This path breaking model was the first that showed the interrelationship between different growing systems of the world, and how in the process of achieving infinite growth, finite natural resources would be depleted forming a Limit to Growth. Increasing pollution and loss of agricultural land would also affect growth and welfare.

1. The Limits to Growth
The Club of Rome
Model
Meadows and Meadows
Prof. Prabha Panth, Osmania University

2. Global Environmental Model
• The Club of Rome model was the first
global environmental model.
• Formulated by Meadows in 1972.
• Based on “Systems Dynamics” developed
by Jay Forrester.
• It uses computer simulation to study
dynamic behaviour of complex systems.
– Systems Dynamics: The structure of any
system is as important in determining its
behaviour as the individual components
themselves.
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3. Infinite Growth is not possible in a
Finite World
• The Club of Model was the first to show
empirically that:
– There are limits to growth of the world
economy due to:
– the finite stock of Non-renewable resources
and,
– the finite capacity of the environment to
assimilate pollution.
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4. Objectives of the Model
• To determine whether:
– The growth rates of population and capital
accumulation can be sustained in the future
– If so, then “how many people, at what level of
wealth, and for how long”
The answer Meadows found, depends on
the physical support available on Planet
Earth for population and economic
growth.
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5. The Model
•
Analyses
the
simultaneous
and
interrelated growth of 5 systems at the
global level
1. Industrial growth
2. Population growth
3. Depletion of Non-renewable resources,
4. Rising malnutrition, and
5. Deteriorating environment
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6. Assumptions
1. Aggregate global analysis
2. Non-renewable resources of the world are
finite and given,
3. Technology is given, there is no technical
progress
4. Present growth rates persist,
5. There is no change in the pattern of growth,
6. Present rates of population growth continue
7. Aggregate pollution
8. Distribution inequalities of food, resources and
capital are included in the model.
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7. Exponential Growth
• First explained by Rev. Malthus as the difference
between Arithmetic (linear) and Geometric
(Exponential) growth.
• Exponential growth suddenly becomes huge, due to
a rising base.
• So limits are reached quicker than expected.
Years
Linear growth
1
(x + 2)
Exponential growth (y
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2)
2
3
4
5
6
10
12
14
16
18
20
10
20
40
80
160
320
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8. Difference between Exponential
and Linear Growth
Exponential
growth
320
Million
Tonnes
16 times
Linear
growth
20
0
1
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6
Years
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9. The Five Growing Systems
• Meadows analyses the pattern of growth
of five growing sectors and their
interactions.
– 1. Non-renewable resources:
• The stock of Non-renewable resources on Earth is
constant.
• Economic development requires larger and larger
inputs of non-renewable resources.
• More the economic growth, more is depletion of
non-renewable resources.
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10. Static Reserve Index
• Static Reserve Index (S) shows the reserve
position or life index of a mineral in the ground.
S = Reserve of Non-renewable resource
Current year‟s extraction
• For example, known reserves of Copper = 1000
million tonnes,
• Extraction in the present year = 10 million
tonnes,
• S copper = 1000 million tonnes = 100 years
10 million tonnes
So it is assumed that the reserve will be
exhausted in 100 years
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11. • But there is a fallacy in this calculation.
• Every year with economic growth, the total
extraction increases.
• With each year‟s extraction, the reserve
stock in the mine decreases.
• Both these lead to faster depletion of the
non-renewable resource.
• The limit will therefore be reached quickly
and unexpectedly.
• Therefore Meadows introduces another
measure called Exponential Reserve Index.
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12. Exponential Reserve Index
• In this index, the increase in growth levels
and the fall in reserves are included to
estimate the life index of a mineral.
• It includes growth rate of extraction on
reserve position.
• He calls it the „Exponential Reserve Index‟
or „e‟
e = ln[(r.s)+1]
r
(ln = natural log, r = average rate of growth of the
resource, and s = static reserve index)
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13. Approaching the limits
A
Copper (1000
million tonnes)
So the
reserves
will be
exhausted
at T0 and
not T1,
because of
increase in
growth
and
decrease in
reserves.
Depletion of copper
B
0
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T0
T1
Years

