Economic science and economic-mathematical modeling
The global crisis, which has required a rethinking of economic knowledge and corresponding economic and mathematical models (EMM), makes us to return to the origins of the economic science and EMM. Thus the exceptional urgency to exit the global crisis gains the Marx theory of reproduction which stu...
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irk-123456789-1319162018-04-07T03:02:52Z Economic science and economic-mathematical modeling Veduta, E.N. Dzhakubova, T.N. Informational technology in economy The global crisis, which has required a rethinking of economic knowledge and corresponding economic and mathematical models (EMM), makes us to return to the origins of the economic science and EMM. Thus the exceptional urgency to exit the global crisis gains the Marx theory of reproduction which study the objective economic laws, and the EMM based on this theory which helps to build the cyber system in order to enter the path of the social progress. The article shows that the EMM, which historical goal was to understand the economic mechanisms deeper, has been developed in two main directions. The article sets out the basic principles of the dynamic model of inter-branch and inter-sectoral balance (MIIB), which can be the basis for the creation of economic cyber system. Глобальна криза, що вимагає переосмислення економічних знань і нових економіко-математичних моделей (ЕММ), на яких ці знання базуються, змушує повернутися до витоків економічної науки і ЕММ. Тому виняткову актуальність для виходу з глобальної кризи набуває теорія відтворення К. Маркса, яка вивчає об'єктивні економічні закони, та ЕММ, яка базується на цій теорії, для побудови кіберсистеми, що допомагає вийти на траєкторію суспільного прогресу. У статті показано, що ЕММ, які історично виникли для більш глибокого розуміння економічних механізмів, отримали розвиток у двох основних напрямках. Розробники першого напряму пішли шляхом ускладнення використовуваного математичного апарату і збільшення кількості параметрів, задаються екзогенно, в описі економічних систем аналізу і прогнозування, заснованого на екстраполяції. Починаючи з 50-х років минулого століття прискорено розвивається саме цей напрямок, який, на думку багатьох дослідників, потрапив у глибоку кризу через неможливість використання ЕММ і економічних теорій, на яких вони базуються, для розробки антикризових заходів. Розробники іншого напряму розвивають ЕММ шляхом все більш повного відображення в моделі дії об'єктивних економічних законів для конструювання економічної кіберсистеми, що припускає використання сучасних інформаційних технологій як інструменту підвищення ефективності управління. По суті, використання кіберсистеми означає перехід управління економікою на принципово нову технологію, необхідну для виходу з глобальної кризи. У статті сформульовані основні принципи динамічної моделі міжгалузевого та міжсекторного балансу, яка може бути закладена в основу створення економічної кіберсистеми. Глобальный кризис, потребовавший переосмысления экономических знаний и базирующихся на них экономико-математических моделей (ЭММ), заставляет вернуться к истокам экономической науки и ЭММ. Поэтому исключительную актуальность для выхода из глобального кризиса приобретает теория воспроизводства К. Маркса, изучающая объективные экономические законы, и базирующиеся на ней ЭММ для построения киберсистемы, помогающей выйти на траекторию общественного прогресса. В статье показано, что ЭММ, исторически возникшие для более глубокого понимания экономических механизмов, получили развитие в двух основных направлениях. Разработчики первого направления пошли по пути усложнения используемого математического аппарата и увеличения количества экзогенно задаваемых параметров в описании экономических систем для анализа и прогнозирования, основанного на экстраполяции. Начиная с 50-х годов прошлого века ускоренно развивается это направление, которое, по мнению многих исследователей, ушло в глубокий кризис из-за невозможности использования ЭММ и экономических теорий, на которых они базируются, для разработки антикризисных мер. Разработчики другого направления развивают ЭММ по пути все более полного отражения в модели действия объективных экономических законов для конструирования экономической киберсистемы, предполагающей использование современных информационных технологий как инструмента повышения эффективности управления. По сути, использование киберсистемы означает переход управления экономикой на принципиально новую технологию, необходимую для выхода из глобального кризиса. В статье сформулированы основные принципы динамической модели межотраслевого и межсекторного баланса (МОСБ), которая может быть в основе создания экономической киберсистемы. 2017 Article Economic science and economic-mathematical modeling / E.N. Veduta, T.N. Dzhakubova // Математичне моделювання в економіці. — 2017. — № 3-4(9). — С. 10-22. — Бібліогр.: 20 назв. — англ. 2409-8876 http://dspace.nbuv.gov.ua/handle/123456789/131916 338.262 en Математичне моделювання в економіці Інститут телекомунікацій і глобального інформаційного простору НАН України |
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Informational technology in economy Informational technology in economy |
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Informational technology in economy Informational technology in economy Veduta, E.N. Dzhakubova, T.N. Economic science and economic-mathematical modeling Математичне моделювання в економіці |
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The global crisis, which has required a rethinking of economic knowledge and corresponding economic and mathematical models (EMM), makes us to return to the origins of the economic science and EMM. Thus the exceptional urgency to exit the global crisis gains the Marx theory of reproduction which study the objective economic laws, and the EMM based on this theory which helps to build the cyber system in order to enter the path of the social progress. The article shows that the EMM, which historical goal was to understand the economic mechanisms deeper, has been developed in two main directions. The article sets out the basic principles of the dynamic model of inter-branch and inter-sectoral balance (MIIB), which can be the basis for the creation of economic cyber system. |
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Article |
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Veduta, E.N. Dzhakubova, T.N. |
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Veduta, E.N. Dzhakubova, T.N. |
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Veduta, E.N. |
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Economic science and economic-mathematical modeling |
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Economic science and economic-mathematical modeling |
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Economic science and economic-mathematical modeling |
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Economic science and economic-mathematical modeling |
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Economic science and economic-mathematical modeling |
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economic science and economic-mathematical modeling |
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Інститут телекомунікацій і глобального інформаційного простору НАН України |
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2017 |
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Informational technology in economy |
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Economic science and economic-mathematical modeling / E.N. Veduta, T.N. Dzhakubova // Математичне моделювання в економіці. — 2017. — № 3-4(9). — С. 10-22. — Бібліогр.: 20 назв. — англ. |
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Математичне моделювання в економіці |
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Mathematical modeling in economy, №3-4, 2017
UDC 338.262
VEDUTA E.N., DZHAKUBOVA T.N.
