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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 The investor fixes fractions of capital to be invested, withdrawn, and consumed, and also the production factor parameter.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. [ABSTRACT FROM AUTHOR]

We consider an investor, whose capital is divided into an industrial investment xt and cash yt, 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 The investor fixes fractions of capital to be invested, withdrawn, and consumed, and also the production factor parameter.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.

• The development of financial subsidies and digital finance can have a positive impact on the level of industrial investment. • Financial subsidies and digital finance can promote the level of industrial investment by easing the financial constraints of enterprises. • Enterprises should ensure the feasibility and profitability of investment projects based on the market environment they are in, in order to better formulate reasonable investment strategies. This study examined the impact of digital finance and financial subsidies on enterprises' industrial investment based on data from China A-share listed companies in Shanghai and Shenzhen from 2011 to 2020. Results show that the development of financial subsidies and digital finance positively impact industrial investment, further easing the financial constraints of enterprises. Based on results, suggestions such as rational resource usage and a clear investment direction are made. [ABSTRACT FROM AUTHOR]