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Kids who grow up poor have a better chance of one day not being poor if they grow up neighborhoods where everyone isn’t poor. But in some cities, affordable housing crises are making that impossible. It’s a quandary.

Economically and racially diverse neighborhoods are sort of a holy grail of urban planning—the ideal of city life, where everyone mingles together and no one demographic group is stuffed in its own forgotten ghetto and true diversity flowers in all of its many manifestations, enriching everyone. (It’s an ideal, okay?) In order to get even close to achieving that, though, cities need decent, diverse neighborhoods that include affordable housing. And that is becoming an unattainable dream.

New housing market research out from Zillow shows that increasingly unaffordable housing markets, particularly in popular cities, are destroying any chance that poorer families might have had of living in economically diverse neighborhoods. Mortgage payments for homeowners tend to be much cheaper than rent payments—but when housing prices soar, it’s impossible for lower income people to buy. They’re stuck renting, even as renting grows ever more onerous. “In major job markets like the Bay Area, New York, and Los Angeles, the median rent requires more than 40 percent of the median income,” Zillow reports. “Renters in Los Angeles can expect to spend nearly half of their income on rent.”

These are the very cities that have historically offered the best chance of economic mobility to poor kids. The diversity of these cities, among other things, makes them exceedingly popular. That popularity leads to higher rents, which make it impossible to save down payments that might allow people to buy and have lower monthly payments. Poorer families are forced out of once economically diverse neighborhoods, thereby decreasing the chance that the kids in those families will grow up to not be poor themselves.

Build more housing. It’s good for cities and for the people in them.