The Limits to Growth (LTG) is a 1972 report that discussed the possibility of exponential economic and population growth with a finite supply of resources, studied by computer simulation. The study used the World3 computer model to simulate the consequence of interactions between the Earth and human systems. Commissioned by the Club of Rome, the study saw its findings first presented at international gatherings in Moscow and Rio de Janeiro in the summer of 1971. The report's authors are Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III, representing a team of 17 researchers. The model was based on the work of Jay Forrester of MIT, as described in his book World Dynamics. The report's findings suggest that, in the absence of significant alterations in resource utilization and environmental destruction, it is highly likely that there will be an abrupt and unmanageable decrease in both population and industrial capacity. Although it faced severe criticism and scrutiny upon its release, the report influenced environmental reforms for decades. Subsequent analysis notes that global use of natural resources has been inadequately reformed to alter its expected outcome. Yet price predictions based on resource scarcity failed to materialize in the years since publication. Since its publication, some 30 million copies of the book in 30 languages have been purchased. It continues to generate debate and has been the subject of several subsequent publications. Beyond the Limits and The Limits to Growth: The 30-Year Update were published in 1992 and 2004 respectively; in 2012, a 40-year forecast from Jørgen Randers, one of the book's original authors, was published as 2052: A Global Forecast for the Next Forty Years; and in 2022, two of the original Limits to Growth authors, Dennis Meadows and Jørgen Randers, joined 19 other contributors to produce Limits and Beyond.
Purpose In commissioning the MIT team to undertake the project that resulted in LTG, the Club of Rome had three objectives:
Gain insights into the limits of our world system and the constraints it puts on human numbers and activity. Identify and study the dominant elements, and their interactions, that influence the long-term behavior of world systems. To warn of the likely outcome of contemporary economic and industrial policies, with a view to influencing changes to a sustainable lifestyle.
Method The World3 model is based on five variables: "population, food production, industrialization, pollution, and consumption of nonrenewable natural resources." At the time of the study, all these variables were increasing and were assumed to continue to grow exponentially, while the ability of technology to increase resources grew only linearly. The authors intended to explore the possibility of a sustainable feedback pattern that would be achieved by altering growth trends among the five variables under three scenarios. They noted that their projections for the values of the variables in each scenario were predictions "only in the most limited sense of the word" and were only indications of the system's behavioral tendencies. Two of the scenarios saw "overshoot and collapse" of the global system by the mid- to latter part of the 21st century, while a third scenario resulted in a "stabilized world."
Exponential reserve index A key idea in The Limits to Growth is the notion that if the rate of resource use is increasing, the number of reserves cannot be calculated by simply taking the current known reserves and dividing them 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 775/1.85=418 years, but the rate of chromium consumption was growing exponentially at 2.6 percent annually. If instead of assuming a constant rate of usage, the assumption of a constant rate of growth of 2.6 percent annually is made, the resource will instead last
ln ( 1 + 0.026 × 418 ) 0.026 ≈ 95 years {\displaystyle {\frac {\ln(1+0.026\times 418)}{0.026}}\approx {\text{95 years}}}
In general, the formula for calculating the amount of time left for a resource with constant consumption growth is:
y = ln ( ( r s ) + 1 ) r {\displaystyle y={\frac {\ln((rs)+1)}{r}}}
where:
y = years left; r = the continuous compounding growth rate; s = R/C or static reserve; R = reserve; C = (annual) consumption.
Commodity reserve extrapolation The chapter contains a large table that spans five pages in total, based on actual geological reserves data for a total of 19 non-renewable resources, and analyzes their reserves at the 1972 modeling time of their exhaustion under three scenarios: static (constant growth), exponential, and exponential with reserves multiplied by 5 to account for possible discoveries. A short excerpt from the table is presented below:
The chapter also contains a detailed computer model of chromium availability with current (as of 1972) and double the known reserves, as well as numerous statements on the current increasing price trends for discussed metals:
Given present resources consumption rates and the projected increase in the rates, the great majority of the currently important nonrenewable resources will be extremely costly 100 years from now. (...) The prices of those resources with the shortest static reserve indices have already begun to increase. The price of mercury, for example, has gone up 500 percent in the last 20 years; the price of lead has increased 300 percent in the last 30 years.
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