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# Limits to Growth

Limits to Growth is a 1972 book modeling the consequences of a rapidly growing world population and finite resource supplies, commissioned by the Club of Rome. Its authors were Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III. The book used the World3 model to simulate the consequence of interactions between the Earth's and human systems. The book echoes some of the concerns and predictions of the Reverend Thomas Robert Malthus in An Essay on the Principle of Population (1798).

Five variables were examined in the original model, on the assumption that exponential growth accurately described their patterns of increase. These variables are: world population, industrialization, pollution, food production and resource depletion. The authors intended to explore the possibility of a sustainable feedback pattern that would be achieved by altering growth trends among the five variables.

The most recent updated version was published on June 1 2004 by Chelsea Green Publishing Company under the name Limits to Growth: The 30-Year Update. Donnella Meadows, Jørgen Randers, and Dennis Meadows have updated and expanded the original version. They had previously published Beyond the Limits in 1993 as a 20 year update on the original material.

## Purpose

The purpose of Limits to Growth was not to make specific predictions, but to explore how exponential growth interacts with finite resources. Because the size of resources is not known, only the general behavior can be explored. The authors state in a subsection titled The Purpose of the World Model:

In this first simple world model, we are interested only in the broad behavior modes of the population-capital system. By behavior modes we mean the tendencies of the variables in the system (population or pollution, for example) to change as time progresses. A variable may increase, decrease, remain constant, oscillate, or combine several of these characteristic modes. For example, a population growing in a limited environment can approach the ultimate carrying capacity of that environment in several possible ways. It can adjust smoothly to an equilibrium below the environmental limit by means of a gradual decrease in growth rate, as shown below. It can overshoot the limit and then die back again in either a smooth or an oscillatory way, also as shown below. Or it can overshoot the limit and in the process decrease the ultimate carrying capacity by consuming some necessary nonrenewable resource, as diagramed below. This behavior has been noted in many natural systems. For instance, deer or goats, when natural enemies are absent, often overgraze their range and cause erosion or destruction of the vegetation.
A major purpose in constructing the world model has been to determine which, if any, of these behavior modes will be most characteristic of the world system as it reaches the limits to growth. This process of determining behavior modes is "prediction" only in the most limited sense of the word. The output graphs reproduced later in this book show values for world population, capital, and other variables on a time scale that begins in the year 1900 and continues until 2100. These graphs are not exact predictions of the values of the variables at any particular year in the future. They are indications of the system's behavioral tendencies only.
The difference between the various degrees of "prediction" might he best illustrated by a simple example. If you throw a ball straight up into the air, you can predict with certainty what its general behavior will be. It will rise with decreasing velocity, then reverse direction and fall down with increasing velocity until it hits the ground. You know that it will not continue rising forever, nor begin to orbit the earth, nor loop three times before landing. It is this sort of elemental understanding of behavior modes that we are seeking with the present world model. If one wanted to predict exactly how high a thrown ball would rise or exactly where and when it would hit the ground, it would be necessary to make a detailed calculation based on precise information about the ball, the altitude, the wind, and the force of the initial throw. Similarly, if we wanted to predict the size of the earth's population in 1993 within a few percent, we would need a very much more complicated model than the one described here. We would also need information about the world system more precise and comprehensive than is currently available.

## Exponential reserve index

One key idea that the book Limits to Growth discusses is that if the rate of resource use is increasing, the amount of reserves cannot be calculated by simply taking the current known reserves and dividing by the current yearly usage, as is typically done to obtain a static index. For example, in 1972, the amount of chromium reserves was 775 million metric tons, of which 1.85 million metric tons were mined annually. (See exponential growth.) The static index is 775 / 1.85 = 418 years, but the rate of chromium consumption was growing at 2.6% annually (Limits to Growth, pp 54–71). If instead of assuming a constant rate of usage, the assumption of a constant rate of growth of 2.6% annually is made, the resource will instead last 93 years ($= ln \left(ln \left(1.0 + 0.026\right) times \left(418 + 1\right)\right) / \left\{ ln \left(1.0 + 0.026\right)\right\}$ (note that the book rounded off numbers)).

