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Учитывая сложную геополитическую ситуацию в мире и действие беспрецедентных антироссийских санкций,Российской Федерации необходимо предпринимать меры, способствующие преодолению рецессии и обеспечивающие экономический рост. Привлечению дополнительных инвестиций в нашу страну поможет сотрудничество со странами Востока, развивать которое можно путем создания исламских финансовых институтов.
Литература:
1. Аль Аззави A.A. К вопросу о специфике фун кционирования исламского банкинга и факторах, останавливающих его развитие на территории РФ { A.A. Аль Аззави // Вестник Государственного университета управления. -2017.- № <1. - С 85-88.
2. Беккин Р.И. Исламская модель беспроцентной экономики и современность // Вести.ик
С. Петерб. ун-та. Сер. 5: Экономика. - 2007. - N02. - С. 79-89.
3. Беккин Р.И, Исламская экономическая модель: перспективы реализации в мусульманском и немусульманском сообществах. URL: http:// www.takafol.ru/arts.php?art=29 (дата обращения: 15.08.2022).
4. Зарипов И.А. Исламские финансы как стратегический ориентир развития России // Вестник финансового университета. - 2016. - № 1 (91).- С 96-110.
5. Куран Т. Исламская экономическая мысль и исламская экономика // Христианство и Ислам об экономике / под ред. М.А. Румянцева, Д.Е. Раскова. - СПб., 2008. - С 279-304.
6. Трунин П.В. Исламская финансовая система: современное состояние и перспективы развития / П. Трунин, М. Каменских, М. Муфтяхетдинова. -М.: ИЭПП, 2009. - 88 с.
7. islamic Financial Services Board, Islamic Financial Services Industry Stability Report. Kuala Lumpur, Malaysia, June, 2021.
МИР В ЭКОНОМИЧЕСКИХ ИНДЕКСАХ, ЗАВИСЯЩИХ ОТ РАЗМЕРА СТРАНЫ. I МИР НА ПЛОСКОСТИ {НАСЕЛЕНИЕ, ВВП}
Сейдаметова Зарема Сейдалиевна, доктор педагогических наук, профессор Темненко Валерий Анатольевич, кандидат физико-математических наук, доцент
Крымский инженерно-педагогический университет имени Февзи Якубова, Симферополь, Республика Крым
Цель исследования - разработать метод и понятийный аппарат для выявления структуры распределения стран на плоскости {Население, ВВП}. Для достижения этой цели введены два новых экономических индекса: "продуктовый индекс" Pi и "демографический индекс" DI. С помощью тождества, связывающего для каждой страны индексы Р/ и DI с индексом экономической продуктивности ЕРЧ выявлено существование глобального экономического параметра - критического значения индекса экономической продуктивности ЕР/. Выявлен экономический смыл этого глобального параметра. Научная новизна заключается в разработке двумерной интервальной классификации государств по масштабу экономики и масштабу страны. Использование этой классификации выявляет в результате фундаментальные черты распределения стран на плоскости {Население, ВВП}, глубоко укорененные в мировой истории и медленно меняющиеся во времени.
Ключевые слова: мировая экономика; экономические индексы; ВВП; население страны; масштаб экономики и масштаб страны; двумерная интервальная классификация.
DOI 10.24923/2222=243X2022=44.10
THE WORLD IN ECONOMIC INDICES DEPENDING ON A COUNTRY'S SIZE I. THE WORLD ON THE {POPULATION GDPj-PLANE
The purpose of the study is to develop a method and conceptual apparatus for identifying the distribution structure of countries on the {Population, GDPJ-plane. To achieve this goal, two new economic indexes have been introduced: the "product index" Pi and the "demographic index" DI. With the help of an identity linking the indices PI and DI for each country with the economic productivity index EPi, the existence of a global economic parameter - the critical value of the economic productivity index EPIwas revealed. The economic meaning of this global parameter is revealed. The scientific novelty of the research lies in the development of a two-dimensional interval classification of states according to the scale of the economy and the scale of the country. The use of this classification reveals, as a result, fundamental features of the distribution of countries on the plane {Population, GDP}, deeply rooted in world history and slowly changing in time. Keywords: world economy; economic indices; GDP; population of the country; an economic scale and a country scale; a two-dimensional interval classification.
