Major banks cut their prime lending rates by one-quarter of a point to 8 1/2 percent yesterday, reflecting a recent decline in interest rates caused by expectations of a slowdown in the economy.

The reduction in the benchmark rate will trim borrowing costs for many corporate and individual borrowers, furnishing a bit of a stimulus to an economy that is certain to turn sluggish in coming months, economists said.

Reagan administration officials welcomed the banks' move, which came amid growing worries that the economy's growth during the election campaign will be so anemic that Republican candidates will be hurt. "Obviously, it's good news," said an aide to Treasury Secretary James A. Baker III.

The banks' action was prompted by a decline in the rates that the banks themselves pay on borrowed funds and on deposits. Those rates have been dropping because of the widespread expectation that an economic slowdown would diminish demand for loans by businesses and consumers. Additionally, the Federal Reserve is thought to be on the verge of easing credit conditions slightly, which is also helping to lower rates.

A fresh harbinger of a slowdown in the economy emerged yesterday when the Commerce Department reported that its composite index of leading indicators decreased in December for the third month in a row. The index, a forecasting gauge that consists of 12 forward-looking statistics such as building permits, dropped 0.2 percent in December, following a revised 1.2 percent decline in November and a revised 0.1 decline in October.

A series of three consecutive decreases in the monthly index has often heralded recessions in the past, but economists said that yesterday's report doesn't necessarily signal a slump this year. One of the main reasons for the November decline was the Oct. 19 plunge in stock prices, which many analysts believe is having only a modest impact on the economy. Stock prices are one of the components of the index.

Nevertheless, the leading indicators provided additional evidence that the economy is likely to decelerate sharply, to perhaps a 1 percent annual rate of growth in the first half of 1988 from the 3.8 percent pace recorded in 1987. Pessimism about the near-term outlook has been mounting since last Wednesday, when the government issued a report on the gross national product that suggested companies will have to cut production and payrolls in coming months to work off bloated inventories of unsold goods.

Thus the prime rate cut "does add some juice to the economy, but we're still looking at a weak six months," said Christopher Caton, an economist at Data Resources Inc., a Lexington, Mass., consulting firm.

The reduction in the prime was the first since early November, when banks lowered the rate from 9 percent to 8 3/4 percent.

Morgan Guaranty Trust Co. announced its prime rate cut shortly after 10 a.m., and was quickly followed by a slew of banks including Citibank, Manufacturers Hanover Trust Co., Chemical Bank, Chase Manhattan Bank, Continental Illinois National Bank and Bankers Trust Co.

The prime is more a bellwether of borrowing costs than a rate that applies to specific borrowers. It used to be the rate that banks would extend to their most favored corporate customers, but in recent years many large corporations have been able to borrow at rates below prime, both from banks and other sources.

Interest charges on many loans are nonetheless tied to the prime, including some consumer rates such as those on home-equity loans.

"As an indication of the likely future trend in rates, this has some psychological impact," said Timothy Howard, executive vice president and chief economist at the Federal National Mortgage Association. Banks usually wait until they are reasonably sure that rates are decisively moving in one direction or another before they adjust the prime.

Howard and other economists attached considerably less importance to yesterday's report about leading indicators. "There's nothing in the leading indicators that we didn't know from watching other various indicators already," Howard said.

According to the Commerce Department, a three-month decline in leading indicators has been followed by recession eight times during the postwar period, but on four occasions that pattern didn't hold true. The most recent instance was in June, July and August 1984. The index dipped in those three months, and the economy slowed significantly soon after. But there was no recession -- which is usually defined as two consecutive quarters of decline in gross national product.

The following indicators contributed to the decrease of the index in December: the average work week, claims for unemployment benefits, building permits, raw materials prices and stock prices.

Indicators that suggested strength in the economy were manufacturers' orders for consumer goods, a slowdown in business delivery times, orders for plant and equipment and the money supply.

December's performance moved the index to 190.7 percent of the 1967 average. Earlier, Commerce had estimated the November decline at 1.7 percent and the October performance as a 0.2 percent increase.

In another report, Commerce said yesterday that sales of new single-family houses fell 6.2 percent in December to a seasonally adjusted annual rate of 603,000. For all of 1987, new single-family home sales totaled 674,000, down 10.1 percent from 1986 sales of 750,000.

The December figure reflected mainly a home-sale slump in the northeast, according to James Christian, chief economist for the U.S. League of Savings Institutions. "We're starting to see the fallout from the stock market crash," Christian said, observing that the buyers most affected and frightened by the market fall tend to live in New York and the surrounding area.

The impact on the rest of the country appears to be significantly milder, Christian said, with new home sales in regions other than the northeast either "up or steady."