In general, the formula for calculating the amount of time left for a resource with constant consumption growth is :

$y=frac\left\{Log\left(1-\left(1-g\right)*frac\left\{R\right\}\left\{C\right\}\right)\right\}\left\{Log\left(g\right)\right\}-1$

Where:
y = years left
g = 1.026 (2.6% annual consumption growth)
R = reserve
C = consumption (annually)

The authors list a number of similar exponential indices comparing current reserves to current reserves multiplied by a factor of five:

Years
Resource Consumption growth rate, annual Static index Exponential index 5 times reserves exponential index
Chromium 2.6% 420 95 154
Gold 4.1% 11 9 29
Iron 1.8% 240 93 173
Petroleum 3.9% 31 20 50

The static reserve numbers assume that the usage is constant, and the exponential reserve assumes that the growth rate is constant. For petroleum, neither the assumption of constant usage or the assumption of constant exponential growth was correct in the years that followed.

Whether intended or not, the exponential index has often been interpreted as a prediction of the number of years until the world would "run out" of various resources, both by environmentalist groups calling for greater conservation and restrictions on use, and by skeptics criticizing the index when supplies failed to run out. For example, The Skeptical Environmentalist (page 121) states: "Limits to Growth showed us that we would have run out of oil before 1992." What Limits to Growth actually has is the above table, which has the current reserves (that is no new sources of oil are found) for oil running out in 1992 assuming constant exponential growth.

## Criticism

Limits to Growth attracted controversy as soon as it was published. Yale economist Henry C. Wallich labelled the book "a piece of irresponsible nonsense" in a Newsweek editorial dated March 13 1972. Wallich's main complaints are that the book was published as a publicity stunt with great fanfare at the Smithsonian in Washington, and that there was insufficient evidence for many of the variables used in the model. According to Wallich, "the quantitative content of the model comes from the authors' imagination, although they never reveal the equations that they used." Considering that the detailed model and Meadows' et al justifications were not published until 1974 (two years after Limits to Growth) in the book Dynamics of Growth in a Finite World, Wallich's complaint about "the peculiar presentation of their work and by their unscientific procedures" had merit at the time.

Similar criticisms were made by others. Robert M. Solow from MIT, complained about the weak base of data on which Limits to Growth's predictions were made (Newsweek, March 13, 1972, page 103). Dr. Allen Kneese and Dr. Ronald Riker of Resources for the Future (RFF) stated:

"The authors load their case by letting some things grow exponentially and others not. Population, capital and pollution grow exponentially in all models, but technologies for expanding resources and controlling pollution are permitted to grow, if at all, only in discrete increments.

Writing for the Michigan Law Review, Alex Kozinski, a United States judge appointed by Ronald Reagan, discussed Limits to Growth at length at the beginning of his review of The Skeptical Environmentalist, calling the authors 'a group of scientists going by the pretentious name "The Club of Rome"'.

As described in the exponential reserve index section, it is claimed that Limits to Growth predicted oil running out in 1992 among other natural resources. It should be noted, however, that the authors of the report accepted that the then-known resources of minerals and energy could, and would, grow in the future, and consumption growth rates could also decline. The theoretical expiry time for each resource would therefore need to be updated as new discoveries, technologies and trends came to light. To overcome this uncertainty, they offered an upper value for the expiry time, calculated as if the known resources were multiplied by two. Even in that case, assuming continuation of the average rate of consumption growth, virtually all major minerals and energy resources would expire within 100 years of publication (i.e., by 2070). Even if reserves were two times larger than expected, ongoing growth in the consumption rate would still lead to the relatively rapid exhaustion of those reserves. On the other hand, reserves may continue to grow, considering the large amounts of minerals in the planet Earth. There is also the possibilities of space mining and recycling.

## Editions

• ISBN 0-87663-165-0, 1972 Edition
• ISBN 0-87663-222-3, 1974 Second edition (cloth)
• ISBN 0-87663-918-X, 1974 Second edition (paperback)
• ISBN 1-931498-58-X, 2004 The 30-Year Update