The Limits to GrowthThe Club of Rome

ModelMeadows and Meadows

Prof. Prabha Panth, Osmania University

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• 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.

Global Environmental Model

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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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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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The Model• Analyses the simultaneous and

interrelated growth of 5 systems at the global level

1. Industrial growth2. Population growth3. Depletion of Non-renewable resources,4. Rising malnutrition, and 5. Deteriorating environment

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Assumptions1. Aggregate global analysis2. Non-renewable resources of the world are

finite and given,3. Technology is given, there is no technical

progress4. Present growth rates persist,5. There is no change in the pattern of growth,6. Present rates of population growth continue7. Aggregate pollution 8. Distribution inequalities of food, resources and

capital are included in the model.

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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 1 2 3 4 5 6

Linear growth (x + 2) 10 12 14 16 18 20

Exponential growth (y 2) 10 20 40 80 160 320

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Difference between Exponential and Linear Growth

Million Tonnes

Years0

Linear growth

Exponential growth

1 6

16 times

20

320

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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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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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• 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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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)

Approaching the limits

0

Copper (1000 million tonnes)

Years

T1

A

Depletion of copper

B

T0

So the reserves will be exhausted at T0 and not T1, because of increase in growth and decrease in reserves.

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Exponential Reserve Index of important minerals

Global Resource

S (years)

Av an gth rate %

e (years)

5 times increase

Aluminium 100 6.4 31 55Coal: 2300 4.1 111 150Copper 36 4.6 21 48Iron 240 1.8 93 172Petroleum 31 3.9 20 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.Prabha Panth

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– 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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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.

Pollution () Assimilative

capacity(+) Industrial Growth

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– 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.

Population – Feedback loops

Population (+) Birth rate

() Death rate

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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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– 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)

Industrial capital

(+) Net Investment (K)

() Depreciation

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– 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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Growth in demand for non-agricultural land

0

Agricultural Land

Time

Constant Supply

Demand for Non agricultural land

A

B

Supply of Agricultural land

T1T0

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The Computer ModelMeadows 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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Interacting SystemsSystem Affected by:

1. Industrial sector (exogenous growth)

Availability of Natural resources

2. Food (exogenous growth)

Pollution, population and natural resources

3. Population (exogenous growth)

Pollution, food and natural resources

4. Natural resources Growth of Industrial sector, population and food sector.

5. Pollution Growth of industrial and food sectors

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Standard Run: Overshoot and Collapse

time1900

Industrial production

Natural resources Population

Pollution

Food

COLLAPSE

C

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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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• 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.

Zero Growth

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Criticism

1. Zero growth rate criticised2. As Natural resources get depleted, price

will rise and signal new resources or new techniques.

3. New reserves will be found4. Zero growth is unfair to less-developed

countries5. Maximum share will still be taken by

developed countries. ----- Prabha Panth