Before revision:  Faced with this paradox, one might hope that a rigorous mathematical approach might help determine which is the truth ] .
After revision:  Faced with this paradox, one might hope that a rigorous mathematical approach might help determine which is the truth ]. 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 .