SAN JOSE — In a sign that the Bay Area’s housing shortage has reached new heights, even having a boatload of cash now may not be enough to land your dream home.

Silicon Valley is experiencing a new shortage of high-end homes, according to a recent report, demonstrating that the availability crisis is finally affecting wealthy homebuyers who had, until now, largely been shielded from the effects of a plunging inventory supply.

There are 42 percent fewer premium homes available in San Jose today than at this time last year — the biggest drop among U.S. cities studied, according to real estate website Trulia. Experts say the disappearance of those high-end homes means higher prices and tougher competition for all homebuyers, not just those in the market for Silicon Valley’s priciest mansions.

“Even homes that are very expensive are harder to find,” said Cheryl Young, senior economist at Trulia. “There’s sort of nothing out there, even if you have cash to burn.”

San Jose’s supply of premium homes has been shrinking slowly, but this year saw an exceptionally sudden drop-off. The supply fell by 11 percent in 2016, rose 6 percent in 2015, and dropped 4 percent in 2014, according to Trulia.

Trulia defines a “premium home” as one in the top one-third of the market — in San Jose, that means homes priced at $2.5 million or more.

The expensive home shortage isn’t isolated to San Jose — Oakland and San Francisco also were among the 10 cities experiencing the biggest dip. Oakland’s premium home inventory plunged 25 percent in the past year, and San Francisco’s fell 23 percent, according to Trulia’s data. Nationwide, the housing market saw a 6 percent drop in premium home inventory — the biggest plunge in more than four years.

“The biggest single factor that determines pricing or value of a home is supply and demand,” said Rick Smith, president of the Santa Clara County Association of Realtors. “If inventory is tiny and there is a demand for properties to be purchased in any given area, the demand will drive the prices up.”

And a low supply of top-tier homes drives up prices across the market — not just for the Bay Area’s elite, he said. Most people in the market for a premium home are shopping because they’re selling a less-expensive starter or trade-up home, Smith said. If they can’t find what they’re looking for, they don’t sell their cheaper home — depriving the market of a more affordable house. To make matters worse, premium homebuyers who can’t find a top-tier home also may “cannibalize” a cheaper home, thereby snatching it away from lower-income buyers who can’t afford to pay as much, said Young.

There are fewer homes available on the lower end of the market, too. The supply of starter homes in San Jose dropped 55 percent this year — in San Francisco, that supply dropped 48 percent, and in Oakland it fell 35 percent, according to Trulia. Homes that cost less than $500,000 are becoming an endangered species in the Bay Area — just 9 percent of Santa Clara County homes fell under that benchmark during the first nine months of 2017, down from 50 percent in 2009.

Homes are now the most unaffordable since Trulia started keeping track in 2012, according to the report. Nationwide, first-time homebuyers would have to pony up about 40 percent of their monthly income to afford a median-priced starter home — nearly a third more than the recommended amount. The numbers are even worse in the Bay Area. First-time homebuyers would have to spend 95 percent of their monthly income to afford a home in San Jose, and 113 percent in San Francisco, according to Trulia. Things are only slightly better in Oakland, where a median-priced starter home costs about 73 percent of a first-time buyer’s salary.

The lack of available homes contributes to those climbing prices.

There are 447 single-family homes for sale in Santa Clara County, down from 573 at around this time last year, Smith said. And more than a third of the homes on the market now are priced at $2 million or higher. Related Articles San Jose’s new median house price, after nation’s sharpest increase

Pending home sales plunge across Bay Area and state

There’s some hope things will get better. A recent Trulia survey found homeowners are more interested in selling now than they’ve been since 2014 — 16 percent said they plan to sell a home in the next two years. But new homes will have to flood the market for buyers to see a substantial impact.

“Unless there’s a really large infusion of inventory, unless a lot of people sell their houses and don’t buy something else, or go into renting, or a lot of new construction happens,” Young said, “we’re not going to see prices drop that precipitously.”