Exact(35)
Solving the optimization problem to determine the optimal effort level, (a^dagger), and the optimal incentive rate, (v^dagger), yields begin{aligned} a^dagger=v^dagger quadtext {and}quad v^dagger=frac{1}{1+alpha sigma ^2}.
Replacing (Pi _tau) and (CE_tau (cdot )) for (Pi) and (CE cdot )) in the original optimization problem, (P), and solving it for the optimal effort decision and the optimal incentive rate yields begin{aligned} a^dagger= 1-tau _w)v^da^dagger= 1-tauand}quad v^dagger=frac{1-tau _w}{(1-tau _c+ktau _c)(1+alpha sigma ^2)}.
In addition, corporate income taxes influence the optimal incentive rate.
Thus, in the first step, we determine sequentially optimal incentive rates under both accounting systems.
The results are consistent with warm glow giving and have implications for optimal incentive design.
Further, knowledge complementary effects and other relevant factors on the optimal incentive coefficient are analyzed.
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