Zinkina Korotayev Malkov 2014 Original Text

8/11/2019 Zinkina Korotayev Malkov 2014 Original Text

http://slidepdf.com/reader/full/zinkina-korotayev-malkov-2014-original-text 1/14

1

Julia Zinkina, Artemy Malkov,and Andrey Korotayev

A Mathematical Model of Technological, Economic, Demographic, and Social Interaction

between the Center and Periphery of the World System

PUBLISHED IN:

Socio-Economic and Technological Innovations: Mechanisms and Institutions / Ed. By Kasturi Mandal,

Nadia Asheulova, and Svetlana G. Kirdina. New Delhi: Narosa Publishing House, 2014. P. 135 –147.

Our previous research1 has indicated that the overall pattern of divergence/convergence betweenthe World System core (the “First World”) and periphery (the “Third World”) may be graphed as

follows (see Fig. 1):

Fig. 1. Dynamics of the difference between the core and periphery with respect

to per capita GDP Note: figures at the Y-axis denote how many times the average per capita GDP in the core washigher than the one in the periphery.2

As we see, in early 19th century the gap in per capita GDP levels between the World Systemcore and periphery was not very significant. However, there was an evident indicator thatdistinguished the World System core countries from the countries of its periphery in a rathersignificant way. We mean the literacy level (see Fig. 2):

1 Malkov A. S., Bogevolnov Yu. V., Khaltourina D. A., Korotayev, A. V. (2010). Toward the system analysis of theworld dynamics: Interaction of the World System core and periphery. Forecasting and Modeling Crises and World

Dynamics. Ed. by A. A. Akayev, A. V. Korotayev, G. G. Malinetsky. Moscow: LKI/URSS, 2010. P. 234 – 248 (inRussian); Malkov A. S., Korotayev A. V., Bogevolnov Yu. V. Mathematical modeling of the Interaction of the

World System core and periphery. Forecasting and Modeling Crises and World Dynamics. Ed. by A. A. Akayev,A. V. Korotayev, G. G. Malinetsky. Moscow: LKI/URSS, 2010. P. 277 – 286 (in Russian).2 Source: Malkov et al . Op. cit. P. 234, Fig. 1. Calculated on the basis of the following sources: World Bank. Op.

cit.; Maddison. Op. cit .



2

Fig. 2. Dynamics of literacy for the populations of the world system core

and periphery3

In the age of modernization the fastest economic and technological breakthrough wasachieved by those countries that had already attained sufficiently high levels of literacy by the

beginning of that age. We believe that this point is not coincidental, as it reflects the fact that thedevelopment of namely human capital became a crucial factor of economic development inmodernization age4. Our earlier research5 has indicated the presence of a rather strong ( R2 =0,86) and significant correlation between the level of literacy in the early 19th century and percapita GDP values in the late 20 th century. This, of course, provides additional support for the

point that the diffusion of literacy during the modernization era was one of the most importantlong-term factors of the acceleration of economic growth6. On the one hand, literate populationshave many more opportunities to obtain and utilize the achievements of modernization thanilliterate ones. On the other hand, literate people could be characterized by a greater innovative-activity level, which provides opportunities for modernization, technological development, andeconomic growth. Literacy does not simply facilitate the process of innovation being perceived

by an individual. It also changes her or his cognition to a certain extent. This problem wasstudied by Luria, Vygotsky, and Shemiakin, the famous Soviet psychologists, on the basis of theresults of their fieldwork in Central Asia in the 1930s. Their study shows that education has afundamental effect on the formation of cognitive processes (perception, memory, cognition). Theresearchers found out that illiterate respondents, unlike literate ones, preferred concrete namesfor colors to abstract ones, and situative groupings of items to categorical ones (note that abstractthinking is based on category cognition). Furthermore, illiterate respondents could not solve

3 Source: Malkov et al . Op. cit. P. 235, Fig. 2. Data sources: Meliantsev V. A. East and West in the Second

Millennium. Moscow: Moscow State University, 1996 (in Russian); Morrison Ch., Murtin F. The World

Distribution of Human Capital, Life Expectancy and Income: a Multi-Dimensional Approach. Paris: OECD, 2006.Table 4; UNESCO. Estimates and Projections of Adult Illiteracy for Population Aged 15 Years and above, by