ECONOMIC SCIENCE
AND ECONOMIC-MATHEMATICAL MODELING
Abstract. The global crisis, which has required a rethinking of economic
knowledge and corresponding economic and mathematical models (EMM),
makes us to return to the origins of the economic science and EMM. Thus
the exceptional urgency to exit the global crisis gains the Marx theory of
reproduction which study the objective economic laws, and the EMM based
on this theory which helps to build the cyber system in order to enter the
path of the social progress. The article shows that the EMM, which
historical goal was to understand the economic mechanisms deeper, has
been developed in two main directions. The article sets out the basic
principles of the dynamic model of inter-branch and inter-sectoral balance
(MIIB), which can be the basis for the creation of economic cyber system.
Key words: Global crisis, reproduction theory, economical cyber system,
strategic planning, economic and mathematical models, EMM, model of
economic balance, models of economic dynamics (growth).
Introduction
The growing threat of the global crisis force the governments of all countries to
develop anti-crisis measures. However, no country has no plan of action as an
algorithm of the recovery from the global crisis.
It is proved that the cyclical economic development based on the phases of the
cycle "inflation – deflation", which was launched during the First World War,
contributing to the concentration and centralization of the global capital, enhances
the deployment of the global crisis and hostilities [1].
These phases of the cycle are served by the monetary theory of Keynes –
Friedman, who consider the Ministry of Finance and the Central Bank as the main
regulators of the economic development. The adherents of institutionalism, in fact,
offer to carry out the certain structural transformation of the economy, depending
on the phase of cycle. The international system of national accounting and the
econometric models applied for forecasting and planning of the economy are the
monetary targets. Almost all modern researchers do not pay attention to the root
cause of crisis – the disparity of economic development. The task of achieving the
proportionality of the economy can not be solved only by monetary and
institutional methods. This task is the task of the strategic planning of the economy,
which provides the organization of social production for sustainable growth of
quality of life.
To access such planning it is required to utilize entirely the possibilities of
modern information technology (IT), which involves the development of the
corresponding dynamic economic-mathematical model (EMM) on basis of which it
is possible to coordinate the orders of final consumers and manufacturers, taking
into account the introduction of new technologies. Implementation of such EMM
will transfer the economy management to the fundamentally new level of
Ó E. Veduta, T. Dzhakubova, 2017
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Mathematical modeling in economy, №3-4, 2017
technology and will allow to carry out the systematic adjustment of the current
global economic model.
The objective of this article is to justify the need for EMM which describes the
force of objective economic laws, to build economic cyber system – the tool that
can release us from the global crisis.
From the specified objectives the following tasks are derived:
– to show the need of using the Marx's theory of reproduction as the scientific
basis for the development of EMM, capable to use the modern IT in strategic
planning of the sustainable economic growth;
– to explore the evolution of EMM from the position of the possibilities of
their practical application;
– to justify the need of the dynamic model of inter-sectoral and inter-branch
balance (MIIB) as a basis for creating the economic cyber system, enhancing the
effectiveness of management decisions.
1. Global crisis as a signal to rethink the basics of economic knowledge.
In the reproduction theory of Karl Marx it had been proved that the transition to a
new type of production relations is primarily determined by the revolutionary
changes in the instruments of labor. So, as soon as the machine appeared, a
revolution in production relations took place – the capitalist mode of production as
a definite system of economic relations with the corresponding material and
technical base became dominant. The machine, overcoming the limited capacity of
man in the area of the synchronous operating of a variety of work tools,
significantly increases productivity of labor. The industrial revolution is considered
to be complete with the advent of machine-made machines, i.e. machine-building
plants, when capitalist industry created its corresponding material and technical
base. This extended process that led to the leading role of industry in the economy,
was given the name of industrialization. The further production development is
associated with automation. If the managing of an ordinary machine involves the
the human brain and hand, the automatic machine replaces them with the control
devices and thereby the productivity overcomes the limitations, associated with the
natural human capabilities.
