Limits to Growth
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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 the consequence of interactions between the Earth's and human systems
The 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.
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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. 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% ansually 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:
| 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 assumtion 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 for oil running out in 1992 assuming constant exponential growth.
Books
- ISBN 0-87663-222-3 Second edition (cloth)
- ISBN 0-87663-918-X Second edition (paperback)
See also
- Donella Meadows' twelve leverage points to intervene in a system
- Economic growth
- Peak oil (Hubbert's curve)
- Energy crisis
External links
- Sound Interview: Dennis Meadows one of the members and authors of the book 09. october 2004 Global Public Media
- Rome Club Conference 2004: Limits of Ignorance
- Uppsala Protocol: how to act when one resource hits it's limit
it:Rapporto sui limiti dello sviluppo
