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This analysis looks wrong to me too, and I think I'd go further than @fmac and say that there are ways to make anyone a net productive citizen. There are probably barriers to accomplishing it, but its theoretically possible.
Adding a homeless / jobless beggar may seem always net negative. But if you can manage to rope in federal funds, or sympathetic donations from other areas you can turn that homeless / jobless beggar into a net bringer of wealth to the town. Or at the other extreme a single billionaire living in a town of ten thousand people. The billionaire basically pays all the taxes of the town. But that tax revenue gives the billionaire enormous leverage over all policy and enforcement. They can get out of just about any legal trouble in the town. They can get any building or new business approved for their friends, or denied for people that they don't like. Those are the theoretical reasons why I think your analysis breaks down.
In practical terms the story of the billionaire is usually more indicative of why towns are happy to add more people. Policy and policy enforcement can be carefully tailored in such a way that tax contributions and government services can be very equally balanced. Wealthy neighborhoods are often full of people who know how to manipulate the levers of local government, and are also full of people that are actively running the local government. Running governments requires human capital, and human capital tends to align with wealth and resources over time. Wealthy neighborhoods get better response times from emergency services, better access to public parks, and those parks are more likely to be kept clean and patrolled by the police. Their roads get repaved and fixed sooner. The schools get more oversight and quality. Successful businesses fill in the commercial space around those neighborhoods. The effects go on and on. The common phrase "you get what you pay for" applies to local government. Its hard to quantify it, but if you live in the different areas it just becomes very noticeable.
One major and obvious problem with your analysis that I saw in the discussion with fmac is that you are way over-counting the cost of schooling for a very simple reason: people aren't in school their entire lives. You need to offset the cost of school based on the number of years of their life that they will be in school. Just like if a road needs to be repaved every three years, you don't count the one time cost of repaving on every year's budget. You divide that spending across the three years. This does method does not even assume any benefits to schooling. To make the math easy lets just say people are only in school for 1/4 of their lives. So if the per student per year cost for a district is $20,000 you should instead think of it as $5,000.
Not if they are young or old enough.
73% of Americans not in paid work are either under 18 or over the Social Security retirement age. Admittedly some of the people over retirement age could work, although blue-collar workers are getting a lot slower at this age, and "net productive citizen" is making the stronger claim that they could work enough to, in expectation, pay for their own healthcare. The other groups of non-workers are the working-age disabled (9% - again most could do some work, very few could work enough to pay for their own healthcare), students (5% - these are people who society is already investing in to make them net productive citizens in the future), SAHMs and other carers (7% - most of these people are net contributors, but not in a way that is legible to the GDP statistics), and the stereotypically unproductive (6% across "temporarily unemployed", "early retirement" and "other").
The vast majority of able-bodied working-age people already are net contributors (40 hours a week at the going rate for reliable low-skill labour is enough almost everywhere across the first world). This is obfuscated by measuring contribution at household level - a typical household contains net-contributor parents and net-leech kids.
The US has federalised the cost of subsidising olds and undergraduates, but mostly localised the cost of subsidising kids. This means it makes sense for communities to try to attract retirees and students (the "eds and meds" strategy) and the federal subsidies that go with them, but to try to keep families with children out. This isn't true in other countries where more of the cost of schools is nationalised and more of the cost of social care for the elderly is localised.
The threshhold for a net productive citizen is very low in my mind.
There is a concept in economics called the velocity of money. Basically money doesn't just disappear when it is spent, it usually get reused and spent on other things. Higher velocity things usually cause more spending and re-spending.
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