Currently the world faced the neсessity to rethink the basics of the
economic knowledge in order to emerge from the global crisis. Economic
theorists, admitting the need for implementation of strategic planning of the
economy, limit themselves by listing the same monetary "anti-crisis" measures
with proposals to restrain or to launch inflation, which means the continuation
of the crisis. During the Second World War the United States significantly
increased their interest in the information necessary for the strategic decision tasks.
A new science – cybernetics appeared and studied the processes of information
processing and attached importance to the feedback in order to create the
automated control systems of different nature, including the economy. The special
importance the US attached to the economic information - the system of national
income accounts, inter-sectoral balance and the mathematical models which could
be used in the electronic computers (computers) for the calculation of
macroeconomic indicators and their relationships for the purposes of anti-cyclical
regulation. Starting from the second half of the XX century, the special attention is
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Mathematical modeling in economy, №3-4, 2017
paid to the automation of production, the introduction of IT systems in production
management processes, transmission of control and monitoring functions to the
automatic machines (robots). This was due to the fact that during the 50s the role
of factor of organization and management had increased dramatically. In the
United States during this period the number of managers in the total working-age
population increased from 40% to 51%, and in the Soviet Union only in the field of
business management the number of employed amounted to 63%. In the US, since
1961, this rapid process was restrained with the help of the automated control
systems (ACS), and the Soviet Union only started these developments [2].
With partial automation the dependence on the reliability of operators is
reserved. The appearance of cybernetic systems (cyber systems) means a transition
to the higher level of automation when cyber machines (IT), performing many
functions of the direct management of the complex systems of various nature
(technical, economic, biological) leave the function of cybe rsystem improving and
creating function of the person who makes the decisions (DMP) to man, due to the
inability to formalize the decision-making process entirely.
Under conditions of the permanent global crisis, accompanied by uncontrolled
growth of administrative structures, the information flows circulating among them,
document flow, and the loss of control over the object – the economy – the
extremely urgent issue becomes the implementation of economic cyber systems.
The ttempts to "make" the economy to get out of crisis on the basis of monetary
and institutional theories failed, because these theories ignore the objective
economic laws that regulate the social reproduction. Development and use of these
theories and the economic and mathematical models by their adherents in order to
justify the proposed anti-crisis measures do not produce the desired results. The
substitution of the object of the strategic planning by document flow and, therefore,
the introduction of IT for its automatization is not conducive to handle the
economy. Moreover, the academic studies, limited by the abstract theoretical
constructions, do not offer the specific practical measures and mechanisms, but at
the same time apply for state doctrine, and can greatly move back the development
and implementation of science-based anti-crisis measures.
Crisis of the modern economic theories and EMM developed on their basis,
fancy for the IT introduction with the aim of document flow automatization,
forced us to return to the origins of the economic science and to rethink the
accumulated experience of EMM for the effective use of modern IT in the interests
of social progress.
If we ignore or block this important area of research, the future will be such as
it is "described" by the Davos Forum President Schwab K. [3]. According to him,
the digital revolution, which starred in the middle of the 50-ies of the last century
and is associated with the introduction of electronics and IT for production
automation, today acquires a systemic character of rapid technological
breakthroughs in areas such as artificial intelligence, robotics, etc. The
revolutionary changes caused by modern IT can, according to K. Schwab, bring
humanity to the following consequences:
– significant increase in productivity, when robots replace people everywhere,
may cause the global changes in the labor market and strengthen the social
inequalities;
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Mathematical modeling in economy, №3-4, 2017
– people will be able to access the huge volume of information and will be
able to express their opinions on various issues, and the authorities will get new
opportunities for the development of surveillance and monitoring systems;
– strong IT influence on the national and international security;
– robotization of mankind – the deprivation of human heart and soul.
Indeed, all these processes will have such a development, if the global crisis
continues. Considering the growing threat to the humanity, it is important to return
to the theory of reproduction. This return does not mean its dogmatic interpretation
of the Soviet school position. In this theory the systematic approach to the study of
the economy is carried out, which means that all of its categories perform the
certain functions in ensuring the dynamics of economic system, which then
changes during the transition to the next type of society. The knowledge of the
reproduction theory is necessary for understanding of force of objective economic
laws discovered by Marx, and their reflection in the EMM. In this connection it is
relevant to recall the words of V.I. Leontiev: "If, before someone tries to give any
explanation to the economic development, he wants to know what the profits,
wages, capitalist enterprise are, from three volumes of "Capital" (from the source)
he can get the more realistic and qualitative information than that one he could find
in ten consecutive reports of the US census Bureau, a dozen textbooks on modern
economy ... " [4].
