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Gibbons Murphy (1992) - Optimal Incentive Contracts In The Presence Of Career Concerns (view source)
Revision as of 22:03, 27 April 2010
, 22:03, 27 April 2010no edit summary
Substituting in our last result we have:
:<math>-\mathbb{E}\left[ e^{-r\left[ c_{1}+b_{1}(\eta +a_{1}+\varepsilon_{1})-g(a_{1})+\beta \left( (1-b_{2}^{*})\left[ \frac{h_{1}}{h_{1}+h_{\varepsilon }}\cdot m_{1}+\frac{h_{\varepsilon }}{h_{1}+h_{\varepsilon }}\cdot (\eta +a_{1}+\varepsilon _varepsilon_{1}-a_{1}^{*})\right]+b_{2}^{*}(\eta +a_{2}^{*}(b_{2}^{*})+\varepsilon_{2})-g(a_{2}^{*}(b_{2}^{*}))\right) \right] }\right\,</math>
Which can be written in certainty equivalent form as:
and so:
:<math>b_{1} =\frac{1}{1+r(\frac{1}{h_{1}}+\frac{1}{h_{\varepsilon }})g^{\prime\prime }(a_{1}^{*}(b_{2}^{*}))} \label{b1} -\beta (1-b_{2}^{*})\frac{h_{\varepsilon }}{h_{1}+h_{\varepsilon }}-\frac{r\beta b_{2}^{*}\frac{1}{h_{1}}g^{\prime \prime }(a_{1}^{*}(b_{2}^{*}))}{1+r(\frac{1}{h_{1}}+\frac{1}{h_{\varepsilon }})g^{\prime \prime}(a_{1}^{*}(b_{2}^{*}))}\,</math>