УДК 339.97:330.43 ВАК РФ 5.2.5/08.00.14
© Seidameto va Z.S., 2022 <S> Temnenko V.A., 2022
Introduction
The world economy can be represented as a set of points-countries in different spaces of economic indices. The purpose of such a presentation can be considered to be the identification of the structural elements of the world economy, i.e., relatively closely related subsets of countries in the space of certain indices.Thereare two types of economic indices: "absolute" indices, which depend on the size of the country (for example, Gross Domestic Product (GDP)), and "relative" ones, which do not depend on the size of the country (for example, Gross Domestic Product Per Capita (GDP/PC)) [1].
The most important "absolute" economic characteristics of any country are the population of the country and the GDP of this country. In this article, we will present a picture of the world on the {Population, GDP}-plane. The article uses statistical data for 2021 from the database [2].
The purpose of this study is to develop a method and a conceptual apparatus for identifying and describing the structure of the distribution of countries on the {Population, GDP}-plane. It structures the following tasks, 1) to introduce convenient dimensioniess and normalized indices PI and Dl instead of the dimensional value of GDP and population size, which make it easy to compare different countries with each other;
2) bring to a dimensioniess form the record of the economic identity linking the GDP, population and the economic productivity of the country, and reveal the geometric meaning of this identity on the{DI, Pl}-plane;
3) to reveal the economic meaning of the global parameter EPIc, which appears in the record of this economic identity; 4) describe in detail the distribution of the countries of the world on the {Dl, PI}- plane; 5) on the basis of this description, create a two-dimensional interval classification of states according to the scale of the economy and the scale of the country.
The theoretical basis of this study was the publications [1 ], [3], [4], [5]. The practical significance of this study lies in the possibility of representing the world economy in the form of a certain matrix, the elements of which are lists of countries included in the same class according to two criteria: the scale of the economy and the scale of the country.
Main part
Economic indices PI and Dl. Instead of the parameter "Population", we will introduce normalized demographic index Dl:
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Dl = -
POP
max{P0P}
100 (%).
(1)
The numerator in this formula (1} "POP" is the population of some country,and thedenominatormaxJPOP} isthe population of thecountry with the largest population in the world in that same year. For many years, the country with the maximum population has been China. In 2021, the population of China was 1412.60 million people [2]. But India is not much inferior to it in terms of population (1392.01 million people in 2021 [2]), and perhaps someday India will be the country with the maximum population. An extrapolation of current trends shows that this could happen in 2023 [6].
The demographic index Dl is expressed as a percentage. Asa rule, we will omit the percent symbol (%) when writing Dl.
Instead of the dimensional parameter GDP, we will introduce a dimensioniess and normalized "product index" PI:
SEIDAMETOVA Zarema Seidaiievna, DScof Pedagogical sciences, Professor
TEMNENKO Valerii Anatoh'evich, PhD of Physics and Mathematical sciences, Associate Professor
Fevzi Yakubov Crimean Engineering-Pedagogical University, Simferopol, RC
PI =
GDP
max {GDP}
100(%).
(2)
GDP = POP ■ (GDP/PC),
(3)
PI = DI
EPI EPL'
(4)
EPI =
GDP/PC max[GDP/PC}
100 (%).
(5)
100 , , EPIC =--(%),
x
(6)
The numerator (2) is the GDP of the country of interest in current US dollars. The denominator of formula (2) is the maximum value of GDP achieved in the worid in the same year, and also expressed in current US dollars. For many years, the country with the highest GDP has been the USA. This country has had the largest economy in the world since 1871 [71. In 2021 ,theGDPof the USA was $22975.5 billion [2].
The product index PI in formula (2) is expressed as a percentage. The percent symbol (%), when writing PI, we will usually omit.
Global economic parameter EPIc. Using the identity:
where
max [POP}
^^GDF}'maXiGDP/PC} ^
Substituting the values of max{POP}, maxfGDP} and max{GDP/PC] given in the text into formulas (7) and (6), we get that in 2021:
h = 8.397,
EPL = 11.909.