The objective economic laws discovered by Marx – cost, savings, time
savings, the proportionality of economic development, the growth of the organic
composition of capital, the formation of prices of production and others, perfoming
in one system, form the mechanism of functioning of the economy and its
development under the influence of the scientific and technical progress. EMM and
the theoretical constructions that ignore or criticize the reproduction theory, that
discovered the objective economic laws, are not able to solve practical problems
and pursue the narrowly selfish goals. A modern interpretation of the reproduction
theory involves the construction of EMM, simulating the operation of objective
economic laws in order to create the economic cyber systems serving to the
cultural, scientific and technological progress of society. In this context, the study
of the evolution of EMM from the point of view of the development of the
fundamental ideas of the reproduction theory is very interesting for science.
2. Balance Models
Historically, the mathematical school of political economy appeared in the second
half of the XIX century. Its founders are considered to be W. Jevons (England), L.
Walras (France) and Pareto (Italy), who used the mathematics to create the models
of economic balance. One of the first representatives of Russian school of
mathematics was V. Dmitriev, whose works were regarded as the theoretical basis
for the creation of MIB and SNA.
The basis of the mathematics school were the ideas of marginalism, explaining
the economic processes with the use a marginal (incremental) values. The
achievements of this school are:
– concept of economic optimum, meaning the best condition of the economic
system in terms of its inherent objective criteria of certain restrictions;
– use of mathematical tools for the analysis of marginal values – the marginal
utility and marginal costs;
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Mathematical modeling in economy, №3-4, 2017
– studies over terms of balance;
– analysis of dependences of demand, prices, income;
– analysis of factors determining the cost of production;
– analysis of relationship of the issues of pricing and the total proportionality
of the economy.
The model of the general economic balance, developed by L. Walras in the late
XIX century, was in fact the first mathematical model that described the
macroeconomic system with the help of micro-economic indicators (in the model a
separate equation is allocated for each item) that characterized the behavior of
producers and consumers. Its contribution to EMM was in application of the
technological coefficients aij characterizing the structure of the cost in the production
units to describe the economy through the system of algebraic equations. This
approach is still the basis of modern EMM.
The task of the optimal behavior of producers and consumers was not set in this
model. However, this problem was set by Walras in his exchange model in which the
demand for the final product is determined by the criterion of maximizing utility,
formulated W. Jevons. He found the main problem of economic science in the study
of consumption, the basic law of which he considered to be the law of diminishing
marginal utility. Under the concept of "utility" Jevons meant an abstract property of
the object to correspond the objectives of consumers. He believed that the total value
of units of goods depended on their quantity, and the utility of the last increment of
the good tends to decrease with increasing amounts of goods [5]. The follower of
Walras, who contributed to the development of the Lausanne school, became
Pareto, who introduced the concept of optimum, named after him - "the optimum
of Pareto" [6]. Pareto optimality means to attain such condition of the economic
system, in which the criterion function value of any participant of the system
cannot be improved without impairing the other participants in the target function
values. The concept of Pareto optimality is widely used in the theories of economic
balance and coordination of interests.
In fact, the creators and researchers of the models tried to describe the
proportionality of the economy development using a static system of algebraic
equations. It was a step forward from the point of view of understanding of the
relationship of producers and consumers in their attempt to achieve proportionality.
Moreover, the authors of balance models contributed significantly to the
understanding of achievement of the optimum system, both in terms of behavior of
individual agents, and the total system. Their introduction of the concepts of
marginal utility and marginal costs proved to be useful for better understanding of
marginal and average cost pricing mechanism in the reproduction theory. Analysis
of the conditions of balance and optimum implemented by Walras, Jevons, and
Pareto had a great influence in the 40th and especially in the 50-ies of XX century on
the economists involved in EMM. The model of Leontiev, who developed the
method of "Input – Output" can be considered as a development of the Walras model
because it also describes the economic system by means of linear equations and uses
the technologic coefficients aij characterizing the cost of production of goods in one
branch in the production of goods in the other industries. At the same time Leontiev
model can be seen as the first step towards the practical use of EMM, as it reflects
the real economy in the existing relationship between the final, intermediate and
gross domestic product.
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Mathematical modeling in economy, №3-4, 2017
While the Leontiev model "Input - Output" (model of inter-branch balance) was
increasingly being used in the state regulation of the economy in the post-war
Europe, Japan, and then in the USSR (1958), the researches in the development of
mathematical balance models of intensified. A typical example of such research was
the balance model of Arrow – Debreu [7]. In this model, besides the criterion
functions of consumers, the target functions of manufacturers - to maximize profits
– were taken into account. The balance in the model of Arrow – Debreu means the
totality of the price vector, the cost – production vectors and vectors of purchasing,
that are optimal for the participants at these prices, and in which the total demand
for each product type, that has a non-zero price, does not exceed its total supply. It
is proved that under the general assumptions, the balance in the model of Arrow –
Debreu exists, although its uniqueness cannot be guaranteed. Balance of Arrow –
Debreu obtains many optimal properties under very general assumptions, in
particular, the balance vectors consumption and costs-production maximize a
balanced sum of the criterion functions of consumers.
