Skyrocketing rents, shrinking incomes and severe cuts in state- and federal-government support for affordable housing have made it far harder for lower-income Bay Area residents to find a place to live, according to a report being released Friday.

The report looks at rents and incomes in Alameda, Contra Costa, Sonoma and San Mateo counties, and concludes that each is more than 10,000 rental spots short of what it would take for everyone of limited means to find an affordable place to live.

People who earn less than 50 percent of the median income in the four counties must spend more than half of their monthly paychecks on rent, according to the report compiled by the nonprofit California Housing Partnership Corp. and the Non-Profit Housing Association of Northern California. Many economists recommend that households spend no more than 30 percent of their income on rent.

The report, which the groups have released annually since 2014, found that state and federal funding for affordable housing in the four counties has dropped 65 percent since 2008.

Meanwhile, in each county the split between rent and income diverged sharply from 2000 to 2015 — with rent shooting up and income dipping.

In Sonoma County, the report found, inflation-adjusted median rent increased 16 percent and renters’ median income declined 6 percent. In Contra Costa County, the median rent went up 25 percent and renter income went down 3 percent.

Alameda County’s median rent shot up 29 percent and renter income dipped 3 percent. And in San Mateo County, the rent figure went up 21 percent and median income fell 3 percent.

Matt Schwartz, president of California Housing Partnership Corp., noted that between the elimination of redevelopment agencies in California, decreased federal funding and the expiration of special state housing bonds, California’s spending on affordable housing has gone down $1.5 billion since 2012. The housing shortage has grown rapidly since then, he said.

“I’ve worked on affordable housing in the Bay Area for 20 years, and it has never been like this,” said Amie Fishman, executive director of the Non-Profit Housing Association of Northern California. “The past couple of years have been an absolute crisis.”

There have been 130 bills introduced since December in the Legislature related to affordable housing. The author of six of them, Assemblyman David Chiu, D-San Francisco, said there is extra urgency because President Trump’s budget proposals could cost the state $700 million a year in urban housing and development funds.

One of Chiu’s bills would eliminate the state deduction for mortgages on second homes and use the resultant $360 million a year to create affordable housing.

Chiu said Gov. Jerry Brown had not moved aggressively on affordable-housing funding in recent years. “We need to move on several fronts on this issue, and we need to do it now,” he said.

Gareth Lacy, a spokesman for Brown, said the governor doesn’t comment on pending legislation. But he said Brown is also keen to add affordable housing, and he pointed to $3.2 billion in the governor’s proposed budget that would add such housing for low-income and homeless Californians.

Kevin Fagan is a San Francisco Chronicle staff writer. Email: kfagan@sfchronicle.com