A martingale approach to the question of fiscal stimulus.

Democrats in the United States argue that government spending can be used to "grease the wheels" of the economy to create wealth and to increase employment; Republicans contend that government spending is wasteful and discourages investment, thereby increasing unemployment. 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. 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.