Some researchers thought it was possible to use this theory to simulate the
planned economy [8].
In the 60s-70s many new versions of models of economic balance appeared,
they had the different ways of formation of consumer income, different participants
and assumptions about their behavior. The attempts to reflect them in the balance
model, to take into account the existence of the collective goods, and so on, was
taken. The ideas of marginalism and balance theory became popular among the
representatives of neoliberalism. Today they are used in the main branches of
economics – demand theory, theory of the firm, and so on. However, developing
the mathematical apparatus of balance models, their supporters, in contrast to the
Leontiev school, do not focus on the use of these models in the modern IT in order
to improve the efficiency of administrative decisions in the economy.
3. Growth models (models of economic dynamics).
Under the models of economic growth (dynamics) the models, in which time is one
of the parameters and the calculation for the next year is based on the calculations
for the current year are understood.
One of the first models of economic dynamics was developed in 1937 by the
American scientist John von Neumann – a model of balanced growth (expanding
economy) [9]. The model suggests that the production output of this period is the
cost of the next period. The concept of stationary trajectories imposed by
Neumann, which is understood as the constant growth of output at its constant
structure, is widely used to predict the possible trajectories of growth in output and
cost estimates. The particular importance for the researchers is the stationary
concept, which is used to determine the optimal trajectory, close to the main, which
is understood as a stationary trajectory, which figures are growing with the
constant, the maximum possible rate. For economic dynamics models it is
mathematically proved that, regardless the initial condition, any optimal trajectory
after some time becomes closer to the main. On the one hand, the value of the von
Neumann model is in attempt to describe the economy as a dynamic system, and in
the introduction of concepts of stationarity and mains, which can be used in the
scenario calculations of economic development. On the other hand, the model gave
the impetus to the use the mathematical programming apparatus for solving a
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system of linear inequalities and for development of the mathematical apparatus
used in it. In particular, a new direction appeared on its base - the theory of games.
The further development of the Neumann model followed the way of its
combination with the other models and complexity of the mathematical apparatus.
Therefore, the Neumann model was developed by the Japanese economist M.
Morishima in 1965 [10], which saw its resemblance to the Marx's schemes,
introduced a number of additional conditions, and a new mode was called the
"model of Marx – Neumann." Other researchers tried to connect the Neumann
model with the model of Walras – Arrow – Debre.
During the 50-70-ies the most important results in mathematical economics
(optimal programming, game theory, the theorem on mains, and others.) were
reached mainly by the professional mathematicians. The mathematical tools
developed by them could be useful for the analysis of some economic phenomena.
The important contribution to the development of mathematical programming
as a tool of EMM had been made by mathematician R. Bellman (USA), who
worked in the field of dynamic programming. He developed the theory and
numerical methods, which was a multi-step process of finding the optimal solutions
for some of the criterion function. His main method was the method of recurrence
relations, the base of which was the optimality principle: if the process of control is
optimum in the first step, it will be optimal for the process, remaining after the first
step [11]. Dynamic programming methods are used for simulation of random
processes such as inventory management, where the costs of storing of the excess
inventory at the reduced demand are compared to the losses from the lack of
reserves at the intensive demand. EMM of the dynamic programming of the
stochastic processes are called Markov chains.
Bellman optimality principle was used in the models of economic dynamics
which had have been used in the practice of the state regulation of economy in the
50-s as the instrument of prediction. These models are, first of all, the growth
model (Harrod, Domar, Solow and others) and the dynamic model of Leontiev. In
the growth models based on Keynesian ideas, in addition to the time factor, the
relationship between capital investment and production was taken into account [6].
Then the growth models became more complex in different directions, mainly used
to account the time lags between investment and production. The further
development of the growth models was the use of the principle of optimality: the
criterion function of the economic system or the criterion function of separate
entities of system, if they have autonomy.
The development was given to two approaches to the modeling of economic
dynamics, that reflected the existence of two directions in the economic research,
conditioned by the existence of two economic systems – the planned economy of
the USSR and the market (oligarchic) economy of the US.
The first approach (constructive) was based on the principle of control of the
economic system, and contained the formulation of the extremal problem in a great
number of the permissible trajectories of movement of economy. These models are
often called the models of optimal economic growth or the welfare models.
The second approach is descriptive, according to which the trajectory of
economic development is the condition of balance which is formed by the
interaction of different entities of system. The developers of these models showed
that in some cases there was the balance theorem, according to which any balance
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trajectory is optimal at the certain criterion function, and vice versa, each optimal
trajectory is balanced at a certain organization of the system entities interaction.
When developing the models of balance and dynamics the Soviet economists
and mathematicians followed two mentioned approaches. The research center was
the development of dynamic Leontiev model [12]. Researches were undertaken in
the following areas: accounting of the criterion function in the model; the
introduction of the variance in the technological production methods that vary with
time, depreciation of funds, different time of construction and development of
facilities; accounting of the lag of capital investments, and so on. In general, the
researches were limited by the introducition of additional exogenous parameters
and the improvement of mathematical apparatus that describies the inter-branch
balance (MIB). The attempts to use the MIB in automation of routine calculations
(ARC) were made [13]. However, these attempts were unsuccessful for the
following reasons.
First of all, the planning process is iterative and the models as the system of
linear equations were static. Secondly, in the modified Leontiev models the law of
proportionality of the economy was ignored, and this law assumed the coordination
of links of producers with the orders of final consumers taking into account the
effect of feedback - balance prices and the law of economy of time, according to
which the effective range of new technologies is calculated: the planned norms of
cost were the exogenously given values.
Such use of mathematical methods in economic research had been criticized
by academic economists. So, V.V. Novozhilov noted that EMM helped you to
systematize the ideas about the functioning of economy, but the most obvious
truths could be missed during their creation [14].
The value of the mathematical models in economy lies in the fact that they
allow us to describe the economic phenomena and to obtain the valid conclusions
in the language of formulas and algorithms. This explains the inclination of the
Western economists to the creation and practical use of econometric models based
on the models of economic balance and growth, the principle of optimization, game
theory, and other old and new economic theories. But, there is another side of these
models. No matter what the actual statistics these models are built on, if the
precondition used in them was false, the calculation results would be biased.
4. Econometric models
Econometrics means the development of mathematical and statistical models of
economics and quantitative assessment of their parameters. A significant
contribution to its formation was made by the studies of the economic cyclicity
made by Clément Juglar, J. Kitchin, S. Kuznetsov and N.D. Kondratyev, who
discovered the "long waves" lasting for 45-60 years [15].
The the Harvard School can be considered as the founder of econometrics. It
was organized in 1914-1918 to study the nature of economic cycles and to forecast
the economic situation using statistical methods and mathematical analysis. The
basic principle of this school was the notion that "the science meant measurement".
According to this, the theory should reveal itself in the result of statistical analysis
that was fundamentally different from the position of the founders of mathematics
in economic theory school [16]. The short-term forecasting models had mostly
extrapolation character. An example of such models was the "Harvard barometer",
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developed under the leadership of W. Pearson in order to assess the "economic
weather" on basis of statistical observations. "Barometer" was a set of three curves
(stock market, commodity market and money market) concerning to which it was
believed that they have nearly the same vibrations with some shift in time. This
made it possible to predict the behavior of one curve, for example, commodity
market, based on the behavior of another, such as the stock market.
In the 20's the ideas of Harvard School were widespread in Europe, where the
opportunistic institutions were created and they studied the statistical data in order
to predict the "economic weather." The all-USSR Market Research Institute
(AUMRI) was created in 1922 in the USSR, whose main task was to study the
economic situation, time series and seasonal fluctuation for the short-term
forecasting of price indices and purchasing power of money. The well-known
scientists of the institute were A. Conus, E. Slutsky and others. In 1926 the League
of Nations established the Committee of Experts who were using the "economic
barometer". Practice showed that the "Harvard barometer" predicted the "economic
weather" in the period of stabilization relatively well, but not during the "storm":
before crisis of 1929-1933 the Harvard University made a forecast of "prosperity"
of the economy.
Due to the crisis of 1929-1933 the United States began to pay a special
attention to the development of econometrics in order to study the problems of the
economic cycle with the help of statistics and mathematics methods. In 1930 the
International Econometric Society was created in the United States. On the first
stage of its development the researches were carried out in the following areas:
– Mathematical school in economic theory, which assumed the use
mathematics and statistics in theoretical studies of the economy;
– Econometrics, which method was essentially statistical and didn’t
investigate cause and effect relationships;
– Mathematical economics as a branch of mathematics devoted to the
development of mathematical tools for EMM.
Among the first Russian developers of econometric models there was G.A.
Feldman, who, being an employee of the USSR State Planning Committee,
developed the first model to the predict the rate of economic growth (1928-1929
years). The basis for its construction became the Marx scheme. The model
reflected the correlation of the national income rate of growth, changes in capital
productivity and labor productivity, the structure of use of the national income.
According to this model the Gosplan calculated the expected rate of growth of the
national income.
Starting with the 30-40-ies econometrics gained the rapid development and
today it is the main method of research of economic processes and forecasting.
If in the the 70-ies the economists - supporters of econometrics considered that
it was necessary to use its methods for the quantitatively confirm of the theoretical
constructions, then starting with the 70-ies the econometric methods are used to
describe the cause-effect relations between the economic parameters. Today
econometrics is actively used by monetarists to substantiate the choice of scenario
of economic development, of a certain type of economic policy.
