Before revision:  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:  We address this economic question of fiscal stimulus as a new optimal control problem generalizing the model of Dutta and Radner 1999 Radner that there exists an optimal strategy and provide rigorous verification proof for the optimality .