ808H3.02 - The Ohio State University Department of...

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