Monday, September 11, 2017

Malthus: Not Wrong But Early



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?”