Many thanks, Wofgang Fengler and Emi Suzuki for such a clearly written note. As a description of the effect of overall population growth on per capita income growth, this is very clear. This is, clearly, a very straightforward relationship.
But I am concerned it could lead to overly simplified conclusions. Populations may be growing because the elderly population is growing rapidly, whereas the working age population is declining and the younger age population is constant. Or population growth may be high because the labor force population is increasing rapidly, while both the old and young age age groups are declining.
Of course, populations with rapidly increasing old-age populations tend to have slower population growth, but not necessarily so. Populations with declining young-age growth rates, and increasing labor force growth rates are frequently those with the highest economic growth rates as well