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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^[1] the consequence of interactions between the Earth's and human systems. The book echoes some of the concerns and predictions of 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 which 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, Jorgen 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.

Contents 1 Exponential reserve index 2 Criticism 3 Notes 4 References 5 Editions 6 See also 7 External links

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 ( (note that the book rounded off numbers)).

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

y = Years left
g = 1.026 (2.6% annual consumption growth)
R = Reserve 
C = Consumption (annual)

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

Resource	Static index	Growth rate	Exponential index	5 times reserves exponential index
Chromium	420	2.6	95	154
Gold	11	4.1	9	29
Iron	240	1.8	93	173
Petroleum	31	3.9	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 assumption was correct in the years that followed due to the OPEC's oil embargo, followed by a return to increasing production.

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 states: "Limits to Growth showed us that we would have run out of oil before 1992" (page 121). 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. (Other examples: [1] [2][3])

Limits to Growth attracted controversy as soon as it was published. Yale economist Henry C. Wallich labeled the book "a piece of irresponsible nonsense" in his March 13, 1972 Newsweek editorial. 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."(Newsweek, March 13, 1972, page 103)

Writing for the Michigan Law Review, Alex Kozinski, a Reagan-appointed judge, 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.

• "To Grow or not to Grow", Newsweek, March 13, 1972, pages 102-103
• Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III. (1972).
  The Limits to Growth. New York: Universe Books. ISBN 0-87663-165-0
• Henry C. Wallich, "More on Growth", Newsweek, March 13, 1972, page 86.

• 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

• Beyond the Limits
• Cornucopian
• Donella Meadows' twelve leverage points to intervene in a system
• Economic growth
• Energy crisis
• Future energy development
• Peak oil (Hubbert's peak)
• Malthusian catastrophe
• Negative Population Growth
• Overpopulation
• Paul R. Ehrlich
• The Population Bomb
• Population Connection
• The Revenge of Gaia
• System dynamics
• Zero Population Growth
• List of countries by fertility rate

• Revisiting The Limits to Growth: Could the Club of Rome Have Been Correct, After All? (By Matthew R. Simmons)
• 1999 Review by Club of Rome member
• The new version "Limits to Growth: The 30-Year Update" (ISBN 1-931498-58-X)
• A Synopsis of Limits to Growth: The 30 Year Update
• Sound Interview: Dennis Meadows one of the members and authors of the book 09. october 2004 Global Public Media
• What was there in the famous "Report to the Club of Rome"?
• Video clip 8.5min: Understanding Exponential Growth
• Uppsala Protocol: how to act when one resource hits its limit

• Chelsea Green Publishing
• MIT System Dynamics Group
• Core Statement of the Institute of Growth Research (summary)