Abstract: This paper discusses the macroeconomic model The Samuelson-Hicks (defined by a system of linear difference equations of the first and second order with constant coefficients). In this case, we study the case when the discriminant of the characteristic equation corresponding to the equation of gross output movement is zero, the corresponding characteristic equation has a single real root of multiplicity two. It is also assumed, to simplify the analysis, that the initial gross output is zero, and the base consumption for each time period over the entire planning horizon is unchanged. The use of methods for solving linear difference equations, as well as differential and integral calculus, allowed the authors to obtain a number of the following scientifically based results: analytical estimates from above for gross output and normalized gross output were found; an alternative derivation of the normalized gross output derivative from the auxiliary parameter expressed in terms of the acceleration factor – one of the parameters of the model under study. In addition, as additional results, algebraic and combinatorial identities with mathematical meaning are obtained. The author's approach used in this article is easy to apply in the same way to two other macroeconomic indicators of the above mathematical model-investment and consumption (if you set the task of minimizing them in a fixed period or at a given planning horizon, as was done for gross output in one of the previous articles devoted to the study of its optimization properties). These results can be useful for both theoretical mathematicians and specialists in the field of mathematical modeling of economic processes.
Index terms: model of Samuelson-Hicks, normalized of the issues, analytical assessments from the top.

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