A powerful impulse to the use the econometrics was given by computers, and
by these means there was the development a statistical analysis of time series, as
well as the rapid development of the world market of loan capital and derivatives.
Statistical models of different countries were integrated into the general system in
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order to understand the international economic relations and predict the global
economy. For example, the project "Link" – a global model of international trade –
was created in 1968 from the Wharton Econometric Forecasting Associates
(WEFA) in order to provide the US Department of State with the advisory
assistance in development of effective measures in the domestic and foreign policy.
The principal disadvantage of econometrics was the study of quantitative relations
in the economy without determining the control parameters and feedback from the
object of management. Econometrics uses essentially the extrapolation methods,
and it limits its practical application in solution of economic problems. Like all
other modern researches of EMM, these studies are in crisis because they are not
able to offer the effective solutions of the practical problems in the economy [17].
According to N. Petrakov, when forecasting of the economy on basis of multifactor
models the internal laws of functioning of the economy as a whole system fall out,
leaving unanswered such important questions as, for example, whether the concept
of efficiency of the economic system is limited by the indicator of rate of
production growth [18].
To carry out the EMM calculations some initial economic information is
required. The modern standardization of the national accounts, calculations of
economic growth, international comparisons and the creation of strong research
departments was organized by the international economic organizations (the World
Bank and the International Monetary Fund, the UN and others) and occurs outside
the system links with the information needs of the great amount of EMM.
To carry out the calculations with the help of new indicators of models (e.g.,
the index of inflation expectations, the country's credit rating, and so on) the
developers require the additional collection of information that leads to its cascade
growth and inefficient use of IT. The groundlessness of the modern economic
theories and EMM that serve the cyclical development is primarily explained by
the the fact that they are not able to offer a way out from crisis cycle to the
trajectory of sustainable economic growth. This can be done only on basis of
implementation of the scientific approach in the construction of EMM, which
suggests in the models the reflection of force of objective economic laws and
creation on their base the cyber systems serving the optimization of management
decisions in the economy.
5. A dynamic model of inter-sectoral and inter-branch balance (MIIB)
The force of the objective economic laws and the EMM experience are reflected in
the dynamic optimization model of inter-branch and inter-sectoral balance (MIIB),
developed by the economist-cybernetics N.I. Veduta [19]. This model can serve as
a basis for creation of cyber system in order to improve the effectiveness of
management decisions. In this model the following principles are realized:
– economy is regarded as the consciously optimized system based on the
mixed ownership of the means of production;
– there is a single criterion of optimality, characterized as an objective
tendency of society to maximize the growth of quality of life (maximization of the
utility growth). Quality of life is determined not only by the non-productive
consumption, but also by the content of the labor process, free time, intended to
meet the social needs;
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– national economy is considered as a complex hierarchical system, which
proposes the hierarchical structure of public administration and the implementation
of systematic approach in the question of defining the "input-output" indicators, the
collection of economic information, its aggregation and disaggregation at different
levels of government (economy – industry – corporation);
– social working time, as the only limiting (unreproducible) factor of social
reproduction is the starting point for planning;
– force of objective economic laws and, above all, the law of value as a
natural regulator of the economy through the proportional balance price deviations
from the prices of producers, and the law of economy of time, which is expressed
in the effective replacement of the old technology with new one in order to
maximize the cost savings are reflected in a dynamic MIIB;
– MIIB as a dynamic system is an iterative process of harmonization of
planned calculations, including the choice of effective technological methods of
production and adjustment the criterion values depending on the production
capacity;
– problem of the efficient distribution of productive investment is solved in
the MIIB simultaneously with the task of optimizing of the structure and volume of
the final non-production goods;
– taking into account the implementation of the model and its improvement
the direction of the Public Administration reform is determined.
The principal difference between the MIIB table from those tables based on
the concepts of the "System of National Accounts 2008" (2008 SNA) and the
Balance of National Economy (BNE) is that MIIB is an absolutely symmetric
matrix, which presents the interlinked accounts of all sectors of the economy.
Correction of the initial MIIB information by recalculation of its indicators in
reliable assessments allows to get rid of the balancing rests presented in other
tables and hidden in the line "gross income" or "profit". Such correction allows to
perform the calculations of the MIIB while retaining the balance of all accounts of
industries and sectors.
Using some of forecast parameters, macro-economic proportions and the
original data over the structure of the final non-production goods, the dynamic
MIIB allows to specify them in the course of the optimization plan calculations.
Conclusion
Exit from the global crisis assumes an appeal to the economic science, which
studies the objective economic laws. These laws were discovered in the
reproduction theory by Karl Marx. The next step in the development of economic
science were to be EMM, as a tool solution of practical problems. With the
appearance of computers the possibility of practical use of EMM in order to
improve the quality of economic management increased significantly.
The first EMM (equilibrium models and growth models) developers
contributed to the use of mathematical formalism to describe the economic
phenomena, which in its turn contributed to the better understanding of the force of
objective economic laws.
