Chase Manhattan Bank, the nation's third-largest, yesterday trimmed its prime rate to 11 1/4 percent from 11 3/4 percent -- only a day after several other major banks cut their prime lending rate a quarter point to 11 1/2 percent.

The falling prime rate -- the key business lending rate -- is a reflection of the banks' declining costs of raising funds. A slowing economy and easier monetary policy on the part of the Federal Reserve Board have been the key factors in reducing interest rates in the money markets, where banks raise a large portion of their funds.

When Citibank and several other banks cut the prime to 11 1/2 percent Monday, analysts said that money costs had declined so much in recent weeks that a bigger cut was justified. So far, only a few smaller banks have followed Chase and only one other money center bank, First National of Chicago, followed Citibank.

William V. Sullivan, vice president and chief money market economist for the securities firm Dean Witter Reynolds Inc., said that the half-point cut in the prime rate announced by Chase is a "more appropriate" level for the prime lending rate, but said that even at 11 1/4 percent, the spread between the cost of money to banks and the charge they levy against their best business borrowers remains very high on a historical basis.

Normally, when money costs are rising, banks raise their lending rates more slowly than their costs increase, and to recoup some of the profits lost when rates are rising, they lower their lending charges more slowly than their costs of funds drop.

But in recent months, banks have been even slower than normal in lowering their rates, attempting to increase earnings that they can add to their reserves. Big banks have a large number of problem loans that have not gotten better in the two years since the end of the recession, and also have a large number of loans to Latin American countries that make both investors and some analysts jittery.

They also have received pressure from regulators to boost their reserves.

The prime rate has been declining since late September, when it stood at 13 percent. Interest rates in the open market began to drop in early September and most have fallen far more than the 1.75 percentage points (175 basis points, in financial parlance) that the prime rate has fallen.

Sullivan and other analysts believe that at current interest rate levels, a prime rate of 11 percent could be justified and they think that bank fund-raising costs will fall even further in coming months.

The prime lending rate is the interest banks charge their best business customers for loans that mature anywhere from three months to a year. The prime rate is also the benchmark for other business interest rates, including loans to small businesses.

There is a more indirect relationship between the prime rate and consumer rates, but as the cost of funds declines, consumer borrowing rates can be expected to decline too. Already, mortgage rates have fallen in recent months.

Big banks raise the bulk of their funds directly from professional investors by selling big-denomination certificates of deposit and other financial instruments. Historically, Dean Witter's Sullivan said, there is at most a 2 percentage-point (200 basis point) difference between three-month CD rates and the prime. With the CDs closing at 8.9 percent yesterday, the spread is 2.35 percentage points at an 11 1/4 percent prime rate and 2.6 percentage points at an 11 1/2 percent prime rate.