(8) №
and dividing (3) by maxfGDP}, we can represent this identity in the following dimensionlessform, linking the indices PI and Dl:
where EPI is the index of economic productivity introduced by us earlier [3]:
The denominator of formula (5) contains the maximum value of GDP/PC achieved in the world in the same year. The EPI index is measured as a percentage, but we will usually omit the percent symbol (%) in the EPI entry.
Luxembourg has been the champion country in GDP/PC economic productivity for a number of years. In 2021, the GDP/PC value for Luxembourg was $136701.396/year [2]. In some years, two states - Monaco and Liechtenstein surpass Luxembourg in terms of GDP/PC. However, data on this economic value for Monaco and Liechtenstein are not every year present in the statistics of the World Bank and the International Monetary Fund. As a rule, other important economic indices Monaco and Liechtenstein are not present in world statistics, forexample, the Corruption Perceptions Index CPI or the budget index BLl [4]. For these reasons, the choice of Luxembourg as the champion country for the denominator in formula (5) is justified.
In formula (4), along with the economic indices ofaparticularcountry,there isa new fundamental economic characteristic of the world economy as a whole EPI:
Formula (4) shows that on the plane of economic indices [Dl, PI] the line EPI^const is a radial line passing through the origin with a slope equal to EPI/EPI(, All countries of the world are located on this plane in a square of 100 100 between the radial lines, corresponding in formula (4) EPI=100 (Luxembourg) and EPI=0.2 -this is the lowest EPI value in the world in recent years demonstrated by Burundi, the least productive country in the world. The radial line ER|=EPS, is the diagonal in this square.
Economic meaning of the global parameter EPIc. Having previously explored the world economy in the three-dimensional space of "relative" economic indices {EPI, BLl, CPI] ([1 ], [3], [4], [51), we found it useful to divide the entire axis of the index EPI into three zones: the "hot" zone (EP!>30%), the "cold" zone (EPI <10-12%) and the "warm" zone between them. In the "warm" zone, we identified two EPI-groups: the EPI-group "UpperWarm" and the EPI-group "LowWarm" with a boundary between them at EPI=s20%. In the "cold" zone, we identified four EPI-groups.The method for establishing the boundaries of EPI-groups is described in [4]. The EPI-groups introduced by us are the structural components of the world economy. Each EPI-group isa set of countries with similar values of the economic productivity index EPI (and, generally speaking, fairly close values of the other two economic indices CPI and BLl).
The boundaries between the "cold" and the "warm" economies on the axis EPI were established by us earlier empirically, based on the peculiarities of the distribution of countries of the world along this axis. This border has changed somewhat from year to year. However, the proximity of this empirical border to the given value of EPi.. (9) allows us to admit the possibility of identifying these two quantities: all countries of the world that are located on the {Dl, Pl}-plane on radial lines with a slope less than one belong
to the "cold" economies. For the "cold" economies, the inequality is satisfied
PI < DI.
(10)
Some "redundancy" ofthe population, defined by inequality (10) on the {DI, PI}- plane, in accordance with identity (4), is equivalent to the inequality:
EPI < EPIr
(11)
Inequality (11) means that this economy belongs to the zone ofthe "cold" economies.
Th e para meter EPi, defined by formulas (6) and (7) depends on the economic characteristics of three different states: China provides max{POP}, USA provides maxfGDP} and Luxembourg contributes max{GDP/PQ to these formulas.
Countries of the world on the plane of economic indices {DI, PI}. Fig. 1 (a-f) shows the distribution ofthe countries ofthe world on the plane of economic indices {DI, PI) in 2021. In each of these six figures, radial lines are drawn corresponding to EPI=100, EPI=30, EPI=20 and EP!=EPI. In the sector lying between the lines EPI=100 and EPI=30 there are the "hot" economies, The exact bottom of the hot economies sector varies between one and two percent on the EPi scale from year to year. The sector between EPI=30and EPI=EPic is where the "warm" economies are located. The EPI=20% line roughly separates the countries ofthe EPI-group UpperWarm from the countries ofthe EPI-group LowWarm. In the sector bounded from above by the diagonal line EPI= EPS, there are the "cold" economies.
