Morgan Guaranty Trust Co., the nation's fifth largest bank, today cut its prime lending rate to 18 1/2 percent from 19 1/2 percent.

The Morgan action is a further indcation of the substantial easing of interest rates in general that has occured during the past three weeks.

The interest rate reductions reflect the slowing of the economy as the long-awaited recession finally seems to be taking hold. Some analysts think that the declines in interest rates also are due to an easing of monetary policy by the Federal Reserve Board.

Morgan, for its part, would not say specifically why it slashed its prime lending rate a full percentage point. A spokesman said the rate reflects the judgement of top management about loan demand and the level of market interest rates.

The prime lending rate, the interest banks charge their best corporate customers for a short-term loan, peaked at 20 percent earlier this month.

Despite the sharp plunge in market interest rates during the last three weeks, banks have been slow to cut their prime rates.

The prime rate charged by major banks ranges from Morgan's 18 1/2 percent to Citibank's 19 1/2 percent. Citibank, the nation's second biggest, cut its rate to 19 1/2 percent from 19 3/4 percent last Friday. Chase Manhatten Bank, which was the first bank to lower the prime from 20 percent, now quotes a 19 percent prime rate.

Industry analysts said that banks are keeping their primes high in relation to other market interest rates in part because they want to make up for lost profits during the period when market rates rose rapidly and narrowed the spread between what banks pay for their money and what they loan it out at.

Usually the prime rate and market interest rates rise and fall together because big banks buy on the open market most of the funds they lend to their big customers. One of the prime sources of funds for banks is big certificates of deposit (usually $1 million or more).

Early this month, banks had to pay 18 percent interest on the certificates of deposit they issued to come up with funds. Now CD rates are about 14 percent.

While CD rates came down 4 percentage points, most banks have lowered their prime lending rate no more than one-half to one percentage point Even with Morgan's sharp cut today, market rates have fallen more than twice as much as have Morgan's charges to its customers.

But many banks, including Citibank, faced profit squeezes during the first quarter. Part of Citibank's earnings reduction -- profits were $4 million less during the first three months of 1980 than in 1979 although revenues rose substantially -- came about because of the bank's big emphasis on consumer lending. State laws put a ceiling on the amount of interests banks can charge consumers, and in most states the usury ceiling was lower than the cost of buying funds on the open market.

Some analysts suggest that banks are keeping their prime rates relatively high to discourage corporte borrowing. The federal Reserve Board has told banks that their loans should grow no more than 6 to 9 percent this year.

The Federal Reserve, the nation's central bank, also seems to be easing up on its stringent monetary policy, perhaps because of the marked slowing of the economy in recent weeks.

One fallout of the reduced market interest rates has been a decline in the rates banks pay consumers. For example, the Treasury announced today that banks may pay no more than 10.5 percent and savings and loan associations no more than 10.75 percent on two and a half year savings certificates.