Before revision:  These arguments cannot both be correct, but both arguments seem meritorious. Faced with this paradox, one might hope that a rigorous mathematical approach might help determine the truth. We address this economic question of fiscal stimulus as a new optimal control problem generalizing the model of Dutta and Radner 1999 . We find  that there exists an optimal strategy and provide rigorous verification proof for the optimality .
After revision:  Today, in 2020, we find ourselves in the midst of another crisis where government spending and fiscal stimulus is again being considered as a solution. In the present paper, we address this question by formulating an optimal control problem generalizing the model of Dutta and Radner 1999 . We find that there exists an optimal strategy and provide rigorous verification proof for the optimality .