Several major banks yesterday cut their prime lending rate to 11 1/2 percent from 11 3/4 percent and economists and bankers said further reductions were in the offing.

It was the fifth time in the last two months that major banks have lowered the prime rate. The reductions were in response to declining rates in the money markets -- where big banks raise the majority of their funds.

White House spokesman Larry Speakes applauded the reduction and said the prime-rate decline should help foster increased economic growth in coming months.

The economy, which had been expanding at a swift pace in the first half of the year, slowed markedly in the third quarter. The slowdown led to a slight decline in the growth of credit demand as well as a noticeable easing in monetary policy by the Federal Reserve Board.

Last week, in a strong signal that it wanted to foster further interest-rate reduction and stimulate both economic and money growth, the Federal Reserve cut its discount rate -- the interest it charges banks to borrow -- to 8 1/2 percent from 9 percent.

Robert Ortner, chief economist for the Department of Commerce, said the economy has slowed markedly, the money supply has not grown at all since June and inflation continues to be low. "In those circumstances, it is entirely appropriate" for the Federal Reserve to take steps to ease policy, he said.

The prime rate is the key interest charge for short-term business lending. Consumer loan rates are not directly tied to the prime, but continued declines in the cost of funds to banks usually leads to reduced consumer rates.

Mortgage rates also have been dropping in recent weeks and most housing economists expect them to fall further.

Citibank, New York City's largest bank, was the first to trim its prime lending charge yesterday and was quickly followed by several other large banks, including First National Bank of Chicago. The prime-rate reduction is expected to become industrywide soon.

Analysts predicted that because the cost of funds to banks has dropped so sharply since early September, the prime rate will continue to drop in the weeks ahead. Edward H. Boss, vice president and senior financial economist at Continental Illinois National Bank, said the prime rate should fall to 11 percent by year's end.

Banks have reduced the prime rate less quickly than the decline in interest they must pay to attract funds, in large part to bolster profits.

Banks have been boosting their loan reserves in recent months -- mainly because their problem loans remain high despite nearly two years of economic recovery -- and they have an added incentive to reduce their prime more slowly than the decline in money market rates.

The prime rate has come down 2 percentage points since September, while open market rates have declined as much as 2 1/2 percentage points.

Continental Illinois' Boss said the Fed's reduction in the discount rate is a signal that the central bank expects monetary policy and interest rates to stay at current levels or below "for a while." He said Fed policy makers would not have reduced the discount rate if they anticipated taking restrictive monetary policy actions in the near future.

But Boss, like many other economists, expects that interest rates will rise next year. He said the stimulative effect of lower rates will boost economic growth and, as a result, private demand for credit will grow in 1985.

By next summer, Boss said, the prime rate could be 13 percent.