And A Flashier Illustration of Quadratic Growth

[This is part of my series on Thomas Malthus’ “Essay on the Principle of Population,” first published in 1798. You can find an overview of all my posts here that I will keep updated: “Synopsis: What’s Wrong with the Malthusian Argument?”]

In my last post, I showed the results of a simple simulation. My general point is that if some development spreads out over land, ie. in two dimensions, and the expansion is slower than the development at a location, then you should expect to see quadratic growth in the aggregate, at least in the growth phase. When further land for expansion runs out, growth should later slow down and come to a halt. Note that I don’t mean by “quadratic growth” that it is always a quadratic function, so this a pars pro toto (a part for the whole): the main behavior is a quadratic increase. For more information on quadratic growth, please turn to my other posts: here, here, here, here, and here.

There are many reasons why this is interesting, but one I am after at the moment is how this may lead to an artifact with “deep history” analyses. The contention with “deep history” is that you can predict outcomes in a cross section much later almost only from when a country made the move to agriculture perhaps millennia ago. Ashraf and Galor call it “time to transition” in their article “Dynamics and Stagnation in the Malthusian Epoch.” The “transition” here is the Neolithic transition to agriculture that began roughly 10,000 years ago. This appears to create very long-run connections: You find…