Macroeconomic Modeling of the Relationship Between Price and Industry Proportions
Authors:   Central Economics and Mathematics Institute of the Russian Academy of Sciences (Moscow, Russian Federation), Grebennikov Valery G. 
Published: December 2021

The article aims to examine one of the most interesting, in the authors’ opinion, applications of the two-sector model of social technology to identify the relationship between the trajectories of the relative price and the relative share of the product in the total output based on the concept of Pareto optimal, or “efficient”, trajectories of economic growth (i.e. trajectories, each point of which belongs to the surface of production opportunities). Within the framework of this concept, the ratio of prices of individual products corresponds to the marginal rates of these products’ substitution. The rates depend on the product (sectoral) structure of GDP, on the one hand, and on the available labor resources and production assets, on the other. The relationship between the investment component of the output and the growth of funds gives rise to a family of efficient trajectories, in the sense indicated above. Each of the trajectories is characterized by the joint dynamics of industry and price proportions; therefore, the main problem of the study is to examine the general properties of such trajectories. The main feature of the model under consideration is the nonlinear production functions of industries. Even the simplest Cobb–Douglas specification generates the dynamics of the main variables of the model described by a nonlinear differential equation of the second order, which cannot be integrated in general form. Therefore, the analysis of the properties of effective trajectories (at least when specific parameters of trajectories are of interest, and not just general criteria for existence and stability) required the development of a program of numerical experiments on a computer, designed for a fairly extensive test of hypotheses and the convenience of presenting and analyzing the results. To begin with, a variant of the twosector model was chosen, in the future it is planned to expand it to a significantly larger number of sectors. The properties of effective trajectories with constant parameters were analyzed: the marginal rate of product substitution (constant price ratio), constant marginal rate of resource substitution (constant ratio of factor payment rates), constant ratio of net output of industries, constant share of investments in GDP, etc. General conclusions are obtained about the conditions for the convergence of such “iso-trajectories” to trajectories with a constant GDP growth rate and about the characteristics of stationary trajectories. Of greatest interest, in the author’s opinion, is the conclusion that the existence and stability of stationary trajectories is determined by the intersectoral ratio of the elasticities of the output with respect to the funds of the sectors under consideration: for an industry producing investment products, this parameter should be of lesser importance. The derived equation, which can be interpreted as an expression of a trend that determines the form of the relationship between the proportions of industry outputs and prices in the economy, opens the way to a meaningful macroeconomic analysis of the relationships between these proportions, depending on the configuration of the parameters of social technology Ai, αi, aij, B and scenarios of their changes over time.