If you have any familiarity with the name Thomas Robert
Malthus it is probably based on the following assumption.

Draw the first quadrant of the cartesian plane.

Draw two functions. The first being f(x)=x and the second
being f(x)=x^2.

Now look and there’s a point where x=x^2.

That point is where growth in the linear function is
surpassed by growth in the geometric function.
As a purely mathematical proposition, it’s easy to see that they
intersect where x=1.

But to complicated the matters, we have those functions
actually stand in for something, then the linear is the growth in production
and the exponential is growth in population. Then you have at that intersection
point the place where human population exceeds the productions of technology
and then people will solve. (I’ll leave his policy prescriptions for another
day). As a thought experiment it seems to work, but it rests on two big
assumptions.

The first is that production is linear. Malthus was writing
at the early stages of the industrial revolution, but we are children of Moore’s
law. Technology has increased at the exponential rate in our lifetimes. Perhaps
he was just on the point of the curve where the exponential function looks
linear. Though this is a gross over-simplification. Moore’s law is just speed
of computer chips and we have to ask what the output of the technological
revolution is that makes our lives better.

The other assumption, of course is that population growth is
exponential. In current times especially in developed economies, that seems the
opposite of true, as western nations are worrying about how to deal with the
aging of populations as the later generation are not having babies at the
replacement rate for the population and countries are making policy to induce people
to have kids.

So, in a way, it looks like on the back of the envelope that
the prime conclusion is exactly backwards. Though the world population is
growing, the rate of growth is slowing and we are on target to peak. Now that
peak is so high that in Malthus’s day it would seem that his population growth
projection is correct, output is such that we haven’t met that point of intersection
point at a large scale.

But just because we haven’t met it yet doesn’t mean we won’t.
Though Malthus takes his inevitable meeting of that point as a reason to keep down
the working class, it can be a valuable metaphor for the inheritors of his economic
though. The entire economic problem is often defined in some way speaking of finite
resources and infinite wants, and that to me is trill true. Though we might not
seem to have gotten close to carrying capacity there have been scares with mass
famines thwarted by the green revolution and worries about peak oil averted by
greater drilling technology. These points can serve as a reminder of the
original Malthusian hypothesis as we deplete resources and create chaos on the
planet. In a way when we look at the most famous conclusion of Malthus the most
important the way to really judge him was not if he was right or wrong. It is
better to ask: “Was Malthus too early?”