THEORETICAL PARAMETRIC ANALYSIS OF THE ISSUES IN THE MODEL OF SAMUELSON-HICKS
This article discusses the economic and mathematical The Samuelson-Hicks model, describing the dynamic changes in macroeconomic indicators such as gross output, consumption and investment in the form of a system of three linear difference equations. Application of methods of mathematical analysis allows to solve the following optimization problem: to determine such values of parameters of the acceleration factor and propensity to consumption, which maximize gross output in a fixed period of time. When the discriminant of the characteristic equation corresponding to the difference equation of dynamics of gross output is equal to zero the variant is investigated. Solving the general problem of optimization of finding the values of the above parameters, when the gross output is maximal on some planning horizon, it is possible to find its explicit representation. In addition, the analysis of normalized gross output (independent of the basic consumption parameter) provided a number of useful estimates, as well as further confirmation of some ratios obtained in one of the earlier articles devoted to the study of gross output in the above model. As a consequence the expansions for some fractional-rational and polynomial functions from the auxiliary parameter are found (expressed through the parameter of propensity to consumption and had an independent algebraic sense).