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In this paper, we use value function iteration and linear interpolation to solve an example of a stochastic, infinite-horizon Ramsey model, which is one kind of dynamic general equilibrium (DGE) model. To obtain an approximation of the policy function’s solution, we pick a grid of capital investments for each period, set the starting value of the value function, build an iterative loop to compute the new value using interpolation, and establish the selection criteria and stop conditions. We model transient shocks to total factor productivity (TFP) and capture the impulsive reactions of consumption, capital, and factor pricing, with the algorithm anticipated to converge in “x” iterations. This concept is helpful and inspiring for assessing financial risk avoidance and dealing with and better comprehending potential shocks.

Keywords: Value Function Iteration, Linear Interpolation, Stochastic Infinite Horizon, Ramsey Model

JEL: C35, C51, C61

As the world’s largest emitter of greenhouse gases, China is actively exploring the best way to address climate change. 2021 marks the official opening of China’s carbon emission trading market. In order to investigate the evolutionary game relationship between carbon emission reduction by enterprises and carbon regulation by the government under the carbon emission rights auction, the article constructs an evolutionary game model between enterprises and the government, and analyzes the influence of carbon penalty, carbon subsidy and carbon emission rights revenue on the behavior of the government and enterprises. The results of the model show that the government’s active carbon regulation measures can effectively promote the energy saving and emission reduction of enterprises, and the carbon emission trading market can play the role of market regulation to promote the goal of “double carbon” and the coordinated development of the region.

Keywords: Carbon credits auction; carbon reduction; evolutionary game; numerical simulation

The relationship between public expenditure and economic growth is obvious, but the direction of the causality is not clear. This paper analyses the relative impact of the different components of public expenditure on economic growth. Specifically, this paper examines whether the level of government expenditure is managed to accelerate economic growth or whether the government expenditure is used excessively which may hurt the domestic economy because of increased taxes and/or high government borrowing. The vector error correction method is applied to the annual time series data for India from 1983 to 2020 for testing the long and short-run causality. The pair-wise Granger causality test indicates one-way causality moving from gross domestic product to total government expenditure and from gross domestic product to government revenue showing that the growth of the economy leads to an increase in both government revenue and expenditure. The estimated error correction coefficient is significantly negative indicating that the speed of adjustment between the shortrun dynamics and the long-run equilibrium is about 0.03%. The results show a stable long-run relationship between public expenditure and economic growth.

The people’s increasing attention to culture and education has caused vicious competition in the education and training industry, and false propaganda has disturbed the market order, and the education and training market is facing the choice of entry and exit. Based on the evolutionary game model, this paper explores the best strategic choice of the three parties involved in the education market by constructing an evolutionary game model of the strategic behavior choice of the regulator, education institutions and students, and using MATLAB simulation analysis to explore the direction of healthy, orderly and scientific development of the education market. The results show that the stronger the supervisory authority rewards (or punishes) the education and training institutions that adopt benign competition with credibility and credit evaluation, the more the education and training institutions tend to choose benign competition. The smaller the extra loss of training for students, the more inclined they are to choose to enroll. The higher the benefit of benign competition (or the cost of vicious competition) for teaching and training institutions, the more inclined they are to choose benign competition.

Keywords: Education and training industry; replicator dynamics; three-part evolutionary game; numerical simulation

This paper presents an analytical approach for estimation of maximum value of profit of an enterprise with account several types of products. Profit maximization gives a possibility to take into account changing of price of products on the market. As an example we consider estimation of profit for the accounting of three types of products. But the introduced approach gives a possibility to change number of products, if necessary.

Keywords: maximization of profit; accounting of changing of price.