Country and by Gender 1970 – 2015. 2010. http://www.uis.unesco.org/en/stats/statistics/ literacy2000.htm.4 See, e.g., Denison E. The Source of Economic Growth in the US and the Alternatives Before US. New York, NY:Committee for Economic Development, 1962; Schultz T. The Economic Value of Education. New York, NY:Columbia University Press, 1963; Scholing E., Timmermann, V. Why LDC Growth Rates Differ. World

Development 16 (1988): 1271 – 1294; Lucas R. On the Mechanisms of Economic Development. Journal of

Monetary Economics 22 (1988): 3 – 42, etc.5 Korotayev A., Malkov A., Khaltourina D. Introduction to Social Macrodynamics: Compact Macromodels of theWorld System Growth. Moscow: KomKniga/URSS, 2006. P. 87 – 91.

6 see also, e.g., Barro R. J. Economic Growth in a Cross Section of Countries. The Quarterly Journal of Economics 106/2 (1991): 407 – 443; Coulombe S., Tremblay J. F., Marchand S. Literacy Scores, Human Capital and Growth

Across Fourteen OECD Countries. Ottawa: Human Resources and Skills Development Canada, Statistics Canada,

2004; Naudé W. A. The Effects of Policy, Institutions and Geography on Economic Growth in Africa: AnEconometric Study Based on Cross-Section and Panel Data. Journal of International Development 16 (2004): 821 –

849; UNESCO. Education for All. Literacy for Life. EFA Global Monitoring Report – 2006 . Paris: UNESCO,2005. P. 143.

0

10

20

30

40

50

60

70

80

90

100

1800 1850 1900 1950 2000

L i t e r a c y r a t e , a d u l t t o t a l

( % o

f p e o p l e a g e s 1 5 a n d a b o v e )

Years

Core

Periphery



3

syllogistic problems like the following one – “Precious metals do not get rust. Gold is a precious

metal. Can gold get rust or not?”. These syllogistic problems did not make any sense to illiterate

respondents because they were out of the sphere of their practical experience. Literaterespondents who had at least minimal formal education solved the suggested syllogistic

problems easily.7 The GDP growth rates in the core were much higher than in the World System periphery

during all the 19th

century and the early 20th

century (see Fig. 3):

Fig. 3. Dynamics of relative annual GDP growth rates in the World System core and

periphery (nine-year moving averages), 1820 – 20078

In 1914 – 1950 the economic growth of both core and periphery experienced powerful

turbulences (actually, they were expressed in the core even stronger than in the periphery, as thecore in this period experienced both more powerful upswings and more profound busts). In the postwar period the GDP growth rates in the core and periphery became quite close to each other,and in the 1950s and 1960s we observe there quite similar (and, at the same time, very high)GDP growth rates. Since the late 1960s one can observe a certain trend toward the decline of theGDP growth rates in the core. Then this decline started in the periphery, but with a certain timelag, whereas in general the GDP growth rates in the periphery began to exceed the ones in thecore. This gap began to grow especially fast since the mid 1980s; since that time one can trace arather steady trend toward the GDP growth rate acceleration in the periphery against the

background of the continuing trend toward its deceleration in the core.In the meantime it is essential to take into account the fact that the periphery lags far behind

the core as regards the demographic transition. In the core it started much earlier; respectively,the first phase there also began much earlier; hence it was much earlier when the coreexperienced the mortality decline9. That is why in the 19th century the population growth rates inthe core were much higher than the ones in the periphery (see Fig. 4).

7 Luria A. R. Cognitive Development . Cambridge, MA: Harvard University Press, 1976; see also Ember C. R. 1977.Cross-Cultural Cognitive Studies. Annual Review of Anthropology 6 (1977): 33−56; Rogof B. Schooling and theDevelopment of Cognitive Skills. Handbook of Cross-Cultural Psychology. 4. Developmental Psychology. Boston:

Oxford University Press, 1981. P. 233−294.8 Source: Malkov et al . Op. cit . P. 237. Fig. 3. Data sources: World Bank. Op. cit.; Maddison. Op. cit. Nine-yearmoving averages (with consecutive decrease of the smoothing window at the edges).

