This paper deals with the problems of stabilizing economic growth using traditional macroeconomic strategies. The goal taken implies a large-scale use of the machinery of the qualitative theory of discrete economic dynamics. A set of economic and mathematical models that take into consideration the specifics of macroeconomic equilibrium in view of neo-Keynesian economics is proposed. It is essential to analyze the residual effect caused by the “dynamic memory” of all previous values in relation to the present moment in time in the investment policy and the consumption structure. When building dynamic models of economic growth of Gross Domestic Product, functional equations of a specific type, such as Volterra difference equations, were obtained. Accordingly, for each of the above functional equations studied, there received a number of inequalities that determine the domains of parametric stability of the equilibrium. Structural constraints of the basic parameters of the multiplier-accelerator model, which can have a significant impact on the distribution of consumption and investment to ensure sustainable growth of national income, are formulated in an explicit form. There indicated conditions for constraining such parameters as the accelerator capacity and marginal propensity to save, which should be taken into account when developing economic and mathematical models for the purposes of forecasting and managing national macroeconomic policies. Graphic illustrations of the obtained solutions to the corresponding difference equations of the national income behavior are presented.