Vol 59, No 2 (2023)

In recent years, based on the traditional theory of value — the labor theory of value and the theory of surplus value, as well as the hypothesis of Jevons, Tesla and Foley, — Chinese and Russian scholars have further adopted the mathematical paradigm of theoretical mechanics for reference to establish a mathematical model system for economics, which is called the new theory of value. Compatible with the traditional theory of value, the new theory of value puts forwardthat the value depends on the force of labor expended in the process of commodity production. While the value appreciation depends on the labor gravitational force generated by the improving dexterity of workmen. That is to say, during the process of production, constant capital and variable capital as kinetic energy and potential energy of value, convert into each other under the value conservation theorem, playing a dominate role in generating value and surplus value of products. In addition, the law of diminishing marginal utility is not an axiom, but a special economic law under unbalanced supply and demand. Obviously, these theoretical conclusions are of great significance, which not only make the traditional theory of value a self-consistent logical system, but also complete the new theory of value by absorbing the rational components from both the classical economics based on the labor theory of value and the theory of surplus value, and neoclassical economics based on the law of diminishing marginal utility. In this paper, we will analyze this problem by investigating the origin of the law of diminishing marginal utility.

The dynamic input-output balance model in the form of a system of differential equations, being digitized by the already published author's methodology, allows solving a wide range of problems of static structural stability of economic systems. Structural dynamics can be optimized by including any variable parameters in the vector and the limit of all model elements. In this paper, inter-sectoral inertias are chosen, and a method is proposed that uses a vector of parameters of an arbitrary (allowed by the model itself) length at the step of the search process. This distinguishes the proposed method from existing ones, making it unique. The uniqueness specified here lies in the removal of the so-called “curse of dimensionality” inherent in the classical optimization problems (numerical search problems) using methods from the coordinate-wise descent to the rich Newtonian-type tools. In this sense, the method is a competitor to machine learning-based optimization of artificial neural networks. At the same time, it does not matter how exactly the task is formalized: it should highlight the target indicators and the vector of variable parameters. It is possible to define and solve many optimization problems by changing the content of the vector of variable parameters according to the corresponding plan of the computational experiment. The paper presents only one example and one optimization stage. The limiting and functional conditions for the operation of the method preserve a linear relationship between the desired increments of the fundamental parts of the eigenvalues of the model state matrix and their sensitivities to control parameters. Such “small” optimization steps are separate and independent problems, the numerical solution of which can be repeated.

The article presents an analysis of the consequences of economic instability caused by the COVID‑19 pandemic for the socio‑economic development of the region. The study was carried on the example of the Sverdlovsk region according to the Federal State Statistics Service. The article sets and solves three research problems. First, to assess how the overall socio‑economic condition of the region has changed because of the COVID‑19 pandemic. Second, to identify the impact of the COVID‑19 pandemic on the nature and structure of the relationship between the socio‑economic indicators of the region. Third, to analyze the impact of the COVID‑19 pandemic on the trends in the socio‑economic indicators of the region, considering their possible delay and seasonal fluctuations. The first task is solved using statistical methods of pattern recognition, the second task — by methods of multivariate correlation analysis, and for the third task stochastic time series models are used. The largest contribution to the division into clusters was made by the number of births, the turnover of public catering and the volume of goods, works and services performed on their own; their dynamics most clearly traces the impact of the COVID‑19 pandemic in the Sverdlovsk region. Multidimensional correlation analysis established that because of the introduction of restrictive and supportive measures, multidirectional trends in the socio‑economic indicators of the region were formed, which violated the previously established relationships between them. Based on the obtained coefficients of the autoregressive model, one can find a certain pattern consisting in the growth of the influence of short‑term (lag 1 and 3 months) and the decrease of the long‑term influence (lag 12 months) change in indicators. According to the calculations obtained, the economy of the Sverdlovsk region during the analyzed period failed to overcome the destabilizing effect of the consequences of the COVID‑19 pandemic.

On the basis of non-parametric formulations of the production program problem (previously known) and the consumer choice problem (new), a computable partial equilibrium model with a non-parametric representation of both supply and demand is proposed. In this model the problems of the producer and the consumer are represented by simultaneous inequalities of the dual problems pair. This converts the problem of finding an equilibrium to minimizing the differences between objective functions in each pair, summarized over producers and consumers. Such a problem, however, may have multiple local optima. Computer tests on artificial data sets confirmed that inserting such “technical” constraints into a computable model, that are always valid in an equilibrium, can effectively direct the search for a solution using the CONOPT4 procedure to the global optimum (to which the sought equilibrium corresponds). In all 36 tests carried out, equilibrium solutions were found on the first try. The result obtained is of significant importance for the creation of tools used at the sectoral level in managing the unstable economic dynamics that are characteristic of periods of change in systems of dominant technologies. Such tools will make better use of the information in the original empirical data.

This paper addresses the core problem of economic growth — the question of the criteria that should be met in order to both satisfy the needs of a growing population and assure preservation of natural environment for future generations. It contains a comparative analysis of classic theory of maximal economic growth with zero-growth theory. A compromise concept of balanced economic growth is presented. In the paper, an unobvious form an industrial function of balanced growth is hinted at, within which maximum allowed (limited) economic growth shouldn’t induce irreparable damage on environment while minimum of the growth assumes increasing of population wellbeing. Among traditional arguments of the industrial function a factor of investments into environmental protection has been introduced. Balance between two competing requirements to economic growth—improvement of population wellbeing accompanied by simultaneous conservation of limited environmental resources —may be achieved, in addition to the use of resource-efficient technologies, through family planning and monitoring of population growth. Condition of balanced growth is convergence of demographic and technological levels of developing and developed countries. Being dangerously close to the limits of anthropogenic pressure on our environment, the international community should assist developing countries’ transition to the demographic trends of the developed world. At the initial stage, acceleration of this process may require negotiations of an international compact among states regarding population growth. Subsequently, fertility patterns and population growth may return to self-regulation. Drivers for this process will be the Index of Human Development, indicators of gender parity, per capita GNP, and educational levels of populations in the countries with high birth rates. Efficient international aid to poor countries should contribute to this process. Comparative advantages and prosperity as a result of moderate population growth have been proven by the historic records of developed countries. These trends can be applied in other countries if they limit birth rates and population growth. It appears that improvements of population-wide quality of life can be achieved not only by promotion of scientific and technological progress, but also by means of demographic revolution, which is the most harmless among all of social revolutions.