Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Том 59, № 2 (2023)
Articles
Аnalysis of marginalism. Part 1
Аннотация
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.
Economics and Mathematical Methods. 2023;59(2):5-18
5-18
Recovering the actual trajectory of economic cycles
Аннотация
The paper deals with the development of a method for restoring the trajectory of economic cycles from estimates of the gross domestic product (GDP). The proposed approach to solve this problem is based on the interpretation of cycles in the form of random oscillations of the income with a certain natural frequency, also called a narrowband random process. The operators (Fourier transforms, filtering, etc.) used to recover the cycle trajectory are linear. Their inherent associativity property allows changing the sequence of implementation of the linear operators above. As a result, it is proposed to start the recovery with bandpass filtering of the GDP function, and after that to parry the influence of the inertia property of the GDP estimator. Taking the qualities of a narrowband random process into consideration made it possible to create a simplified procedure to recover the cycle trajectory. In the example of the Kuznets swing, the acceptability of this procedure is demonstrated for the practical econometrics. The developed method is applicable in problems that require knowledge of the trajectory of the considered cycle.
Economics and Mathematical Methods. 2023;59(2):19-25
19-25
Optimization of structural dynamics of the economy in the framework of the “input-output” methodology
Аннотация
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.
Economics and Mathematical Methods. 2023;59(2):26-38
26-38
Modeling the socio-economic development of Russia using big data and data from field experiments
Аннотация
The purpose of the article is to study the prospects of socio-economic development of Russia from the point of view of transition to economic autarky. The study includes a cluster analysis of trends and patterns of socio-economic development of Russia, as well as neighboring countries (CIS). As a comparison base, data were used on countries that have passed (South Korea and Japan) or are passing (Iran) through a full-scale experiment of economic autarky with varying degrees of success. Statistically processed big data reflected in the Countries' Prosperity Index (Legatum Prosperity Index) by the end of 2021 were used as the information base of the study. The study also conducted a simulation of the socio-economic development of Russia, taking into account the accumulated potential, based on a taxonomic method related to the group of economic and mathematical methods of decision-making on a set of attributes (Multiple Attribute Decision Making, MADM). The results of the study show that Russia does not have the necessary development potential to switch to successful models of economic autarky, which were implemented in South Korea and Japan at the time. Russia is capable of further implementing an inertial model of socio-economic development, and is also capable of transitioning to an economic autarky of the Iranian type. The same conclusion applies equally to the countries of the near abroad (CIS). The results obtained can be used as an information base for decision-making in the field of public administration and regulation of socio-economic and socio-political processes.
Economics and Mathematical Methods. 2023;59(2):39-53
39-53
Impact of the COVID-19 pandemic on the socio-economic development of the region
Аннотация
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.
Economics and Mathematical Methods. 2023;59(2):54-67
54-67
Rationing and market: Structure and stability of equilibria
Аннотация
In recent years, state control of the economy has increased in many countries. A number of states try to influence prices in key areas of economy, in particular by selling resources at fixed prices within given quotas. However, in real economies the governments cannot prevent economic agents from reselling rationed goods at the free market. The study of impact of rationing on the market prices is a difficult and challenging problem. In the present paper we consider an equilibrium model in which part of the goods within the limits of quotas is sold at fixed prices while the remaining goods are sold at market prices; the goods bought at fixed prices can also be resold at market prices. Economy depends on parameters, viz. total resources, incomes of the participants, quotas, and fixed prices. For special values of parameters, this model reduces to pure exchange and fixed income models and, in a sense, is a combination of these models. Basing on known properties of these special cases and using techniques of elementary differential topology, we study the existence of equilibria and their properties. Depending on the values of parameters, a (sufficiently general) economy may have a finite (even or odd) number of equilibria, and in an important special case when total resources are subject to rationing and the total cost of allocated quotas coincides with the total income of the participants the equilibria form a one-dimensional manifold. We consider a generalized tâtonnement process and study its convergence under certain assumptions. It is shown that in our setup convergence of tâtonnement to an equilibrium may involve endogenous inflation.
Economics and Mathematical Methods. 2023;59(2):68-86
68-86
Computer testing of a non-parametric partial equilibrium model prototype
Аннотация
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.
Economics and Mathematical Methods. 2023;59(2):100-111
100-111
Optimal solution for immunizing arbitrarily scheduled multiple liabilities
Аннотация
Immunization, a control tool for interest rate dependent changes in the value of an asset portfolio given a similar dependency for a target liability portfolio, is central to portfolio management. A vast body of academic literature describes various immunization models either for the case of a single liability payout or assuming a specific change in the yield curve, or both. This paper is the first to propose an immunization solution for the case of multiple liability payouts assuming arbitrary changes in the yield curve. For the case of multiple liability payouts, we generalize M-Absolute, which is a risk measure proposed by Nawalkha и Chambers (1996), and estimate the proximity of payment streams with EMD (the Wasserstein distance) which is a well-known tool in machine learning. In line with Fong and Vasicek (1984), it is shown that portfolio’s interest rate risk is constrained to a product of two factors with one factor, EMD between asset and liability streams, being only dependent on the portfolio structure and the other factor, the sup-norm of the function of interest rate shocks, being solely determined by changes in the yield curve. We also show the unimprovability of the estimate and obtain, in an explicit form, a computational procedure for the optimal immunizing portfolio. The results are practically applicable as exemplified by the immunization of an annuity-type security with a portfolio of government bonds.
Economics and Mathematical Methods. 2023;59(2):87-99
87-99
Issues of balancing economic growth and the state of the environment
Аннотация
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.
Economics and Mathematical Methods. 2023;59(2):112-121
112-121
On simplification of the transport problem solution with ecological criterion
Аннотация
The possibility of neglecting the penalty component in solving the transport problem (TP) with an environmental criterion is analyzed, when, along piece-rate payment, fixed additives are assigned, due only to the fact of a specific transportation, and not to the amount of transported cargo (penalties). It was found that, while the threshold ratios of the standard deviations of tariffs and fines in a TP with a single optimal plan can be grouped quite tightly, in a TP with a non-unique optimal plan, their use is not effective due to the large spread. However, the possibility of applying the “looping” method proposed by the authors, when the TP is solved many times, in which penalties are added to the tariffs, divided first by the maximum possible transportation, then by the transportation plan at the previous step, allows neglecting the “penalties” if the loop ends at the first step. The disadvantage and reason for the approximate nature of the “looping” method is the possible presence of other cycles with local minima. The possibility of the “exclusions” method presented in the paper is also considered, when for a TK with n suppliers and m customers cells are excluded in descending order of fines if the remaining parts of capacities and capacities are sufficient. The ability to distribute transportation after R = (nm – (n + m – 1)) steps allows you to ignore tariffs when choosing a plan. The disadvantage of this method, equivalent to allocative least cost method is the possible difficulties in arranging transportations after R steps of exclusion made under the assumption of a “saturated” use of cells.
Economics and Mathematical Methods. 2023;59(2):122-127
122-127
128-130
131-132