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Holmstrom (1999) - Managerial Incentive Problems (view source)
Revision as of 21:16, 6 April 2010
, 21:16, 6 April 2010no edit summary
Utility of the Manager is given by:
<math>U(w,a)=\sum_{t=1}^{\infty }\beta ^{t-1}[w_{t}-g(a_{t})]\,<\/math>
where: <math>\beta\,<\/math> is the discount factor, <math>w_{t}\,<\/math> are wages, <math>g(\cdot)\,<\/math> is the cost of effort, and <math>a_{t}\,<\/math> is the effort.
Output is given by:
<math>y_{t}=\eta + a_{t} +\varepsilon_{t}\,<\/math>
where <math>\varepsilon\,<\/math> is noise and <math>\eta\,<\/math> is the ability of the manager, such that <math>\varepsilon _{t}\sim N(0,\frac{1}{h_{\varepsilon }})\,<\/math>, and <math>\eta \sim N(m_{1},\frac{1}{h_{1}})\,<\/math>.
The market will set wages:
<math>w_{t}(y^{t-1})=E[y_{t}|y^{t-1}]=E[\eta |y^{t-1}]+a_{t}(y^{t-1})\,<\/math>
The manager will best respond by choice an effort sequence:
<math>\underset{\{a_{t}(y^{t-1})\}_{t=1}^{\infty }}{\max }\;\sum_{t=1}^{\infty}\beta ^{t-1}[Ew_{t}(y^{t-1})-Eg(a_{t}(y^{t-1}))]\,<\/math>
===Two Period Model===
Wages are paid in advance so in the second period the agent exerts no effort. In equilbrium <math>a_{1}^{*}\,<\/math> is correctly anticipated.
