A Simple Model for Targeting Industrial Investments with Subsidies and Taxes

Dmitry B. Rokhlin and Gennady A. Ougolnitsky ()
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Dmitry B. Rokhlin: Regional Scientific and Educational Mathematical Center, Southern Federal University, 344090 Rostov-on-Don, Russia
Gennady A. Ougolnitsky: Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 344090 Rostov-on-Don, Russia

Mathematics, 2024, vol. 12, issue 6, 1-18

Abstract: We consider an investor, whose capital is divided into an industrial investment x t and cash y t , and satisfy a nonlinear deterministic dynamical system. The investor fixes fractions of capital to be invested, withdrawn, and consumed, and also the production factor parameter. The government fixes a subsidy fraction for industrial investments and a tax fraction for the capital outflow. We study a Stackelberg game, corresponding to the asymptotically stable equilibrium ( x ∗ , y ∗ ) of the mentioned dynamical system. In this game, the government (the leader) uses subsidies to make incentives for the investor (the follower) to maintain the desired level of x ∗ , and uses taxes to achieve this with the minimal cost. The investor’s aim is to maximize the difference between the consumption and the price of the production factor at equilibrium. We present an explicit analytical solution of the specified Stackelberg game. Based on this solution, we introduce the notion of a fair industrial investment level, which is costless for the government, and show that it can produce realistic results using a case study of water production in Lahore.

Keywords: taxes; subsidies; industrial investment level; equilibrium; Stackelberg game (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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