Hollis B. Chenery compared the manufacturing sectors in a variety of countries and found that, all else being equal, if one country was twice as populous as another, output per worker was 20 percent larger. This is a very large positive effect of population size no matter how you look at it. More relevant are studies of industries as wholes. Though the best analyses are dated, their data are surely still valid. This effect is very large.
Productivity goes up roughly with the square root of output.
That is, if you quadruple the size of an industry, you may expect to double the output per worker and per unit of capital employed. The effect Chenery saw in economies as wholes, together with the effects seen in individual industries, constitute strong evidence that a larger and faster-growing population produces a greater rate of increase in economic efficiency. The phenomenon called learning by doing is surely a key factor in the improvement of productivity in particular industries and in the economy as a whole. A doubling in the cumulative production of a particular airplane led to a 20 percent reduction in labor per plane. The economic importance of learning by doing clearly is great, and the role of a larger population in speeding learning by doing is clear.