On Malthus's "An Essay on the Principle of Population"

The gist of Malthus's "An Essay on the Principle of Population" is generally summarized as follows.

"Population, when unchecked, increases in a geometrical ratio; subsistence increases only in an arithmetical ratio." (Population, when unchecked, increases in a geometrical ratio; subsistence increases only in an arithmetical ratio.)

However, the original text of "An Essay on the Principle of Population" is not necessarily summarized so neatly.

The actual "Essay on the Principle of Population" is written as follows*.
*The following citations use "Selected Works of British Economics" (Kenkyusha) as the text. Page numbers refer to this book.
The Japanese translation is by Grok.

It may safely be pronounced, therefore, that population, when unchecked, goes on doubling itself every twenty-five years, or increases in a geometrical ratio.

(ibid.p31)

Therefore, it can be safely asserted that if population is not checked, it will double every twenty-five years and increase in a geometrical ratio.

Taking the whole earth, instead of this island, emigration would of course be excluded; and, supposing the present population equal to a thousand millions, the human species would increase as the numbers, 1, 2, 4, 8, 16, 32, 64, 128, 256, and subsistence as 1, 2, 3, 4, 5, 6, 7, 8, 9.

(ibid.pp.35-36)

If we consider the entire earth instead of this island, emigration would of course be excluded. And, assuming the current population is one billion, the human species would increase according to the numbers 1, 2, 4, 8, 16, 32, 64, 128, 256, and the means of subsistence would increase according to 1, 2, 3, 4, 5, 6, 7, 8, 9.

Although no difficult mathematical formulas appear in Malthus's "An Essay on the Principle of Population,"
"Population, when unchecked, increases in a geometrical ratio; subsistence increases only in an arithmetical ratio."
If Malthus's assertion is expressed as a mathematical formula, it becomes the following.

This is often cited in mathematics books as a basic example of differential equations (and logistic curves).

Mathematical Model (Grok's explanation)

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