King County’s median price of single-family homes sold last month was $480,000, 7.3 percent higher than a year ago, as buyers reckoned with tight inventory and a slow pace of new-home construction.

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King County’s median price of single-family homes sold last month was $480,000, 7.3?percent higher than a year ago, as buyers reckoned with tight inventory and a slow pace of new-home construction.

The number of single-family and condominium listings was 31 percent lower than a year ago, the widest that gap has been so far this year, according to data released Thursday by the Northwest Multiple Listing Service.

Housing experts consider a five-month supply of listings the minimum for a healthy balance between buyers and sellers. King County, with just over a month’s supply, hasn’t seen that level since 2010. Seattle’s supply is less than a month.

Given such tight supply, homes that do come on the market are gone quickly. Across King, Snohomish, Pierce and Kitsap counties, last month’s volume of pending sales — purchase contracts that haven’t yet closed — made it the second best October on record, said J. Lennox Scott, chairman and CEO of the John L. Scott brokerage.

“The market will remain hot through the winter,” he said.

Buyers may pine for more choices, but construction of new single-family homes isn’t capable of meeting the enormous appetite.

In the first nine months of this year, agencies in the tri-county area issued permits for 6,557 single-family homes and 13,581 multifamily units, according to the National Association of Home Builders.

Compared with last year, the number of permits for single-family homes is down 2 percent. Permits for multifamily housing are up 39?percent.

Homebuilders say the biggest challenge they face is the shortage of land for sale, despite government planners’ position that King County has a sufficient supply.

“They say there’s available land, but there’s not, because there’s not willing and able sellers for that land,” said Kelley Moldstad, Seattle division president for Toll Brothers. “In Redmond, there might be 20 people with 5-acre farms. They’re never going to sell.”

Like homebuilders, consumers priced out of central King County are going north or south until they find what they can afford. “That’s why you’re seeing the North End and South End jumping in pricing,” Moldstad said.

In October, median prices of single-family homes sold increased the most in the suburbs: The median jumped 17 percent over the year to $449,950 in North King County and also 17 percent in Southwest King County, to $297,824.

The trend, combined with relatively few homes for sale, is supporting price gains outside King County, too. Snohomish County’s median was $365,000, up 11.3 percent over the year. The median in Pierce County was $255,250, a 10.5 percent increase, and in Kitsap, $258,500, 3.4 percent higher.

Meanwhile, in Seattle, the median price rose 7.8 percent to $555,000. The Eastside’s median price was $667,000, up 8.3 percent.

Builders who redevelop sites in the city have to pay a premium for a lot, Moldstad said.

“The land is very, very precious, so they’ll try to put as much density as they can,” he said. “Be open to different types of product, other than your standard 7,000-square-foot lot with a two-car garage and 2,500-square-foot home.”

The condominium market, which was battered more severely than single-family homes in the last recession, is seeing a resurgence. The median condo price was $291,000 in King County, 18?percent higher than a year ago, and $269,000 in Snohomish County, up 14.6?percent, according to the MLS.

In downtown Seattle, the median condo price in October was $539,000, 35 percent higher than a year ago.

While that number is skewed higher by sales of luxury units at the new Insignia towers, agents say they expect international buyers and downsizing baby boomers will stoke demand for downtown condos.

“Traffic has gotten significantly worse, and people are just less inclined to sit on the road,” said Windermere broker Jeff Reynolds. “It’s going to continue to be a trend until we have a lot more transportation options or we alleviate some of those issues.”