# How does low population growth increase the effect of accumulated wealth

This passage comes from page 10 of the translation of Thomas Piketty's book Capital in the Twenty First Century:

If the rates of population and productivity growth are relatively low, then accumulated wealth naturally takes on considerable importance, especially if it grows to extreme proportions and becomes socially destabilizing.

Why does low population growth exacerbate the effect of accumulated wealth?

Intuitively, I would think that an increasing population would mean more potential employees, thereby allowing already wealthy people to more easily offer low wages. By contrast, I would intuitively think that low population growth, and the resultant scarcity in employees, would force the wealthy individuals to offer higher wages.

Piketty's essential argument is that when the $r$ is the rate of return to wealth and $g$ is the economic growth rate, you will see wealth and economic power concentrate in the hands of the few when $r \gt g$. This presumes that the wealthy will reinvest their returns from wealth rather then spending it on consumption.
Low productivity improvements will lead to low growth in GDP per capita, and combining this with low population growth will then lead to low growth in total GDP, so these combined will lead to smaller values of $g$ than seen previously when both productivity and population were growing more quickly. This is probably not particularly controversial.
• the impact of low productivity improvements and low population growth on $r$, and therefore on whether the gap between $r$ and $g$ would in fact widen
• empirical evidence of whether $r \gt g$ has been true historically and globally
• whether further concentrations of wealth may in future change $r$
• whether Piketty's preferred solution of global wealth taxes and taxes on very high incomes (designed to reduce $r$) might also have an effect on $g$, and if so then in which direction and by how much