MACROECONOMIC DYNAMIC MODELS

Introduction. The article is devoted to the description of two macroeconomic models, namely the Keynes and Samuelson-Hicks models, which show how the GDP (gross domestic product) moves to the equilibrium position. Equilibrium GDP occurs when the total amount of output produced (aggregate supply) equals the total amount of output that can be bought (aggregate demand). The basis for determining the equilibrium GDP is the planned aggregate expenditure, which is the monetary equivalent of aggregate demand. According to the theory of Keynes [1, 2], the equilibrium GDP is the volume of production that is equal to the planned total costs. If the GDP exceeds the planned total costs, this indicates the occurrence of overproduction, which is accompanied by an unplanned increase in commodity stocks, which prompts enterprises to reduce GDP to the equilibrium volume. If the GDP is less than the planned total costs, then this is a sign of underproduction, which is accompanied by an unplanned decrease in commodity stocks, which prompts enterprises to increase GDP to the equilibrium volume. A production cycle with a period of one year is natural for the economy, so the paper considers discrete versions of Keynes' models. Purpose. The Keynes and Samuelson-Hicks models have long since become classics and have entered textbooks. Therefore, the author's goal was to carry out a more detailed analysis of Keynes' dynamic model and various scenarios of the movement of GDP towards equilibrium. In the Samuelson-Hicks model, the asymptotic stability of the solution was investigated, which was usually declared, but not proved. Methods. The main results are obtained on the basis of the theory of difference equations [3], as well as general logical and mathematical methods of proving the results. Results. A detailed analysis of the behavior of GDP over time in the Keynesian model is carried out, depending on the initial state, both in conditions of excess demand over supply, and vice versa. For the Samuelson-Hicks model, a complete proof of the asymptotic stability of its solution is proved if the acceleration coefficient is less than unity. Of course, these results are mainly methodological in nature.