The downturn in Southern California's economy and high housing costs pushed the number of homeless in Los Angeles County upward by as much as 16% during the last year, according to a new survey released Wednesday.

The report, released by the Shelter Partnership, a support organization for shelters and homeless programs, estimated that at least 38,400 people are without shelter on any given night. That number reflects the most conservative estimate; a more broadly premised analysis would indicate as many as 68,600 people are homeless each night.

By comparison, the same survey last year estimated the number of homeless as being between 36,800 and 59,100. The increase is 4% at the low end of the spectrum and 16.1% at the high end.

Homeless advocates attributed the rise to recessionary job cutbacks and the county's astronomical housing costs and noted that the figures were compiled before scores of businesses--and jobs--were destroyed in recent civil unrest.

"Los Angeles continues to live up to its dubious distinction as the homeless capital of the United States," said Bob Pratt, president of the Volunteers of America, a social services organization. "We continue to ignore the needs of people in terrible distress, and we always end up paying dearly. Society can either pay now or pay later, and the pay-later is symbolized in the recent unrest."

Ann Reiss Lane, president of the Shelter Partnership Board of Directors, called the increase "alarming, although not surprising." Between 1980 and 1988, she said, the cost of renting a small apartment in Los Angeles rose by 110%.

According to 1990 Census figures, the median monthly rent in Los Angeles County in 1990 was $626, and the average homeowner was forking over $1,137 a month in mortgage payments and other housing costs. In fact, housing was so expensive that nearly half of the county's renters and a third of its homeowners were spending more than 30% of their incomes on shelter, which has typically been the rule of thumb for housing expenditures.

The housing bite was even bigger for those living on a minimum wage, which provides an income of roughly $800 a month, said Ruth Schwartz, executive director of the Shelter Partnership.

"Some of these people are paying up to 80% of their wages just for housing," she said.

The study--perhaps the most comprehensive local count of its kind--was the third annual survey of homelessness by the Shelter Partnership, which uses existing welfare statistics, combined with numbers gathered by city homeless outreach programs to count the homeless.