Fig. 1a represents a 100x100 square on the {DI, Pl)-plane. In this figure, the vast majority of countries are concentrated in the lower left corner with small values ofthe indices DI and PI, This figure explicitly indicates the names of only a few countries with large values of the DI and PI indices: USA (Dl=23.52, Pl=100), China (CHN, DM100, PM75.91), India (IND, DM98.24, PI =13.23). In this figure (and in others too), the names of countries are presented in abbreviated form, in accordance with the ISO standard [8]. in addition to thesethree leading states in fig. la, in the 25x25 square in the lower left corner ofthe figure, the names of only two countries are shown: Japan (JPN, D!=8.88, Pl=21.47), which has the highest PI value inthis square, and Indonesia (IDN, DI—19.27, PI=5.16} with the largest DI value in this square. It can be considered that these two countries set some lower bounds on Dland Plfora special small group of three huge states USA, China, India. Using a term borrowed from astrophysics, we will
use the term "SuperGiant" to designate the states of this trio of states. At the same time, we will distinguish between an economy and a country: if DI>DijrM, then the economy belongs to the SuperGiant class on the economic scale; if PI>Pf|№r then the country belongs to the SuperGiant class on the country size scale. Accordingly, USA, China and India belong to the SuperGiant on the country scale class; USA and China also belong to the SuperGiant on the economy scale class. India does not belong to the SuperGiant on the economy scale class: the PI value for India is less than the PI value for Japan. This difference between the scale ofthe country and the scale of economies allows us to detect some structure of the world economy on the plane of economic indices and build a two-dimensional classification of states and territories on this plane. This classification will complement the previously mentioned one-dimensional classification along the axis EPI, dividing the world's economies into "hot", "warm" and "cold" ones.
Fig. lb is an enlarged part of fig. 1 a: this is a 25x25 square in the lower left corner of fig. la. This figure shows the ISO abbreviated names of all countries that have either Dl>5 or Pl>5 within this figure. Inside the small 5x5 box, the abbreviated names of only two countries are inscribed: Netherlands (NLD), which has the highest PI value in this box (Pl=4.43), and Thailand (THA) with the highest Di value in the 5x5 box (DM4.95).
We will use the term a "Giant Economy" to describe a state that has an economic index PI in the interval 5<PI<PIjpn. We will use the term a "Giant Country" to describe a country that has an economic index DI in the interval 5<DI<DIidn. For example, in accordance with fig. 1 b, Japan (JPN), Germany (DEU) and Russian Federation (RUS) are Giant Economies and Giant Countries. Italy (ITA)and Canada (CAN) belong to the Giant Economies class, but do not belong to the Giant Countries class. In accordance with fig. lb Pakistan (PAK) and Nigeria (NGA) belong to the Giant Countries but do not belong to the Giant Economies. The choice of the lower limit Pl=5% for the Giant Economies class Is due to the fact that in the band 0<D1<5 there isa fairly large gap in the PI index between Spain (ESP, PI-6.20), which is classified by this criterion as the Giant Economy and Netherlands (NLD, Pl=4.43}( which is not included in the Giant Economies class by this criterion.
The fig. 1 c shows an enlarged view of a small 5x5 square located in the lower left corner of fig. 1 b. We show on the fig. 1 c the abbreviated names
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e f
Fig. \. Countries of the world on the plane of economic indices {Dl, PI} in 2021
of all countries with PI >1% and/or DI>1%. In the small square in fig. 1c, in the lower left corner with a size of 1 xl, the abbreviated names of only two countries are indicated: Greece, which has
the maximum PI value in this small square (GRC, PI—0.94) and Rwanda (RWA, 01=0.92), which has the largest Dl in this small square.