14. Exponential Reserve Index of
important minerals
Global
Resource
Aluminium
Coal:
Copper
Iron
Petroleum
S
(years)
100
2300
36
240
Av an gth
rate %
31
3.9
6.4
4.1
4.6
1.8
e
(years)
31
111
21
93
20
5 times
increase
55
150
48
172
50
At present rates of extraction, all important minerals of
the world will be exhausted in the next 100 years!
Even a 5 times increase in reserves will push the limit
by only a few years.
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15. – 2. Pollution:
• Pollution levels increase with population, industrial
and agricultural growth.
• Because all three systems are growing, pollution
levels are also growing.
• A certain amount of pollution can be absorbed by
the environment,
• But after the threshold is reached, pollution will
grow exponentially and infinitely.
• There are no inbuilt mechanisms to control growth
of pollution and no stabilising factors that can
mitigate it.
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16. Pollution – Feedback loops
• Economic Growth adds to pollution (positive
feedback)
• Some pollution is absorbed by the environment.
This is called Assimilative Capacity (negative
feedback). It reduces the pollution levels.
(+) Industrial
Growth
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Pollution
( ) Assimilative
capacity
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17. Population – Feedback loops
– 3. Population Growth:
•
Population growth is also exponential, as explained
by Malthus.
• Death rate reduces population (negative feedback)
• Birth rate increases population (positive feedback)
• Death rate has been falling, leading to population
explosion.
(+) Birth rate
Population
( ) Death rate
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18. Population and Environment
• More population requires:
– More food
– more natural resources,
– causes more pollution
• Per capita consumption is also increasing
• Thus resource depletion and pollution are
driven by
– increase in population, and
– Increase in per capita consumption
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19. – 4. Industrial Growth:
• Increase in industrial growth depletes natural
resources and creates increasing pollution..
• Growth of capital i.e. Net Investment adds to
capital stock ( K) (positive feedback loop)
• Depreciation reduces capital stock (negative
feedback loop)
(+) Net
Investment
( K)
Industrial
capital
( ) Depreciation
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20. – 5. Nutrition and Food Availability
Increasing population, industrialisation and
urbanisation place great pressure on
agricultural land.
•
•
•
•
Land is finite.
Agricultural land diverted to non-agricultural use.
Use of chemical inputs destroy the soil.
Diminishing returns in Green Revolution
techniques.
• Skewed distribution of food,
• Malnutrition in less developed countries.
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21. Growth in demand for nonagricultural land
Demand for Non
agricultural land
A
g
r
i
c
u
l
t
u
r
a
l
A
Constant
Supply
B
L
a
n
d
Supply of
Agricultural land
0
T0
T1
Time
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22. The Computer Model
Meadows applies System Dynamics, taking
global data (1970) to analyse the total
impact of all the five growing systems.
• Extrapolates from 1900 into the future.
• Results compatible till 1970, when the
book was written.
• Future scenario of world growth may
follow the above path traced by the
computer model
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23. Interacting Systems
System
1. Industrial sector
(exogenous growth)
2. Food (exogenous
growth)
3. Population
(exogenous growth)
4. Natural resources
5. Pollution
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Affected by:
Availability of Natural
resources
Pollution, population and
natural resources
Pollution, food and natural
resources
Growth of Industrial sector,
population and food sector.
Growth of industrial and food
sectors
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24. Standard Run: Overshoot and Collapse
C
Natural resources
Population
Pollution
Food
Industrial production
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1900
COLLAPSE
time
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25. Policy conclusions
• Meadows suggested that there should be
“Global Equilibrium.”
• A piecemeal solution will not solve the
problem of collapse,
• All variables have to be attacked
simultaneously due to
• Interaction and interrelated impacts of
growth of economic and environmental
variables.
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26. Zero Growth
•
•
Industrial growth should be made zero
Investment = Depreciation.
Stabilise population growth. Growth rate
of population should be zero,
Birth rate = Death rate.
•
Change in technology:
Less polluting techniques.
Renewable resource technology
•
Less-developed countries may be
allowed to grow for some more time.
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27. Criticism
1. Zero growth rate criticised
2. As Natural resources get depleted, price
will rise and signal new resources or new
techniques.
3. New reserves will be found
4. Zero growth is unfair to less-developed
countries
5. Maximum share will still be taken by
developed countries.
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Prabha Panth