Morgan Guaranty Trust Co. slashed its prime lending rate a full percentage point today, from 18 1/2 percent to 17 1/2 percent, as the widening recession continues to reduce loan demands by businesses and to lower interest rates generally.

A number of other major banks -- including New York's Chase Manhattan and Chicago's First National -- cut their prime lending rate from 18 1/2 to 18 percent.

Harris Trust & Savings Bank, Chicago's third biggest, but its prime rate to 18 percent early today, then trimmed it to 17 1/2 percent later in the morning after Morgan announced its big reduction.

In the last few weeks short-term interest rates have fallen dramatically. The prime rate, the interest a bank charges its best corporate customers for short-term loans, has fallen from a record 20 percent, but that decline hasn't been nearly as steep as the drop in other interest rates.

Analysts said the cut in Morgan's prime, as well as the reductions by other banks, reflect both the declining costs of funds to the bank as well as an attempt to capture new loan business. In the last few weeks businesses have cut back sharply their bank borrowings.

Since early April the rates banks have to pay on big certificates of deposit -- one of their sources of funds -- has dropped from 18 percent to less than 11 percent.

At the same time, the rates big companies have to pay to borrow in the market directly, rather than from their banks, has fallen about the same amount, from 17 percent to 11 percent.

Big, financially secure companies can sell commercial paper (essentially a corporate IOU) to come up with funds rather than borrow from a bank. The Morgan cuts and the trims by other banks, is an attempt to narrow the gap between commercial paper rates and bank loan rates.

Morgan, the nation's fifth-biggest bank, makes many of its loans to the bluest of blue-chip customers who find it easy to borrow in the commercial paper market.

Leon Gould, an economist for Commercial Credit Corp., said the decline in business demand for credit is not as great as the huge fall-off in bank borrowings might suggest.

Gould noted that between Jan. 1, 1979 and April 23, 1979, bank loans grew $6.9 billion, while in the same period this year, they grew only $2 billion.

But the amount of commercial paper issued last year was $3.7 billion while so far this year it has increased $8.3 billion.

Nevertheless, according to data compiled by the economic consulting firm Data Resources Inc., even the growth in commercial paper has slowed in recent weeks, although it is still growing at a 44 percent annual rate.

Most analysts are convinced that the steep decline in interest rates in recent weeks is exaggerated and that at some point in the future they will begin to rise again.

"There's a lot of psychological factors that hit the short-term market," according to Richard Peterson, chief economist for Continental Illinois National Bank.

Peterson said that when rates took off sharply in mid-March, they rose faster than could be justified by events in the economy and that the recent decline is too fast as well.

The Federal Reserve, the nation's central bank, used to try to control interest rates, keeping them from rising or falling too fast, through its actions in the government securities market. But the Fed has shifted its sights in recent months and is aiming its monetary policy at controlling the growth of the money supply rather than worrying about interest rates.

Because the money supply -- currency in circulation and checking accounts -- has been falling much faster than the Fed wants it to, the central bank has been pumping funds into the economy to try to get the growth of the money back on the Fed's target.

Actions like Morgan's today, it they result in an increase in business borrowing, should trigger renewed growth in the money supply.