■IM^.PHL
We will use the term a "Big Economy" to refer to states that have an economic index PI in the interval 1<PI<5. We will use the term a "Big
Country" to refer to states that have an economic index Dl in the interval 1<D!<5. For example, according to fig. 1c, Saudi Arabia (SAU, 01=2.51 f
PM3.62)and Poland (POL, DM2.68, PM2.93) belong simultaneously to the Big Economies and the Big Countries classes. According to fig. 1c Israel (ISR, DI =0.66, PM2.09) is the Big Economy but not the Big Country. Kazakhstan (KAZ, DM1.35, PM0.83) is the Big Country, but not the Big Economy.
The choice of the lower bound for the Big Economies at the level of Pl=1% is rather conditional. This choice can be motivated by the fact that in the band 0<DI<1%, there is the relative gap in the index PI between New Zealand (NZL,PM1.08), classified according to this criterion to the class of the Big Economies and Greece (GRC, PI=0.94), which is not included in the Big Economies class according to this criterion.
Thefig. 1 d is an enlarged view of the small 1 xl square located in the lower left corner of fig. 1c. We show on the fig. 1 d the ISO abbreviated names of all countries with PI>0.2 and/or Dl>0.2. In a small square 0.2x0.2 in size, located in the lower left corner of fig. Id, the abbreviated names of only two countries are given: Latvia (LVA, Dl=0.13, Pl=0.17), which has the highest PI value within this small square, and Jamaica (JAM, DM0.19, PI =0.066), which has the highest value Dl inside this small square.
We will use the term a "Medium Economy" to designate a state with an economic index PI in the interval 0.2<P!<1 (%). We will use the term a "Medium Country" to refer to a country that has an economic index Dl in the interval 0.2<Di<1 (%).
For example, according to fig. Id Hungary (HUN, DM0.69, PM0.80) and Kuwait (KWT, DM0.34, PM0.59) are the Medium Economies and the Medium Countries. Qatar (GAT, DM0.18, PM0.78) and Slovenia (SLV, DM0.15, PM0.27) are the Medium Economies but do not belong to the Medium Countries class. Bolivia (BOL, DM0.84, PM0.17)and Honduras (HND, DM0.72, PM0.12)are the Medium Countries but do not belong to the Medium Economies class.
The choice of the lower bound PM0.2 for the Medium Economies class can be motivated by a rather large relative gap along the PI axis between Slovenia (SLV, PM0.27), classified by this criterion as the Medium Economy class, and Latvia (LVA, PM0.17), by this criterion not included in the Medium Economy class.
Thefig. 1 eisan enlarged viewofa small square 0.2x0.2 in size, located in the lower left corner of the previous fig. Id. We show on fig. 1e in abbreviated form the names of all countries with Pl>0.04 and/or Di>0.04. Inside the small square 0.04 0.04 in size, located in the lower left corner of fig. 1 f, the names of only two countries are shown: Maldives(MDV, DM0.027, PI =0.022), which has the
largest PI index in this small square, and Cabo Verde (CPV, DM0.03985, PM0.0085), which has the largest index Dl in this small square.
We will use the term the "Small Economy" to describe a state that has an index PI in the range 0.04<PI<0,20. We will use the term the "Small Country" to describe a country that has Dl in the range 0.04<DI<0.20,
From fig. 1e it follows that, for example, Bahrain (BHR, DM0.105, Pi=0.169)and Estonia (EST, DM0.094, PI =0.1 58} belong to the "Small Economies" class and the "Small Countries" class. Iceland (ISL, DM0.026, PM0.111) and Malta (MLT, DM0.0365, PM0.0748) are the "Small Economies" but do not belong to the "Small Countries" class. Guyana (GUY, DM0.0558, PM0.0331 }and Eswatini (SWZ, DM0.0806, PM0.0204) are the "Small Countries", but do not belong to the "Small Economies" class.
The lower bound on the index PI for the "Small Economies" class is rather arbitrary. Its choice can be motivated by the fact that in the band 0<D!<0.04 there isa fairly large gap in the index PI between the Bahamas (BHS, DM0.0275, PM0.0484), included in the "Small Economies" class, and the Maldives (MDV, DM0.0272, PM0.0220), which by this criterion are not included in the "Small Economies" class.
