With the election of Emmanuel Macron, Western Europe is now controlled by an almost entirely childless elite- the leaders of Germany, France, the UK (and Scotland), Italy, the Netherlands, Sweden, and the European Commission have zero biological children between them. This is another way in which the US is still quite different from Europe: within-race, well-off native-born men in the United States are more likely to be fathers than poorer men. Native-born women are slightly less likely to be mothers if they themselves have higher earned incomes, although since women in wealthier households are much more likely to be married, many women with low earned income are in quite wealthy households.
Among 25-54 year old parents, there isn’t much of a relationship– high-income mothers have fewer children than low-income mothers, and high-income fathers have about the same number of kids as low-income fathers, but it’s all over a fairly small range.
Across the country, there’s a fair amount of variation in where high-income men have more kids (though not always where you’d expect), but almost everywhere they are likely to have some kids.
The main reason why, overall, lower-income Americans have more kids than higher-income Americans (and why the under-18 population is poorer than the nation as a whole) is because of immigration- immigrants have more kids and immigrant parents are disproportionately low-income.
Update: In case you’re wondering what the deciles above represent in terms of income: