The Malthusian Regime

I am late to a debate going on between Bryan Caplan and Greg Clark over the Malthusian Regime. Bryan essentially takes the stance that decreases in population should not be seen as key in raising the standard of living. Presumably because of increasing returns to scale in the production of technology.

However, it seems straight forward to me that that increasing returns in one factor of production are temporarily outweighed by decreasing returns in another. Overtime as technology accumulates the overall functional form moves from decreasing to increasing returns. That shift represents the transition from the malthusian regime to the modern epoch.

Below is a simple numerical example of this type of thing. Income is a constant returns to scale function in technology(we are thinking of ever more advanced capital), labor, and land.

Technology does not depreciate and its accumulation rate is increasing in the total population level. The population grows a steady 2%. Land is fixed.

At first income per capita is decreasing because land is fixed. However, eventually enough technology accumulates that its increasing returns production dominates the fixed quantity of land.

One has to remember, however, that population effects the growth rate of technology, not its level and that the underlying capital accumulation is driven by income, perhaps even income per capita if you consider minimum consumption constraints.

Therefore, it is possible that far from delaying the industrial revolution the black death brought on the industrial revolution by increasing per capita income at a high level of technology.

Basically what helps in this model is to build up a big population to increase the technology level and then to wipe a bunch of them out to increase income per capita. The historically unusual combination of technology and wealth will rocket you forward.