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Fiscal stimulus as an optimal control problem

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  • Philip A. Ernst
  • Michael B. Imerman
  • Larry Shepp
  • Quan Zhou

Abstract

During the Great Recession, Democrats in the United States argued that government spending could be utilized to "grease the wheels" of the economy in order to create wealth and to increase employment; Republicans, on the other hand, contended that government spending is wasteful and discouraged investment, thereby increasing unemployment. 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 Radner & Shepp (1996). The model allows for the company to borrow continuously from the government. We prove 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 behaviors among firms who receive fiscal stimulus.

Suggested Citation

  • Philip A. Ernst & Michael B. Imerman & Larry Shepp & Quan Zhou, 2014. "Fiscal stimulus as an optimal control problem," Papers 1410.6084, arXiv.org, revised Apr 2021.
    • Handle: RePEc:arx:papers:1410.6084
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    References listed on IDEAS

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    1. Radner, Roy & Shepp, Larry, 1996. "Risk vs. profit potential: A model for corporate strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 20(8), pages 1373-1393, August.
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