Population Dependence on Energy

Sam Birer
November 28, 2010

Submitted as coursework for Physics 240, Stanford University, Fall 2010


Thomas Malthus recognized in the late 1700s that biological growth has the capability to outstrip the growth of the resources necessary to sustain life, regardless of what those resources may be. [1] Those who have predicted a total Malthusian catastrophe after the world runs out of crude oil and easy energy have been labeled dangerously leftwing by political opponents, who time and again point to the steady march of technology as humankind's eventual savior. [2] While it is impossible to say exactly what technologies will develop between the present and the date in the future when oil and then coal run out, it seems likely that energy crises can never be completely averted.

A Modern Perspective

Economist Kenneth Boulding wrote extensively on the impact of technological advancement on the human condition, and by 1971 he had developed his "Utterly Dismal Theorem," in direct contradiction to the CATO Institute's assertion that "all aspects of material human welfare are improving in the aggregate." [2] This theorem states that:

Any technical improvement can only relieve misery for a while, for so long as misery is the only check on population, the [technical] improvement will enable the population to grow, and will soon enable more people to live in misery than before. The final result of [technical] improvements, therefore, is to increase the equilibrium population, which is to increase the sum total of human misery. [3]

Energy production is certain to be a major stumbling block for human growth and the world's development in the future, as in many ways it is as much of a limiting resource as food production. Even if we discover methods to expand our current ability to produce energy, we will continue to run into problems as the population increases to reflect our gains. And unlike food in the original Malthusian scenario, current energy production is not based on renewable resources, so there is no guarantee that there will ever be a rebound.

Carrying capacity Model

During the pre-industrial period, the global population may have peaked around a half-billion, which is a good number of non-industrialized people to imagine that the world capable of supporting. Based on energy growth from that date to the present, there is a remarkable level of correlation between global energy output and population. [4] Per capita energy consumption at the present date can be shown to be: [5,6]

(4.7 × 1020 J/Year) / (6.8 × 109 Persons) = 6.9 × 1010 J/Person-Year

This allows the construction of the following function, with x representing total world annual energy output in joules:

Global Population (x) = (1.42 × 10-11) x + (5 × 108 )

At some point in the future, it is inarguable that the world's hydrocarbon supply will run out, and we will need to rely entirely on other forms of energy. At this moment in time, approximately 15% of our energy comes from non-hydrocarbon sources, which is only enough to support around 1.5 billion of the world's nearly 7 billion current inhabitants. [4] While it is not encouraging, and so-called alternative energy sources are by no means perfect alternative, this demonstrates the likely grave consequences if society chooses to sweep the energy production problems under the carpet.

© 2010 Sam Birer. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] T. R. Malthus, "An Essay on the Principles of Population," ed. by P. Appleman (Norton,1976).

[2] J. M. Simon, "The State of Humanity: Steadily Improving," CATO Policy Report 17, No. 5, 131 (1995).

[3] K. E. Boulding, Collected Papers, Vol. 2 (Colorado Associated Univeristy Press, 1971), p. 137.

[4] "International Energy Outlook 2010," U.S. Energy Information Administration, DOA/EIA-0484(2010), July 2010.

[5] "BP Statistical Review of World Energy 2010," British Petroleum.

[6] "U.S. and World Population Clocks, U.S. Census Bureau.