American cities are changing and San Francisco is in the vanguard of that change. The great American metropolises of the 20th century got that way because they attracted vast migrations of country people and immigrants, forcing them into more or less radical equality and propinquity. Despite all efforts to stop it -- some of which, like rent control, may be counterproductive -- San Francisco is rapidly careening towards a state where ONLY high-income white and Asian college-educated professionals and the long-term homeless can afford to live there.

San Francisco is a microcosm for American inequality, pushing all its residents toward extreme wealth or relative poverty.

San Francisco's expensiveness seems as natural and eternal as the fog pouring through the Golden Gate. And the main culprit is not surprising: According to a 2013 survey by financial publisher Kiplinger, the city’s housing costs are nearly three times the national average. Earlier this year, the National Low Income Housing Coalition calculated that the hourly wage necessary to rent a two-bedroom “fair-market-rate” apartment in San Francisco is $37.62, higher than in any other metro region in the United States. (A fair-market rent is equivalent to the 40th percentile of the typical rent for a standard unit.) The numbers for actual market-rate rents are just as bad. Estimates vary, but in November 2013, data compiled by the real estate site Trulia pegged the median monthly cost of a two-bedroom apartment in San Francisco at $3,250—the highest of any metro region in the country. By September 2014, the same measure had jumped to $3,600.

Of course, San Franciscans also tend to make more money than people living in more affordable regions. Census data from 2013 place the median household income of the San Francisco–Oakland–Hayward metropolitan area at $79,624, behind only the D.C. region. Ironically, that’s almost exactly the annual income required to afford a fair-market rent for a two-bedroom apartment, which means that half of the people living here can’t actually afford what a “fair” market demands. (It also means that those currently enjoying rent-controlled units—at least the ones whose landlords aren’t threatening evictions—are very lucky indeed.)

Which brings us again to the pressing question: Why, when it has become economically irrational to do so, do we stay?

Getting clarity on this mystery requires a detour into how economists think about a couple of concepts, the first being happiness. Happiness, as it is generally understood, implies that one is feeling good in the moment. If we were motivated solely by happiness, we’d move to whatever place made us the most happy and stay there until circumstances changed. And, to be sure, San Francisco traditionally scores well on various happiness surveys. The well-regarded Gallup Healthways Well-Being Index, for example, ranks San Jose and San Francisco as the two happiest large cities in the United States. (That shouldn’t be too surprising. Happiness—as defined by how people report their own “sense of well-being” in surveys—usually tracks income. The more money, the more well-being.)

But there’s more to living in the big city than happiness. There’s also that second concept, one much beloved by economists: utility. “Utility,” says University of Michigan economist Justin Wolfers, “is whatever the hell it is that makes you better off.” It’s a broader concept than happiness alone: You could be living in San Francisco because you need access to its job market, or because you think that your children will be better off in the future, or because you’re a member of a tight-knit, protective community, or because walking or taking BART to work is more convenient than a two-hour stop- and-go freeway commute. Questions of utility are what inform our crucial decisions; happiness, as economist Gary Becker has written, “is just an input into the utility function.” When the issue is boiled down to utility, the reason why someone will pay $3,000 a month for a hole-in-the-wall becomes clearer.

“The short answer is because the place is worth it,” says Richard Florida, author of The Rise of the Creative Class and director of the Martin Prosperity Institute at the University of Toronto. He describes a kind of virtuous cycle: A hot job market attracts highly skilled workers, and a region with a huge agglomeration of talented workers in turn attracts new businesses. If you are a software entrepreneur looking to staff up quickly, for example, it’s impossible to beat San Francisco. But, Florida adds, people don’t live in San Francisco just in order to work there. The city is also inherently attractive. The abundant amenities that San Francisco provides more than justify its high cost for those who can afford it, he says, and they convince many who can’t really afford it to give city living a try anyway.