# Limits to Growth

Limits to Growth was a 1972 book modeling the consequences of a rapidly growing global population, commissioned by the Club of Rome. Donella Meadows was its lead author. The book used the World3 model to simulate[1] the consequence of interactions between the Earth's and human systems.

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.

## 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 418 years ( = 775 Mmt/1.85 Mmt/year), but the rate of chromium consumption was growing at 2.6% annually (Limits to Growth, pages 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(ln(1.0 + 0.026) (418 + 1))/ln(1.0 + 0.026)) (note that the book rounded off numbers).

In the book, they list quite a few of these exponential indices for both the current reserves, and for five times the current reserves:

ResourceStatic indexGrowth rateExponential index5 times reserves exponential index
Chromium4202.695154
Gold114.1929
Iron2401.893173
Petroleum313.92050

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.

The exponential index has often been misquoted, 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.

## Criticism

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 for 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" has merit.

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 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”.' [2]. Another harsh critic of Limits to Growth was Lyndon LaRouche, who authored a 1983 book There Are No Limits to Growth and included the Club of Rome prominently in his view of a global Malthusian conspiracy. [3]

Nevertheless, many today think that the overall message was accurate: the resources of the Earth are finite and are thus, inevitably, subject to natural limits.[4]

## Notes

1. ^  The models were run on Dynamo, a simulation programming language.

## References

• "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: University Books. ISBN 0-87663-165-0
• Henry C. Wallich, "More on Growth", Newsweek, March 13, 1972, page 86.