The Malthusian Trap

The Malthusian Trap ensures that gains in income per person through technological advances are inevitably lost through subsequent population growth. An its most basic the Malthusian Trap an expression of the sustainability problem, which could also be called the Sustainability Trap. Thus the Malthusian Trap is an important abstraction to understand.

The trap as described by Thomas Malthus

The trap is named after Thomas Malthus, who first identified it in 1798 in his Essay on the Principle of Population. Early in his essay he famously states that: 1

I think I may fairly make two postulata:

First, That food is necessary to the existence of man.

Secondly, That the passion between the sexes is necessary and will remain nearly in its present state.

These two laws, ever since we have had any knowledge of mankind, appear to have been fixed laws of our nature.... Assuming then my postulata as granted, I say, that the power of population is indefinitely greater than the power in the earth to produce
subsistence for man.

Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will shew the immensity of the first power in comparison of the second.

By that law of our nature which makes food necessary to the life of man, the effects of these two unequal powers must be kept equal. This implies a strong and constantly operating check on population from the difficulty of subsistence. This difficulty must fall somewhere and must necessarily be severely felt by a large portion of mankind.

"The effects of these two unequal powers must be kept equal" means that after a disturbance (such as a new technology or lost of a key food source) the system will seek equilibrium, where the pressure of population growth is checked by the system's new carrying capacity.

For example, if a new invention doubles agricultural productivity, that doubles food per person. Health, longevity, and quality of life go up. But so does the survival rate due to better nutrition. Over a few generations this causes population to increase. As it rises, food per person falls, until it's back to the same equilibrium level of subsistence it was at before. The population is trapped into a subsistence level of life.

The modern expression of the Malthusian Trap
is the IPAT Equation

The Malthusian Trap can be expressed as a simple formula:

The IPAT Equation

The equation is I = P x A x T. This is short for:

Environmental Impact = Population x Affluence (consumption per person) x Technology (impact per unit of consumption)

The trap occurs because of the IPAT equation. Once the I in the equation, environmental impact, reaches the maximum an ecological niche can support the PAT factors have reached their limits. Population (P) cannot go up unless consumption per person (A) or impact per unit of consumption (T) goes down. Maximum population is thus trapped by whatever a society’s I, A, and T factors are.

Unless the laws of physics change the trap is inescapable. Typically what happens is a new technology comes along, such as an improvement in agriculture. This reduces T because there is less environmental impact per unit of consumption. This in turn raises A, affluence or consumption per person. Because people have more to eat population goes up. Population then rises until P times A times T equals I.

At this point the insidious nature of the trap takes hold. Due to replication and competition for survival of the fittest, P continues to grow and A starts to fall, because P times A times T cannot be greater than I except for cases of temporary overshoot. A continues to fall until consumption per person reaches starvation level. That puts the brakes on further growth of P. The end result is A is back where it started. P has grown some, but the same mass misery and poverty a society started out in before invention of the new technology has returned.

To summarize, as the PAT factors grow, total impact rises until it hits the carrying capacity of the system. After that, if one PAT factor rises then another must fall so that carrying capacity is not exceeded. If capacity is exceeded, that overshoot only can be temporary due to delays in the effects of the impact. As soon as those effects arrive, P or A will fall so that total impact does not exceed carrying capacity.

The Malthusian Trap is thus the equivalent of the sustainability problem. For the climate change problem, the natural resources depletion problem, the deforestation problem, and many more, the effects have not yet fully arrived.

Escape from the trap via the Industrial Revolution

Thomas Malthus pointed out there was no escape from the Malthusian Trap, also called The Iron Law of Population. He was right about the past, but not about the future, because soon the Industrial Revolution appeared. Population and affluence per person soared. The world had at last escaped the Malthusian Trap, as shown in this graph: 2

Graph of four modes of human history

Have we really escaped the Malthusian Trap?

Of course not. Escape is always only temporary. Sooner or later it's time to pay the piper. Civilization will soon enter Mode 4. It will be collapse or, if we manage to solve the problem, it will be sustainable and population need not collapse as shown on the graph. In no case will population continue to climb as in Industrial Growth Mode 3.


(1) The Malthus quotes are from an online copy of the complete Essay on the Principle of Population.

(2) The Four Modes of Human History graph is from Common Property Rights: A Process Driven Approach to Solving the Complete Sustainability Problem, a book.

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A Farewell to Alms

The best account of the Malthusian Trap, the Industrial Revolution that seemingly ended the trap, and why the Industrial Revolution occurred in England that we know of may be found in Gregory Clark's A Farewell to Alms: A Brief Economic History of the World, 2007.

Part One of the book is The Malthusian Trap: Economic Life to 1800. Up until then, modern man was no better off that his distant ancestors, in terms of health and average lifespan.

Part Two covers The Industrial Revolution. It presents explosive new data, collected in the period from 1200 to 1800 in England, that shows how evolutionary forces produced a suite of behavioral traits that were favorable to igniting the Industrial Revolution. The traits were "hard work, patience, honesty, rationality, curiosity, and learning." These were so far ahead of other nations, and so concentrated in London, that that's where the Industrial Revolution began.