The rationale for the use of response functions in formalizing the tasks of economic management of the region

The paper presents studies of linear models of economic dynamics of the Neumann-Gale type, taking into account their possible stationarity, presents an analysis of existing classification approaches to the concept of optimality, presents their advantages and comparative characteristics, it is noted that the first type model open connects the concept of optimality with discounted maximization total utility. The first considers a closed system, the technological description of which includes the reproduction of all the resources necessary for development, including labor. Such a system has no external goals; its natural end in itself is development at the maximum pace. This is the most abstract and idealized scheme, but on the other hand it was it that made it possible to develop such fundamental concepts as equilibrium, a ray of (Neumann) balanced growth. Later, the apparatus of the closed model was replenished with the concepts of “direct and inverse Bellman operators”, “effective functional” (“potential”) of the model, etc. The second approach involves explicit accounting for consumption. Here the description becomes open, consumption is derived from the "technology" and described using the utility function. A new approach to the concept of “optimal development strategy” is proposed, a detailed analysis of the corresponding model is given. The article consists of three sections. 1 - staging part; 2 - analysis of the model with illustrative examples; 3 - conjugate (dual) model. The last section contains the main result on the connection of the optimal trajectories of the direct and dual problems. The paper provides an overview of literary sources in the subject area, as well as an economic interpretation of the results.