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:<math>g^{\prime }(a_{1}^{*})=\beta \cdot \frac{h_{\varepsilon }}{h_{1}+h_{\varepsilon }}\in (0,1)\,</math>
As <math>g^{\prime }(a_{1}^{*}) < 1\,</math>, it must be the case that <math>a_{1}^{*} < a^({FB}\,</math>. Likewise if the agent lives for <math>T\,</math> periods then <math>a_{T}^{*} = 0\,</math>, so effort declines from the first period onwards.
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