Later the EMM was developed mainly in the direction of the complexity of
the mathematical apparatus that turned the EMM into the object in mathematical
research.
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Another direction of EMM development is the econometric models, on basis
of which the forecast calculations are conducted, they extrapolate the current
trends, without giving an algorithm for solving the current economic problems.
However, the denial of the EMM and its substitution with the abstract
theoretical constructions that reject all scientific research and practical experience,
and, in fact, are lobbying the narrow selfish interests through the designation of
certain priorities, does a great harm to the proportional development of the
economy. The task of the economic science was formulated in the XIX century as
"systematization of laws obtained by the theory, regularity and observations in
order to control the various manifestations of the practical economic and social life
of the society and the State" [20].
Today the dynamic MIIB based on the objective economic laws allows to
implement the cyber systems in the management of the national (global) economy
to ensure the sustainable growth in the quality of life.
REFERENCES
1. Veduta E.N. Regnum. https://regnum.ru/news/innovatio/2150578.html (accessed August
24, 2016).
2. Veduta E.N. Strategiya i ekonomicheskaya politika gosudarstva. [The strategy and the
economic policy of the state]. Moscow: INFRA-M, 2016.
3. Schwab K. https://www.foreignaffairs.com/articles/2015-12-12/fourth-industrial-
revolution. (accessed: July 22, 2016).
4. Leontiev V.I. Sovremennoe znachenie ekonomicheskoy teorii K. Marksa.
Ekonomicheskie esse. Teorii, issledovaniya, fakty i politika. [The modern value of Marx's
economic theory. Economic essays. Theory, research, facts and policy]. Moscow:
«Politizdat», 1990.
5. Blaug M., Jevons W. 100 velikikh ekonomistov do Keynsa. [100 great economists before
Keynes.] Saint Petersburg: Ekonomikus, 2008.
6. Blaug M. Ekonomicheskaya mysl' v retrospektive. [Economic thought in retrospective.]
Moscow: Delo, 1994.
7. Berndt E. Praktika ekonometriki: klassika i sovremennost'. [Practice of Econometrics:
Classic and Modern]. Moscow: Yuniti-Dana, 2005.
8. Katsenelenboygen A.Y., Movshovich Y.V., Ovsienko Y.V. Vosproizvodstvo i
ekonomicheskiy optimum. [Reproduction and economic optimum]. Moscow: Nauka, 1972.
9. Gale D. Teoriya lineynykh ekonomicheskikh modeley. [The theory of Linear Economic
Models]. Moscow: Inostrannaya literatura, 1963.
10. Morishima M. Ravnovesie, ustoychivost', rost (mnogootraslevoy analiz). [Balance,
stability, growth (multisectoral analysis)]. Moscow: Nauka, 1972.
11. Bellmann R. Dinamicheskoe programmirovanie. [Dynamic programming]. Moscow:
Inostrannaya literatura, 1960.
12. Cheremnykh Y.N. Matematicheskoe modelirovanie narodnokhozyaystvennoy dinamiki.
[Mathematical modeling of the dynamics of national economics]. Moscow: Znanie, 1987.
13. Dzhakubova T.N. Ekonomika i matematicheskie metody. [Economics and
Mathematical Methods]. №6 (1988).
14. Novozhilov V.V. Problemy izmereniya zatrat i rezul'tatov pri optimal'nom planirovanii.
[Problems in measurement of costs and results in optimal planning]. Moscow: Nauka, 1972.
15. Berndt E. Praktika ekonometriki: klassika i sovremennost'. [Practice of Econometrics:
Classic and Modern]. Moscow: Yuniti-Dana, 2005.
16. Edited by Rumyantsev A.M. Ekonomicheskaya entsiklopediya. Politicheskaya
ekonomiya. [Economic Encyclopedia. Political Economy]. Vol. 1. Moscow: Sovetskaya
entsiklopediya, 1972.
https://www.foreignaffairs.com/articles/2015-12-12/fourth-industrial-revolution
https://www.foreignaffairs.com/articles/2015-12-12/fourth-industrial-revolution
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Mathematical modeling in economy, №3-4, 2017
17. Polterovich V.M. http://mathecon.cemi.rssi.ru/vm_polterovich/files/
Crisis_Economic_Theory.pdf (accessed July 22, 2016).
18. Petrakov N.Y. Izbrannoe. [Selected works]. Vol. 1. Saint Petersburg: Nestor-Istoriya,
2012.
19. Veduta N.I. Sotsial'no effektivnaya ekonomika. [Socially efficient economy]. Moscow:
REA imeni G.V. Plekhanova, 1999.
20. Brockhaus F.A., Efron I.A. Entsiklopedicheskiy slovar'. T. 79. [Encyclopedic
Dictionary.] Saint Petersburg: Semenovskaya tipolitografiya, 1890−1907.
Been received for revision 12.01.2017.
http://mathecon.cemi.rssi.ru/vm_polterovich/files/ Crisis_Economic_Theory.pdf
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