Fig. 1 f shows an enlarged view of a small square of size 0.04x0.04 located in the lower left corner of the previous fig. 1e. This figure shows the countries with the lowest values of the economic indices Di and PI for 2021. This figure shows the names of all the countries and territories in the figure.
We will use the term the "Very Small Economy" to describe states and territories that have a Pl<0.04. We will use the term the "Very Small Country" to describe states and territories that havea Dl<0.04.
All states shown in fig. 1f belong to the "Very Small Economies" class and the "Very Small Countries" class.
Table 1 presents a description of the two-dimensional interval classification of states and territories of the world introduced here by the scale of the economy (index PI} and the scale of the country (index Dl).
This two-dimensional interval classification allows us to represent the world economy in the form ofa certain matrix 9^(lsa<6;i<)?< 6), the elements of which are lists of states that have the number « in terms of the country scale and the number p in terms of the scale of the economy. For example, matrix element q32 contains a list of countries belonging to the "Big
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Country, the Giant Economy"-class. In 2021, this list q32 contains seven countries.
Table 1 .Two-dimensional interval classification of states and territories of the world according to the scale of the economy and the scale of the country
We will denote this matrix Qaß by the term the Global Scaling Matrix. We will discuss this matrix in a separate publication.
Conclusions
In this paper new economic indices PI (the Product Index) and Dl (the Demographic Index) are introduced. When using the identity linking the PI and Dl indices with the economic productivity index EPI, the existence of a certain global economic parameter was revealed: the critical value of the economic productivity EPS,r dividing the world's economies into low-productive ones ("cold" economies, EPI< EPI)and highly productive ones ("warm" and "hot" economies, EPI> EPS,).
The study of the distribution of countries on the plane of economic indices {Dl, PI} made it possible to construct a two-dimensional interval classification of the countries of the world
according to the scale of the economy and the scale of the country.
References:
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A scale level number A scale level name Interval of the indices Dl and PI values
1 SuperGiant a SuperGiant Economy: PI>PIjpn=21 .47
a SuperGiant Country: DI>DljpN=19.27
2 Giant a Giant Economy: 5<PI<PIjpn
a Giant Country: 5<DI<DIjpn
3 Big a Big Economy: 1<Pls5
a Big Country: 1<DI<5
4 Medium a Medium Economy: 0.2<PI<1
a Medium Country: 0.2<DI<1
5 Small a Small Economy: 0.04<PI<0.2
a Small Country: 0.04<DI<0.2
6 Very Small a Very Small Economy: Pl<0.04
a Very Small Country: Dl<0.04
МИР В ЭКОНОМИЧЕСКИХ ИНДЕКСАХ, ЗАВИСЯЩИХ ОТ РАЗМЕРА СТРАНЫ, II. ГЛОБАЛЬНАЯ МАТРИЦА МАСШТАБОВ
Сейдаметова Зарема Сейдалиевна, доктор педагогических наук, профессор Темненко Валерий Анатольевич, кандидат физико-математических наук, доцент
Крымский инженерно-педагогический университет имени Февзи Якубова, Симферополь, Республика Крым
Цель исследования - на основании двумерной интервальной классификации стран по масштабу экономики и масштабу страны представить мировую экономику в виде набора элементов некоторой матрицы (}вр размерностью 6x6 (Глобальной Матрицы Масштабов). Первый индекс в матрице соответствует масштабу страны. Второй индекс соответствует масштабу экономики. Матрица существует в двух видах: 1} числовая матрица, элементом которой является число стран, имеющих соответствующие масштабы (уровень масштаба по размеру страны равен а, 1 < а < 6/ уровень масштаба по размеру экономики равен ¡}, 1 < (,); 2) матрица списков, элементами которой являются списки стран с соответствующими масштабами страны и экономики. Научная новизна заключается в публикации глобальной матрицы масштабов как в виде числового объекта, так и в виде матрицы списков. Исследование этой матрицы выявляет в результате фундаментальный закон мировой экономики: закон диагонального доминирования глобальной матрицы масштабов. Эко-
