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 . Further, we prove a few interesting mathematical properties of our solution, providing deeper insight into this important politico-economic debate and illustrating how the fiscal stimulus from the government may affect the profit-taking behavior of firms in the private sector .
After 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 ; rigorous verification proofs for its optimality are provided. We proceed to prove that government loans increase the expected net value of a company. We also examine the consequences of different profit-taking behavior of firms in the private sector .