Major banks across the nation lowered their prime lending rates yesterday from 9.25 percent to 9 percent, a response to government infusions of money into the economy and a signal that interest rates on many kinds of consumer and home loans are on their way down.

Although the prime rate is used principally as a base for setting rates on short-term business loans, it is increasingly linked as well to personal lines of credit and home-equity loans.

Changes in the prime also influence changes in rates for auto loans and home mortgages.

The Federal Reserve, which oversees the nation's supply of money and credit, has been adding to the amount of cash in the banking system to calm the wildly gyrating stock and bond markets. One result of the increased supply of money has been a decline in the price of money -- interest rates.

Yesterday's decrease, started by Citibank and quickly followed by many other large banks, was the first industrywide reduction in the prime rate since August 1986.

Two banks, Chemical and Marine Midland, cut their prime rates from 9.75 to 9.25 percent Tuesday after other banks did not follow the half-point increase they attempted last week.

Before the stock market collapsed on Monday, interest rates in general had been on the rise since late last year.

Just two weeks ago, major banks raised their prime rates to 9.25 percent, the level they abandoned yesterday.

Economists suggested that, although the financial markets remain very volatile, further reductions in the prime are possible if the market rates that help determine it stay as low as they are.

"We have had some very dramatic {downward} moves in interest rates in the last few days. It appears as if the whole structure of rates is coming down," said Robert J. Genetski, chief economist of the Harris Trust & Savings Bank of Chicago.

Banks not only were passing on some of the reductions in interest rates they pay for funds, but also were demonstrating a fear the economy will weaken as a result of the stock market crisis, some analysts said.

Several of those interviewed said the prime reduction was being made in a climate of uncertainty.

"With the trillion-dollar or so reduction in American wealth {the amount by which the stock market has declined since its August peak}, the chances of there being a recession in 1988 are now substantially higher," said Kenneth T. Mayland, chief economist of First Pennsylvania Corp. in Philadephia. "Everybody knows interest rates fall in a recession."

It was partly to counter this fear that the Federal Reserve, through the buying of government securities, forced down a key market rate onloans between banks earlier this week.

The so-called federal funds rate, which had been running at 7.75 percent last Thursday, was about 7 percent yesterday after falling as low as 6 percent Wednesday.

Federal Reserve sources said the central bank was not jawboning commercial banks to induce them to lower their prime rate, and many of the banks that cut the rate yesterday said they were merely following the recent sharp reductions in market rates.

"Banks are middlemen. They buy money at wholesale rates and sell it at a retail rate," Mayland said. "Since the cost of funds has gone down, banks are marking down the price they charge for funds."

With those markdowns could come reductions in rates on consumer lines of credit and home-equity loans, which often are adjusted on the basis of changes in the prime.

Other interest rates, particularly those on adjustable-rate home mortgages, are tied to rates on government securities, which also have fallen sharply in recent days. Even rates on credit cards, which run far above other market rates, increasingly fluctuate with the prime.

The Treasury said yesterday the average return on a $9.26 billion auction of 52-week bills was 6.45 percent, down from 7.32 percent at a similar auction on Sept. 30.