Assuming that 50-60% of the population of cities is working is probably too high. As a simple example, the third table at https://www.health.ny.gov/statistics/vital_statistics/2016/t... data for New York City for 2016. Total population is 8,537,673. Population under 18 is 1,798,888. Population over 64 is 1,155,075. That's 35% of the population right there.
Some of them might be working, of course. For the kids, this is not likely to be more than 10% (which would be _all_ the 16 and 17 year olds, pretty much). For the seniors, let's guess 33% (pretty much everyone under 70). That leaves 28% of the population in the kid-or-senior age range and not-working and 7% in the kid-or-senior age range and working.
To get to 50% overall working with those assumptions, you need 43% of the population to be prime age and working. The prime age population is 65% of the total. So you need 43/65 = 66% of the 18-65 age population working. But in 2017 (yes, I know, a year later; I haven't found the 2016 equivalent) https://www.osc.state.ny.us/reports/economic/labor-force-tre... claims a labor force participation rate of just about 60% for NYC (see page numbered 14 in the document, page 17 of the PDF). And that's the rate for 25-64, which should be higher than the 18-64 rate, because as the document notes "people between the ages of 16 and 24 are more likely to be in high school or college".
Page 15 of the document (page 18 of the PDF) does show labor force participation rates for 16-24 and 65+ in New York State and our "33%" above for seniors was likely a significant overestimate based on that, though it's hard to tell: NYC labor force participation may not match the overall state very well, obviously.
Anyway, under the (imo optimistic) assumptions above, something like 45% of the overall population of NYC is in the labor force. Or in other words if you ignore the 18% of the population that is children under 15, it's about 55%. So your estimate was pretty close if you ignore the existence of kids...
Or put another way, if the prime-age labor force participation rate is 60%, there's no way that 60% of the overall population is working. Just not possible.
I appreciate your statistics but I'm not quite sure how they are related to our discussion.
Most of the kids in NY state are living under the care and support of their parents and aren't working, therefore they shouldn't even be a factor in population/labor force participation metric.
Additionally, many of the old people who aren't working shouldn't be factored in either because they are receiving quite high pensions to live from, as well as social security.
When you factor this in, my initial ratios still stand. Out of the 325m people living in the USA, 45% are working (145m). When subtracting the 30% of Americans who are retired or under the care of parents, you are removing 100m people.
Therefore, as you say, the "prime age" labor force participation rate is 65% (145m/225m).
Applying this ratio to my original numbers, 45.5 million people are laborers in the Northeast. The other 25m either used to be laborers or are protected financially by laborers.
We cannot possibly say that an area like Amarillo TX, with just 100,000 laborers, is indicative of some nationally sustainable trend where cost of living is cheap and wages are still high.
This denies the existence of an extremely large block of humans, who are struggling despite earning decent money.