9 See, e.g., Chesnais. Op. cit.; Korotayev, Malkov, Khaltorina. Op. cit .

-1

0

1

2

3

4

5

6

7

8

9

1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010

A n n u a l G D P g r o w t h r a t e s ( % )

Years

Periphery

Core



4

Fig. 4. Population dynamics of the World System core and periphery (thousands,

logarithmic scale), 1820 – 200810

However, after the Second World War the demographic transition in the World System corecountries was finished, the fertility there dropped down, and the population growth rates declineddramatically. In the meantime, during the same period most periphery countries were well in the

first phase of demographic transition (according to Chesnais’11 classification) – the death rates inmost periphery countries declined very significantly, whereas the birth rates still remained atvery high levels. As a result, in the majority of periphery countries the population growth ratesreached in the 1950s and 1960s their historical maximums. In these decades, equally high annualrates of GDP growth were accompanied by the population growth rates in the periphery beingmuch higher than in the core. As a result, per capita GDP growth rates in the core continued toexceed the ones in the periphery (see Fig. 4); correspondingly, in the 1950s and 1960s the gap

between the core and periphery continued to widen (see Fig. 5):

Fig. 5. Dynamics of relative annual per capita GDP growth rates in the World System core

and periphery (nine-year moving averages), 1820 –

200712

On the other hand, in the same decades most countries of the periphery managed to achieve asharp increase in literacy (and some other important indicators of the human capitaldevelopment), which, on the one hand, stimulated the GDP growth, and, on the other hand,contributed to a very significant decrease of fertility and population growth rates. As a result, inthe early 1970s the per capita GDP growth caught up with the ones in the core, and since the late1980s the average GDP growth of the periphery began to exceed more and more the one of the

10

Source: Malkov et al . Op. cit. P. 238, Fig. 4. Data sources: World Bank. Op. cit.; Maddison. Op. cit .11 Chesnais’ (Op. cit.).

12 Source: Malkov et al . Op. cit. P. 239, Fig. 5. Data sources: World Bank. Op. cit.; Maddison. Op. cit . Nine-yearmoving averages (with consecutive decrease of the smoothing window at the edges).

100 000

1 000 000

10 000 000

1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010

P o

p u l a t i o n ( t h o u s a n d s )

Years

Periphery

Core

-1

0

1

2

3

4

5

6

7

182 0 184 0 186 0 188 0 190 0 192 0 1940 1960 198 0 200 0 202 0

A n n u a l p e r c a p i t a G D P g r o w t h r a t e s

, %

Year

Core



5

core. As a result the relative gap between the per capita GDP of the core and periphery began todecrease.

Note that the slowdown of economic growth rates in the core and the acceleration of growthrates in the periphery were accompanied (and to a considerable extent were caused) by thefollowing processes-trends: 1a) the decrease of the share of investments in the GDP of the core(since the early 1970s); 1b) the increase in the share of investments in the GDP of the periphery

(since the early 1990s); 2a) the decrease of the macroeconomic effectiveness of the investments7

for the core (since the late 1960s); 2b) the increase in the macroeconomic effectiveness of theWorld System periphery (since the early 1990s) (see Figs. 6 and 7):

Fig. 6. Dynamics of the share of investments in the GDP of the core and periphery, %,

1965 – 200513

Fig. 7. Dynamics of the effectiveness of investments in the GDP of the core

and periphery, 1965 – 200514

Thus, the results of our previous research suggested the presence of semi-unconditionaldivergence between 1800 and the late 1960s, the situation of the absence of either salient

13 Source: Malkov et al. Op. cit. P. 240, Fig. 6. Notes: The World System core was identified for the calculations presented in this diagram with the high-income OECD countries, whereas the World System periphery wasidentified with the rest of the world. Data source for the calculations: World Bank 2010. Seven-year movingaverages (with consecutive decrease of the smoothing window at the edges).

14

Source: Malkov et al. Op. cit. P. 242, Fig. 8. Notes: The World System core was identified for the calculations presented in this diagram with the high-income OECD countries, whereas the World System periphery wasidentified with the rest of the world. Data source for the calculations: World Bank Op. cit. Seven-year movingaverages (with consecutive decrease of the smoothing window at the edges).

19

20

21

22

23

24

25

26

1965 1970 1975 1980 1985 1990 1995 2000 2005

Core Periphery

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

1965 1970 1975 1980 1985 1990 1995 2000 2005

Co re P eri ph ery



6

unconditional divergence or unconditional convergence for the 1970s and 1980s, and the presence of semi-unconditional convergence for the 1990s and 2000s.

Model description

In the two-component model the world was divided into the core and the periphery. The coreincludes high income OECD countries (the USA, Japan, Western Europe etc.). The periphery

includes all other countries (except for post-socialist countries of Eastern Europe and formerUSSR). At the first stage the model (1)-(2)-(3) was tested for each of the two regions separately:

l)aSN( =dt

dN 1 , (1)

dS

dt =bNS

, (2)

l)cSl( =dt

dl 1 . (3)

N is the population of the Earth, l is the proportion of literate population, S is the “surplus”

product produced at the given level of the World System technological development per capita; a, b, c are constants.This approach did not give any reasonable results, as in 1820 the periphery population exceededthe core population fourfold, while the core’s S exceeded that of the periphery less than twice,and the equation (2) of GDP and technology growth rapidly accelerated the GDP growth in the

periphery. Moreover, the indicators of the two selected regions were clearly interrelated in someway, so the equations of the one-component model could be just for the region’s “own”

parameters, but not for the parameters “induced” by the other region.

At the second stage we proposed a hypothesis that at certain conditions the periphery could

“catch up” with the center through the diffusion of the technologies developed in the center(which actually proceeds along with the capital diffusion). Naturally, this phenomenon cannot beregarded unilaterally, as the diffusion of capital and technology to the periphery becomes

possible only at both center’s economic benefit (connected with the costs decrease) and at the

appearance of a sufficient quantity of literate labor force in the periphery. Quantitative feature ofthe “convergence force” was chosen as follows:

p

pc

pc L

S S

S S C

.

The model also accounted for the factor of resource limitations and fundamental limitations.It should be noted that the accuracy of the mathematical description of the World System

macrodynamics regarded by the model significantly increases (especially for the latest decades)if the model accounts for a 25 – 30-year-long lag between literacy growth and the acceleration ofeconomic growth rates. This is not surprising, as the databases that we used (first of all, onesaffiliated with UNESCO) commonly regard literacy rate as the proportion of literate populationaged 15+. That is why literacy level growth (which has lately been proceeding almost only in theThird World countries) occurs each year due to the increase in the proportion of literate 15-year-olds (thanks to the gradual increase of primary education enrollment rate).

However, the growth of the proportion of literate 15-year-olds does not lead to any significantincrease of economy growth rates, as even in modern developing countries the majority ofliterate 15-year-olds do not get involved into manufacturing, but continue their education (evenif they start working in manufacturing, they are likely to get only low-qualified jobs where their

literacy does not lead to any remarkable productivity growth). The effect of literacy rate growth



7

within this given age cohort is likely to reveal itself only in 25 – 30 years when the representativesof this age cohort achieve the maximum level of their professional qualification.

Thus, the following lags were introduced into the model: 30 years between the literacy growthand the corresponding GDP per capita growth, and 10 years between the literacy growth and thecorresponding slowdown of the population growth rates.

Since late 19th century Kondratieff waves have been clearly observed in time series, especially

for economy growth rates. Thus, Kondratieff behavior with a 40 to 60-year-long period wasexternally introduced into the model.15 In the wave dynamics downswing phases are 1929 – 1947and 1973 – 1987, while upswing phases are 1895 – 1929, 1947 – 1973, and 1987 – 2008.

The following equations are proposed for the formalization of what has been said above. Let N c be population in the core, thousandsS c be “surplus” GDP per capita in the core

Lc be literacy rate in the core N p be population in the periphery, thousandsS p be “surplus” GDP per capita in the periphery

L p be literacy rate in the peripheryand the system of equation looks as follows:

)())(1)(()()(

)()(

1)30()()(

)()())10(1)(()()(

lim

t K t Lt S t Lc=dt

t dL

t K G

t Gt Lt S b=

dt

t dS

t C t N t Lt S t N a=dt

t dN

cccc

c

ccc

c

pcccc

c

(4)-(6)

)()()())(1)(()(

)(

)()()()(

1)30()()(

))10(1)(()()(

lim

t C t Lt K t Lt S t Lc=dt

t dL

t C t S t K G

t Gt Lt S b=

dt

t dS

t Lt S t N a=dt

t dN

c p p p p

p

c p p p

p

p p p p

p

(7)-(9)

G = N cS c + N pS p Global GDP, $ thousands

p

pc

pc L

S S

S S C

“convergence coefficient”describes the interaction of thetwo components of the system

Glim = $400 trillion dollars Fundamental limitation K (t ) Kondratieff dynamics

Table 1 states the values of equations’ coefficients and basic data:

Table 1. Values of equations’ coefficients, basic data

Core Periphery «Convergencecoefficient»

ac 2,1∙10- N c 1,6∙10 a p 3,3∙10

- N p 9,0∙10 α 4,0∙10-

bc 2,7∙10- S c 580 b p 3,7∙10- S p 120 β 4,0∙10-

cc 1,4∙10- Lc 0,42 c p 5,0∙10- L p 0,10 γ 1,0∙10-

Component α N pC describes the migration from the periphery to the core, while the migrationfrom the core to the periphery is negligible. We suppose that the volume of migration is

15

Korotayev A., Tsirel S. 2010. A Spectral Analysis of World GDP Dynamics: Kondratieff Waves, Kuznets Swings,Juglar and Kitchin Cycles in Global Economic Development, and the 2008 – 2009 Economic Crisis. Structure and

Dynamics 4/1: 3 – 57. URL: http://www. escholarship.org/uc/item/9jv108xp;16 Following Angus Maddison (Op. cit.) calculations here and below are made in рinternational 1990 dollars, PPP.



8

proportionate to the periphery literacy rate and to GDP per capita discrepancy between the coreand the periphery (as it is mostly literate people in search for better lives who migrate).

Component β S cC describes the diffusion of capital and technology to the periphery. Wesuppose that both capital and technology start flowing actively only at a sufficient literacy levelof the interacting regions (this is why C is included into L p), as well as t a sufficient GDP percapita discrepancy S between the regions.

Component γ LN pC describes literacy diffusion to the periphery.Second equations of the system (dynamics of S ) are to be regarded separately. Kremer-Jones

equation looks likedT

dt =bNT .

It describes the dynamics of technology development. Kremer and Jones supposed that therelative technology growth rates are proportionate to population number: the more people, themore inventors17. It should be accounted here that Kremer and Jones imply summing theinnovation, i.e. not only does a larger number of people produce more innovations, but they

produce more complementary innovations, not repeating ones. This is possible only if the massof people represents a coherent system. Kremer and Jones regarded the equation for the World

System and stated that it would not work for it separate parts.Indeed, as we have seen above, the periphery having a much larger population did not produce a larger number of innovations than the core. Among other circumstances it wasconnected with the fact that the periphery did not represent a holistic system, and did not “sum

up” its inventions: the innovations made in Africa did not develop the Latin America

innovations, neither did they improve the living standards of South Asia.With regard to this we proposed an alternative equation for technology growth which in our

model is associated with S :

bSL=dt

dS .

The growth rates of technology and GDP per capita are proportionate to literacy rate. Thus, we

suppose that namely literacy provides for the additivity of the innovations.From the point of view of the basic one-component model of the World System development,

replacing N for L does not “spoil” the dynamics, because, as we have seen above, N is proportionate to L almost in the whole diapason of the demographic transition.

Retrospective numerical calculation from 1800 till 2010

Fig. 8 presents the results of quantitative calculation on the time diapason from 1800 till 2010

17 Kremer M. Population Growth and Technological Change: One Million B.C. to 1990. The Quarterly Journal of Economics

108 (1993): 681 – 716; Jones Ch. I. The Shape of Production Functions and the Direction of Technical Change. The Quarterly Journal of Economics 120 (2005): 517 – 549.



9

Fig. 8. Parameters of order. Empirical and theoretical curves

Core Periphery

P o p u l a t i o n ( b i l l i o n s )

P e r c a p i t a G D P

( t h o u s a n d s o f i n t e r -

n a t i o n a l d o l l a r s * )

L i t e r a c y ( % )

*Constant international 1990 dollars, PPP. Here and below black curves stand for thecalculation, while grey marks represent historical data.

Fig. 9 describes dynamics of the difference between the core and the periphery as regards percapita GDP. Fig 10 presents economic growth rates of the core and the periphery.

0.1

0.2 0.3

0.4

0.5

0.6

0.7

0.8

0.9

18001850190019502000

Н а с е л е н и е

( м и л л и а р д

с е л е н и я

в * )

0

1 2

3

4

5

6

7

1800 1850 1900 1950 2000

0.5

1 1.5

2

2.5 3

3.5

4

4.5 5

1800 1850 1900 1950 2000

0

20

40

60

80

100

18001850190019502000

Г р а м о т н о с

т

0

20

40

60

80

100

1800 1850 1900 1950 2000

0

5

10

15

20

25

30

1800 1850 1900 1950 2000

В В П

н а д у ш

( т ы с я ч и д о л



10

Fig. 9. Difference between the core and the periphery with respect to per capita GDP

