In one of the most agonizing disconnects of the Bay Area’s surging economy, far more people want to buy a home than want to sell one, making this the tightest housing market in the nation.

Would-be homebuyers are crowding into scarce open houses and battling for the few available, leading to rising prices, rapid sales — many homes sell within a week — and frustrated house hunters.

“This is the most sustained period of low inventory I’ve seen in 20 to 24 years,” said Chris Trapani, head of the Sereno Group in Silicon Valley.

Many homeowners are still reeling from the housing bust and waiting for their homes to recover value before they sell. Others are afraid that if they sell, they won’t find another home because of the shortage. Homeowners who refinanced at last year’s low interest rates also may be happy to stay where they are.

At the same time, the Bay Area tech boom has heightened demand in the three tightest markets in the U.S. According to online real estate site Trulia, which tracks how inventory is keeping up with demand, the East Bay has the tightest supply, followed by the South Bay and the Peninsula, including San Francisco.

It could be a year or more before the market rights itself, Trapani said.

The limited market and high prices have pushed first-time homebuyers either to the outer fringes of the Bay Area or kept them renting even though rents are among the highest in the nation.

“For every six-figure software engineer, you have people working in the service industry, in restaurants and retail and living in very high-density situations or moving further out where there’s affordable housing or rental housing,” said Leslie Appleton-Young of the California Association of Realtors.

It would take less than two months to sell all the homes listed for sale in Santa Clara and San Mateo Counties, far below the six months that’s considered a balanced market, according to the association. Alameda and Contra Costa counties are not much better off, at slightly more than two months.

There were 5,639 homes for sale in April, up from a low of 4,890 in 2013 but down 28 percent from April 2012, when 7,867 homes were on the market in the East Bay, Peninsula and South Bay, according to a ZipRealty analysis of listings.

“It’s really a dire situation,” said Doreen Roberts of Master Key Realty in Fremont. Roberts helped a young couple buy a house in Newark after they lost one to a bidding war that drew 26 offers and sold for $90,000 over the asking price.

“We definitely ran into a problem where there weren’t many houses and a lot of people were bidding on them,” said her client, Ken Taylor, a digital engineer with a tech firm in North San Jose. Taylor and his wife, April Burton, a freelance graphic artist, looked at houses for a month without finding much.

“We would spend a full day and see six or seven houses, but that was all the houses in our price range that were on the market,” said Taylor. “A lot of them had interesting problems with permits and occupants we didn’t want to deal with.”

When a three-bedroom, two-bath home in Newark came on the market, they grabbed it for $575,000 — $20,000 over asking price — and gave the sellers three weeks’ free rent. “We accepted that because that’s just how it is,” he said.

In such a competitive market, prices have mushroomed and created “a crisis of affordability,” said David Stark, public affairs director of the Bay East Association of Realtors. “It’s hard to find your next home, which makes you reluctant to put your home on the market.”

Prices of single-family homes were up 17.1 percent in April from the previous year across the Bay Area, according to DataQuick. The Bay Area has the two metropolitan areas — San Jose and San Francisco — with the highest median home prices in the nation.

John and Tracy Timble watched their neighbor’s Pleasant Hill home sell for $100,000 over the asking price of $650,000 three months ago, and decided the time was ripe to sell and move out of the area.

They listed their home — which had a pool, better location and a view their neighbor’s home didn’t have — for $780,000 and waited at a Starbucks while their agent, Laura Wucher of Better Homes and Gardens Real Estate in Contra Costa County, took offers.

“We had two separate cash offers in addition to four other offers,” Timble said. “We couldn’t believe it. We received the first cash offer for $850,000 and we were just ecstatic.” The final winning bid was for $880,000.

Although inventory is still low, it is increasing with the summer home buying season, and that may ease some of the pressure.

But some of that recent inventory growth may be because owners are overpricing their homes and those homes are not selling. Sales of single-family homes dropped 5.5 percent in April from the previous year across the nine-county Bay Area, according to real estate information service DataQuick.

The recent increase in inventory “is not providing a lot of relief in the market in part because you do have some overpriced listings,” said Appleton-Young of the California Association of Realtors. “That tends to happen at this stage in a cycle.”

There are plenty of reasons why potential sellers are keeping their homes off the market.

Some are behaving like investors with a hot stock, trying to “time the market” by holding onto their properties in the hope of selling at the peak, said Don Cruz Datanagan, East Bay manager for ZipRealty.

“There are people now who sold their house a year ago, and who saw the appreciation go up 20-plus percent since then,” he said. “They’re already wishing they hadn’t.”

Others are holding back because they’re worried that they’ll end up as renters, unable to find their next home.

“It’s a musical chairs situation, and they don’t want to be one stuck without a chair,” said Svenja Gudell, director of economic research at online real estate site Zillow.

And some have a low-interest rate mortgage from refinancing in the past couple of years. That makes it cheaper to stay in place, and has many homeowners putting their move-up plans aside and improving the homes they live in.

“We call it ‘improve-not-move,'” said Kelly Kockos, Wells Fargo’s national senior vice president for equity lending. “In the home equity business, we love that.”

Kabir Chahal, and his wife, Labina Patel, who work at Silicon Valley tech companies, want to move but are reluctant to part with a mortgage with a low interest rate.

They bought their Almaden Valley home three years ago for $800,000, refinanced at 3.875 percent. They could sell for about $1 million, Chahal said, but the houses they might consider buying are priced at $1.1 million to $1.2 million, and there aren’t many available that they really like.

“We are going to keep looking, but both me and my wife realize we are not going to get so lucky this time around,” said Chahal. “If things don’t work out, we’re not going to overpay.”

Contact Pete Carey at 408-920-5419 Follow him on Twitter.com/petecarey