Bay Area home prices stalled out for a second straight month in April, a sign they may have reached their limit despite the region’s robust economy and rock-bottom unemployment.

The median price paid for a new or existing home or condo in the nine-county region was $850,000 in April, up 2.4% from the previous month but unchanged from April 2018. In March, the median price dipped a scant 0.1% from the same month last year, according to a report released Thursday by research firm CoreLogic.

“We are seeing more price reductions, more contingent sales, we are not having the spring we had last year,” said Joan Ulibarri, a Compass real estate agent on the Peninsula.

In April of last year, the median home price was up 13.3% year over year, CoreLogic said, and in Santa Clara County alone, it was up a breathtaking 27.6%.

According to a separate study from the California Association of Realtors, the median price paid for an existing single-family home in April fell 2.2% from April 2018 in the Bay Area, the only region in the state with a price drop. Statewide, the median price rose 3.2%. For existing condos, the median price dropped 5.2% in the Bay Area and fell 0.3% statewide.

“There are more active listings, a lot more to choose from” in the Bay Area, said Jordan Levine, the association’s deputy chief economist. There has also been a shift in the mix of sales, with fewer high-end sales and more entry-level sales. That lowers the median price, which is the price at which half of homes sold for more and half for less.

Looking at the median price paid per square foot adjusts somewhat for the mix of homes sold. For the Bay Area, the median price paid for a single-family home was $563 per square foot in April, up slightly from $561 last April. For condos, the median price paid per square foot dropped to $596 from $629.

“Compared to other regions in the state, the Bay Area is way past previous highs set during the last cycle,” which ended around 2007, Levine said. “Affordability is undermining demand (in the Bay Area). It’s becoming harder and harder to see the same amount of price growth we sustained through the current cycle. The economy is strong, but at the end of the day, people still have to make those monthly mortgage payments. There is an upper bound in the Bay Area where people can actually afford homes.”

Compass agent Virginia Supnet put it another way.

“Buyers are being a lot pickier,” she said. “They’re getting their sanity back.”

Supnet, who works on the Peninsula and the Coastside, concurred that sales are still brisk at the lower end but sluggish at the higher end. Where those two ends meet depends on the location.

In Half Moon Bay, anything priced from $900,000 to $1.5 million is still moving quickly. But Supnet has a listing on Miramar Drive in Half Moon Bay that’s been on the market since December. After two price reductions, it’s listed at $2,390,000, with 4,140 square feet of space, ocean views, a home theater, gym and wine cellar.

“People love it,” she said, “but it’s either not in their price range or they could afford it but they think, ‘Do I really need all this space?’”

In Menlo Park, “anything under $2 million would be gone in an instant. Once you start getting to $3 million or $3.5 million,” things slow down. “I think people are tired of overpaying,” she said.

In some cases, they’re going elsewhere. New census data showed that the Bay Area’s estimated population growth over the past two years slowed dramatically compared with the previous six.

Steve Salta and his wife are moving July 1 from San Francisco to Portland because they’ve outgrown the two-bedroom, 1,000-square-foot home they’re sharing with their two boys, ages 6 and 2, and a dog.

“My wife and I really wanted to stay here,” he said. “I love the idea of raising my children in an urban environment, a major market where you step outside and any type of food is there, any type of people are there. We love that.”

But a three-bedroom home in a good school district would have cost at least $2 million, including likely renovations.

“If we tried to stay here, with our financial situation and income, we’d be house poor and in a very risky situation” if one of them lost their job, Salta said. “As much as we love the Bay Area, it would be irresponsible of us to spend our money this way considering we have two young kids we are trying to provide for.”

In Portland, where Steve Salta grew up, they can move into a home his family owns. His wife, Michelle, is self-employed and Steve can keep his job in business development at Healthline, a medical information website, and come to the San Francisco office once a month.

It’s too soon to say what impact this year’s crush of Bay Area initial public offerings will have on the housing market. The two biggest companies to go public — Lyft in March and Uber in May — are trading below their IPO prices. A number of smaller ones — such as Shockwave Medical, Zoom Video Communications, Silk Road Medical and PagerDuty — have soared. But employees generally can’t cash in their company stock or options until six months after their IPO dates, and that won’t be until fall.

Although the number of Bay Area homes on the market in April was higher than last April, it was still low by historical standards. That means “there is still lots of demand,” Levine said. “If you inject the local economy with lots of cash, that’s going to exacerbate the existing supply constraints.”

It’s worth noting that the median price in San Francisco County alone hit a record high — $1.4 million — in April, surpassing the $1.38 million record set in March, according to CoreLogic. Many of the companies with this year’s biggest IPOs, including Uber, Lyft, Pinterest and Levi Strauss, are based in San Francisco.

Kathleen Pender is a San Francisco Chronicle columnist. Email: kpender@sfchronicle.com Twitter: @kathpender