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Holmstrom (1999) - Managerial Incentive Problems (view source)
Revision as of 20:59, 27 April 2010
, 20:59, 27 April 2010→Infinite Horizon with varying ability
So must conclude that the variance tends to a steady state and not to zero. This in turn leads to steady state effort, which we can solve for by equating the marginal benefit to the marginal cost of a change:
:<math>g^{\prime }(a^{*}) &=&\beta (1-\mu ^{*})+\beta ^{2}\mu ^{*}(1-\mu^{*})+\beta ^{3}(\mu ^{*})^{2}(1-\mu ^{*})+\cdot \cdot \cdot=\frac{\beta (1-\mu ^{*})}{1-\beta \mu ^{*}}\,</math>
Which in turn leads to Holmstrom's proposition 1 that the stationary effort is <math>a^{*}\leq a^{FB}\,</math> and only equal to first best if <math>\beta =1,\,\frac{1}{h_{\varepsilon }}>0\,</math>, and <math>$\frac{1}{h_{\delta }}>0\,</math>
