Another thought on migration and population density

Why is Kansas so sparsely populated, while Manhattan is brimming with souls? Anyone in Kansas can move to Manhattan and vice versa. So what gives?

I say it's because the marginal productivity of labor in the sectors in which Kansas has a comparative advantage (specifically, agriculture) is much higher than the marginal productivity of labor in the sectors where Manhattan has an advantage (everything else, more or less). With modern agricultural techniques, one farmer can cultivate an immense amount of acreage. The surplus rural population in the United States long ago left for the cities. The reason Bangladesh is so densely populated and so very poor is that the surplus Bangladeshi population cannot freely move to Manhattan (or wherever else). Thus they are trapped in a situation where each additional person has a miniscule marginal product (globally speaking) and the people are thus desperately poor.

It's a vicious cycle, because the very low marginal product of each person keeps wages very low, meaning that families need more workers to support themselves, keeping family sizes up. Further, the low wages make investing in capital goods less economical compared to just buying more labor. In the United States, rural workers fed up with low wages left, driving up wages and making investment in capital goods more appealing, which further reduced the demand for agricultural labor, driving more workers to the city, until we reached the point we are at now, with Kansas being so sparsely populated that you'd need about 235,000 Kansan square miles to get the population of New York City. Kansas is immensely productive with a low population, while NYC is immensely productive with a high population, and the differences in wealth between the two are, on a global scale, so small as to be nonexistent. (A rural Kansan might envy a wealthy Manhattanite, but to a Bangladeshi, both are fabulously wealthy.)

I think this argument also answers the anti-free trade argument I've heard, claiming that free trade impoverishes countries whose comparative advantage, on the open market, is in agriculture or resource extraction. What impoverishes those countries isn't free trade, it's the existence of national borders and the accompanying restrictions on migration. If Kansas were an independent country, it'd be brimming with the desperately poor today. Instead, they all moved to the city. Globally, we need to let the same dynamic work.