A Solvable Time-Inconsistent Principal-Agent Problem

We consider the dynamic contract model with time inconsistency preference of principal-agent problem to study the influence of the time inconsistency preference on the optimal effort and the optimal reward mechanism. We show that when both the principal and the agent arc time-consistent, the optimal effort and the optimal reward arc the decreasing functions of the uncertain factor. And when the agent is time-inconsistent, the impatience of the agent has a negative impact on the optimal contract. The higher the discount rate of the agent is, the lower the efforts provided; agents tend to the timely enjoyment. In addition, when both the principal and the agent are tone-inconsistent, in a special case, their impatience can offset the impact of uncertainty factor on the optimal contract, but, in turn, their impatience will affect the contract.