The nation's economy grew at a healthier rate last quarter than previously believed, the government said yesterday.

But Commerce Secretary Juanita M. Kreps said it is likely a tax cut will still be needed next spring to prevent a slump in the second half of 1978.

The Commerce Department revised its estimates of "real" gross national product, or actual economic output, and said the economy grew at an annual sate of 4.7 per cent from July through September, rather than the anemic 3.8 per cent rate reported earlier.

It takes a 4 per cent growth rate just to keep unemployment from rising.

The department also said that corporate profits after taxes fell 0.6 per cent last quarter after soaring the previous three-month period. It was the first quarter in which after-tax profits have fallen since the doldrums of late 1976.

The revised estimates for GNP were good news for the Carter administration. While the 4.7 per cent pace is not quite as robust as some officials would like to see, it nevertheless is rapid enough to cut into unemployment, now 7 per cent.

Still policy-makers are worried enough about possible levelling-off late in 1978 that the administration is continuing to develop plans for a new tax cut next January to stimulate the economy.

Kreps said at a news conference yesterday that a tax cut should be considered despite the third-quarter performance. She said recent improvements in both consumer spending, and capital investment by business "were still disappointing."

The revision in the GNP figures was unusually large. The earlier estimates are prepared on the basis of one of two month's data for most sectors of the economy. Yesterday's figures included later statistics.

However, most of the increase came from factors that analysts conceded are not likely to continue into the current quarter. The largest were greater-than-expected inventory building by business and a one-month narrowing of the trade deficit.

Meanwhile, the department reported that the rate of inflation, as measured by the GNP price index, was 5 per cent last quarter, rather than 5.1 per cent as recorded in preliminary estimates. The rate in the second quarter was 7.1 per cent.

Separately, the Federal Reserve Board announced that the nation's factories operated at 82.8 per cent of capacity in October, down slightly from 82.9 per cent in September and 83 per cent in August. These rates are regarded as sluggish.

Coincidentally, the improvement in the third quarter appeared to make it somewhat less likely that the economy's performance in the current quarter would exceed the previous pace. Neither the trade balance nor the inventory sector is expected to provide a second shot in the arm.

Analysts generally are expecting the growth rate for the current quarter to be somewhere between a 4.5 and 5.5 per cent annual rate. The administration has been hoping the growth rate would average 5 per cent or so through the middle of 1978. The second-quarter rate this year was 6.2 per cent.

The decline in profits stemmed partly from recent setbacks in the steel industry. Because of continued slow sales and competition from imports, several major steel makers have reported huge losses. Bethlehem Steel Corp. lost $477 million last quarter, an industrial record.

However, some of the decline stemmed from falling values of inventories, particularly in the food industry, which has been hit by plummeting food prices. Domestic profits from current production, a firmer measure of the profit picture, rose 5.4 per cent, from 11.8 per cent before.

The third-quarter figures spurred new concerns about the economy. Sen. William Proxmire (D-Wis.), chairman of the Banking Committee, urged the administration to expand its planned $15 billion to $20 billion tax cut to as much as $25 billion if needed.

In the report on GNP, the larger than expected jump in inventories pushed total business stockpiling $2.2 billion over earlier estimates. Late-breaking figures on the trade situation sent net exports $2.5 billion above preliminary reports.

The changes in profit levels brought after-tax profits to a new annual rate of $103.7 billion, while profits from current production rose $7.6 billion to a $147.8 billion rate. Dividends rose $2 billion to a new pace of $42.3 billion.