Wednesday 12 August 2020

Gregory Clark on the Malthusian Trap

I've really enjoyed reading Gregory Clark's book A Farewell to Alms. It's been on my must-read-soon list for a long time, but I finally got to it over the last couple of weeks. I'll post a proper review of the book tomorrow, but in the meantime I wanted to focus on Clark's exposition of the Malthusian Trap - an explanation of why income per capita barely changed between ancient times (or even earlier) and the start of the Industrial Revolution. I've been a critic of Malthusian ideas in the past (e.g. see this post), so reading about this model was a good learning experience for me.

The basic model is laid out in the diagrams below (Clark credits this diagrammatic representation to a chapter by Lee and Schofield in this 1981 book). The x-axis on both diagrams is income per person. The top diagram shows the relationships between birth rate (BR) and income per person, and death rate (DR) and income per person. Notice that the birth rate increases with income per person. Higher incomes lead to more births on average. Notice also that the death rate decreases with income per person. Higher incomes lead to fewer deaths. That all seems rather intuitive. When the birth rate is equal to the death rate, the population is in a steady state (neither growing nor shrinking). That happens at an income per person of y*, and a population of N.

The bottom diagram shows the relationship between population and income per person, and this is where things get interesting. If income per person was to increase above y*, then we end up at an income per person of say y0 (with population N0). At that level of income per person, the population starts to increase over time (because in the top diagram, the birth rate is now higher than the death rate). And as population increases, it pulls income per capita down on the bottom diagram, until eventually the economy ends up back at the steady state income per person of y*.

The same thing happens in reverse if income per capita were to fall below y*. In that case, the death rate would exceed the birth rate, and the population would decrease over time. And as the population decreases, it pushes income per capita up until the economy ends up back at the steady state income per person of y*.

You might wonder why income per person and population are negatively related. Clark explains that it relates to diminishing marginal productivity of land:

In the preindustrial era land was the key production factor that was inherently fixed in supply. This limited supply implied that average output per worker would fall as the labor supply increased in any society, as long as the technology of that society remained unchanged. Consequently average material income per person fell with population growth.

In other words, because each additional person employed on the land would be less productive than other workers already working the land (diminishing marginal productivity), average productivity per worker would fall as more workers worked the land, and so average incomes would decrease as well.

And so, because the economy would always end up eventually back at the steady state income per capita of y*, income per capita remained fairly constant for thousands (or even tens of thousands) of years. Clark notes that:

English wages in 1800 on average were about the same as those for ancient Babylon and Assyria, despite the great technological gains of the intervening thousands of years.

However, the model is not just interesting for that fact. You can also use it to show some fairly perverse effects that the Malthusian Trap had on society. Consider what would happen if the general level of health in the population improved (such as through improved sanitation). As shown in the diagram below, that would imply a decrease in the death rate at every level of income - the death rate shifts down from DR0 to DR1. Now at the previous steady state income per person y0* (with population N0), the birth rate is higher than the death rate. The population will start to increase, and as a result income per person falls, eventually reaching the new steady state income per person of y1* and a higher population of N1. The improved sanitation perversely leads to lower income per person - it makes people worse off! As Clark notes:

This Malthusian world thus exhibits a counterintuitive logic. Anything that raised the death rate schedule - war, disorder, disease, poor sanitary practices, or abandoning breast feeding - increased material living standards. Anything that reduced the death rate schedule - advances in medical technology, better personal hygiene, improved public sanitation, public provision for harvest failures, peace and order - reduced material living standards.

On the other hand, consider the impact of an improvement in production technology that raises income per person at any level of population. This shifts the curve in the bottom diagram to the right, as shown in the diagram below. Society would temporarily be at a higher income per person y0 (with population N0), but since at that level of income per person, the birth rate exceeds the death rate, population would increase, with the economy eventually ending up back at the steady state income per person y*, but with a higher population of N1. As Clark notes:

In the preindustrial world, sporadic technological advance produced people, not wealth.

This model is very cool. I wish there was time for me to include it in the first week of my ECONS101 class, as a way of motivating the substantial change in income per person that arose after the Industrial Revolution. Indeed, that is what Clark uses the model for in his book (but more on that tomorrow).

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