The nation's economy was not quite as weak at the end of last year as first reported because of more government spending and business investment than preliminary estimates showed, the Commerce Department said yesterday. However, inflation was worse than originally reported.

The nation's gross national product declined at an annual rate of 4.7 percent in the final quarter of 1981--revised from an original 5.2 percent drop--while prices as measured by the GNP deflator rose by 9.3 percent rather than 8.4 percent first reported. For 1981 as a whole, GNP rose by 2 percent, after allowing for inflation.

Many economists predict a further steep decline in the GNP during the current quarter as climbing interest rates have stalled recovery. President Reagan last week backed off from his administration's predictions of an early economic recovery. However, Deputy Treasury Secretary R.T. (Tim) MacNamara said yesterday, "We do feel very strongly that the recession will end this spring."

Treasury Secretary Donald T. Regan also said the economy should be showing positive growth by the second quarter of this year, and predicted the prime would be lower than its present 17 percent by then. He did not specify an exact figure, but agreed with the committee's suggestion that the prime could be 13 percent to 14 percent.

Meanwhile, several small banks yesterday lowered their key prime lending rate from 17 percent to 16 1/2 percent in what could signal a reversal of this year's rising rates. Major banks moved their prime rates up to the 17 percent mark just last week after several weeks of rising money market rates had added to the banks' costs.

The recent rise in rates had accompanied a surge in money growth that puzzled analysts, who looked for slack money growth and lower interest rates because of the recession. However, a report Friday that the money supply had dropped by $3.1 billion in the latest week suggests that the Federal Reserve has managed to choke off the unwanted money increase. This drop encouraged rates to decline yesterday in anticipation of an easier Fed stance, some analysts said.

"The Fed has adopted a slightly less restrictive stance in response to the $3.1 billion drop in M1 and the precipitous decline in economic activity," commented Philip Braverman, a senior economist at Chase Manhatten Bank. There had been some easing of short rates late last week even before the money report, with the Federal funds rate on funds the banks lend each other overnight dropping to slightly more than 14 percent by Friday.

In recent months, interest rates have tended to move upwards when an increase in the money supply is announced and vice versa. This apparent perversity reflects market expectations that the Fed will move against any unexpected or unwanted change in the money supply, some experts say.

The Commerce Department GNP report showed that in current dollars federal government purchases were $6.9 billion higher than first estimated, business fixed investment was up $4.9 billion and net exports up $4.8 billion from the preliminary report. Bigger falls in consumer spending and inventory investment partially offset these revisions.