Morgan Guaranty Trust Co., the nation's fifth-largest commercial bank, lowered its prime lending rate yesterday to 11 1/2 percent, becoming the first major institution to drop its benchmark business rate below 12 percent since last August.

Analysts predicted that, although other short-term lending rates appear to have leveled off after droppping sharply since mid-April because of the severe recession, the bank prime rate will continue to drop during the next several weeks to the 10-percent to 10 1/2-percent range.

Meanwhile, the President's top inflation fighter, Alfred Kahn, said a tax cut is necessary to combat growing unemployment.

Kahn, speaking to reporters after an address to an American Stock Exchange gathering, said that with inflation easing and unemployment growing a tax cut should be put into place to stimulate the sagging economy.

But Kahn said that huge spending programs designed to combat the recession would be the wrong approach. "Any major expenditure would be the wrong way to go," Kahn said.

The inflation rate, which had risen at an annual pace of about 18 percent last spring, has subsided to a 12 percent pace in recent weeks (as measured by the consumer price index), and some economists think it will run at a 6-percent to 7-percent rate during the last half of the year.

Kahn told reporters that there is no one who doubts "that a tax cut is inevitable" and said that timing is the only question. Administration economists currently are studying a major, multiyear tax cut program beginning early next year.

The severe recession, which economists say began in January, has pushed the unemployment rate up from the 6 percent range at the start of the year to 7.8 percent last month. Administration officials have said unemployment could climb to 8.5 percent before things start to get better. In 1974-75, during the worst economic slowdown in the postwar period, the unemployment rate reached 9 percent.

Because of the sharp economic contraction, demand for credit has subsided sharply and, as a result, interest rates have declined, too.

The prime lending rate -- the interest rate top corporate customers pay for a short-term loan -- was 20 percent in mid-April. Other short-term rates, such as the federal funds rate (the interest banks charge each other for overnight loans of excess reserves) have fallen from about 18 percent to less than 9 percent.

Loan demand at the nation's major banks, which climbed sharply during the first three months of the year, fell about as quickly during April and May. Business loans are not growing at all now, said Richard Peterson, chief economist or Continental Illinois National Bank, Chicago's largest.

He said that although short-term interest rates appear to have leveled off, the prime rate did not come down as quickly as did other rates and likely will continue to fall until about mid-July, when it hits 10 percnet of 10 1/2% percent.

No major banks followed Morgan's lead yesterday, although Manufacturers of Los Angeles lowered its rate to 11 1/2 percent and a small St. Louis bank reduced its prime rate to 11 percent.

Because the Treasury has been reducing the size of its regular bill offerings in recent weeks to keep within the temporary debt ceiling of $879 billion, bill rates have fallen faster than they otherwise would have because of the reduced supply. (When investors bid up the price of bills, the rates fall.)

However, perhaps as further indication that the fall in short-term rates is near an end, at the Treasury's regular auction of 3- and 6-month bills, interest rates rose even though the agency had cut the size of its auction.

The Treasury had planned to sell $7.8 billion but cut that amount to $7 billion yesterday morning because of the debt ceiling. The agency said it may have to reduce the size of its $3.25 billion note offering planned for today.

The Treasury Department also announced yesterday that it will postpone an $8 billion auction of Treasury bills scheduled next Monday unless Congress raises the debt ceiling.

The current debt ceiling of $879 billion expires on June 30. Without action by Congress, the ceiling would drop to $400 billion.

The department said the $8 billion auction is for bills to be issued July 3. Half the total is for 91-day bills and half for 183-day bills.

In another development yesterday, the American Retail Federation released a poll claiming to show that for the first time a majority of Americans believe inflation can be beaten. The poll, conducted for the federation by Cambridge Reports Inc., showed that 70 percent of the people interviewed believed prices would once again be stable.

"This starting turnaround in inflation psychology is unprecedented in our nearly six-year monitoring of nationwide attitudes toward inflation," the survey firm said. At the same time, the poll showed that a clear majority of the people surveyed still see inflation as the nation's top economic problem.

Ironically, while the poll showed a majority believe prices eventually will stabilize, an even greater majority said they have little confidence in the government's ability to solve the inflation problem.