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MIAMI — For rent and utilities to be considered affordable, they are supposed to take up no more than 30 percent of a household’s income. But that goal is increasingly unattainable for middle-income families as a tightening market pushes up rents ever faster, outrunning modest rises in pay.

The strain is not limited to the usual high-cost cities like New York and San Francisco. An analysis for The New York Times by Zillow, a real-estate website, found 90 cities, including Seattle, where the median rent — not including utilities — was now more than 30 percent of the median gross income.

Zillow, which is based in Seattle, calculated the historical average using data from 1985 to 2000.

In Seattle, rent as a percentage of income has risen to 31 percent, from a historical average of 23 percent. Los Angeles was at the top of the list, rising to 47 percent, from 34 percent. In New Orleans, it more than doubled, to 35 percent from 14 percent.

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Nationally, half of all renters are now spending more than 30 percent of their income on housing, according to a comprehensive Harvard study, up from 38 percent of renters in 2000. In December, Housing Secretary Shaun Donovan declared “the worst rental-affordability crisis that this country has ever known.”

Apartment-vacancy rates have dropped so low that forecasters at Capital Economics, a research firm, said rents could rise, on average, as much as 4 percent this year, compared with 2.8 percent last year.

But rents are rising faster than that in many cities even as overall inflation is running at little more than 1 percent annually.

One of the most expensive cities for renters is Miami, where rents, on average, consume 43 percent of the typical household income. Stella Santamaria, a 40-year-old math teacher, has been looking for an apartment in Miami for more than six months.

“We’re kind of sick of talking about it,” she said of herself and fellow teachers in the same boat. “It’s like, ‘Are you still living with your mom?’ ‘Yeah, are you?’ ‘Yeah.’ ”

After 11 years as a teacher, Santamaria makes $41,000, considerably less than the city’s median income, which is $48,000, according to Zillow.

Part of the reason for the squeeze on renters is simple demand — between 2007 and 2013 the U.S. added, on net, about 6.2 million tenants, compared with 208,000 homeowners, said Stan Humphries, the chief economist of Zillow.

For many middle- and lower-income people, high rents choke spending on other goods and services, impeding the economic recovery. It may get worse before it gets better. Apartment builders have raced to build more units, creating a wave of supply that is beginning to crest.

But demand has shown no signs of slackening. And as long as there are plenty of upper-income renters looking for apartments, there is little incentive to build anything other than expensive units.

As a result, there are in effect two separate rental markets that are so far apart in price that they have little effect on each other. Cities have been left to address the problem on their own, with some granting exceptions to their own zoning laws to allow for things like micro-apartments.

Miami has allowed some variances to its urban plan for such projects as Brickell View Terrace, which will have 176 units in a prime location near a Metrorail station.

Ninety of the units will be affordable for people making 60 percent of the median income, 10 for people making less, and the rest will be market rate.

But a seemingly insatiable demand for luxury condos in Miami has caused land prices to soar, making affordable-housing projects harder to build anywhere close to downtown.

Moving farther out is cheaper, but the cost savings on housing can be quickly wiped out by transportation costs.

A 2012 study by the Center for Housing Policy found that Miami was the most expensive metropolitan area in the country when housing and transportation costs were combined.

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