H o w

m a n y t i m e s i s t h e p e r c a p i t a G D P o f t h e

C o r e h i g h e r t h a n t h e o n e o f t h e P e

r i p h e r y



11

Fig. 10. Indicators of economy growth rates. Empirical and theoretical curves

Core Periphery

A n n u a l G D P g r o w t h r a

t e ( % )

A n n u a l p e r c a p i t a G D P g r o w

t h

r a t e ( % )

FORECAST

The model check on the basis of historical data shows that it describes rather accurately the maintrends connecting such key variables of the global dynamics as the world population, GDP, andeducation. This result allows us to use the model not only in retrospective, but also forforecasting as well. The forecast horizon was chosen as half a century, as this is the characteristictime scale for the variables specified. The forecast is based on the model that takes into accountthe latest Kondratieff wave. The results of the calculations made according to the model allowmaking the following forecast: the reduction of the core-periphery discrepancy which has beenobserved since early 1970s (and has been especially fast since the late 1980s) will continue in the

forthcoming decades but will be much slower than in 1998 – 2013 and by 2050 this discrepancy(in GDP per capita) will decrease from 7:1 to 4.5:1.

Economy growth rates in the core will go down to 1%. In the periphery this indicator willsignificantly go down around 2030 (GDP growth rates will fall to 3% per year, while GDP percapita growth rates will fal to 1.7%); however, by 2050 these indicators will rise somewhat,reaching 3.5% and 2.5% accordingly.

One of the most important results of the proposed forecast looks as follows. Our inertial 18 population forecast exceeded significantly the UN medium population forecast (marked by greyasterisks in Figs 11 – 12). This forecast indicate that with the inertial development scenario theWorld System will significantly exceed the Earth’s carrying capacity in the second half of our

18 The inertial forecasts were generated by the mathematical model (4)-(9) with those values of parameters that

produced the best fit with the empirical data for the last two centuries.

0

1

2

3

4

5

6

1800 1850 1900 1950 2000

Т е м п

ы р о с

н и я ( % )

-1

0

1

2

3

4

5

6

7

8

1800 1850 1900 1950 2000

-1

0

1

2

3

4

5

6

1800 1850 1900 1950 2000

Т е м п ы р о с т

В В П н а д

у ш

-1

0

1

2

3

4

5

6

1800 1850 1900 1950 2000



12

century, which can lead to catastrophic consequences (see Fig. 12). Our further research hasmade it possible to identify the zone of the risk of such sociodemographic catastrophes inTropical Africa19.

Interestingly, sustainable development scenario is possible only at radical increase of thecore’s support for the peripheral educational programs (especially in Tropical Africa). In thecalculations, the results of which are shown in Fig. 12, the value of the coefficient “responsible”

for education diffusion (γ coefficient in equation (9) above) was increased twice in comparisonwith the value characteristic for the current time.

19 Goldstone J., Korotayev A., Zinkina J. Social-Demographic Risks of Humanitarian Disasters in Tropical Africa

and Means of Their Prevention. Submitted for publication in the Population and Development Review ; KorotayevA., Zinkina J. Decrease of Fertility as a Factor of Sociopolitical Stabilization in the Least Developed Countries.World Dynamics. Regularities, Trends, Perspectives. Ed. by A. Akayev, A. Korotayev, S. Malkov. Moscow:KomKniga/URSS, 2013. P. 243 – 263.



13

Fig. 11. World population and GDP. Inertial scenario. Forecast up to 2100a) World population, billions

* medium UN forecast

b) World GDP, trillions of dollars

6

7

8

9

10

11

12

13

14

2 0 2 0

2 0 4 0

2 0 6 0

2 0 8 0

2 1 0 0

т р и л л и о н ы

0

50 100

150

200

250

300

350

400

2 0 2 0

2 0 4 0

2 0 6 0

2 0 8 0

2 1 0 0



14

Fig. 12. World population and GDP. Sustainable development scenario. Forecast up to 2100a) World population, billions

* medium UN forecast

b) World GDP, trillions of dollars

6

6.5

7

7.5

8

8.5

9

9.5

10

2 0 2 0

2 0 4 0

2 0 6 0

2 0 8 0

2 1 0 0

т р и л л и о н ы

0

50

100

150

200

250

300

350

2 0 2 0

2 0 4 0

2 0 6 0

2 0 8 0

2 1 0 0

Documents

Zinkina Korotayev Malkov 2014 Original Text