The Carter administration received a moderately encouraging bit of economic news yesterday: American business finally may be beginning to increase its capital spending - a move needed to bolster the economy.

The latest survey by the Commerce Department shows U.S. corporations expected to increase their spending for new plant and equipment by 5.3 per cent after adjustment for inflation.

While that still would be lower than most analysts have hoped, it would mark a definite step-up from the last major sampling, conducted in June. The increase projected then amounted to 4.9 per cent, using revised inflation data.

At the same time, The department reported that actual outlays for new facilities and equipment came in more strongly than had been predicted. Spending for the period rose at a 4.5 per cent annual rate to $150.8 billion.

The department's surveys traditionally are somewhat more bearish than those of both private forecasters and actual developments. Most analysts now see capital outlays up 7 to 8 per cent this year, after adjustment for inflation.

The Carter administration has hoped for a 7 to 8 percent increase in 1978, and would prefer to see a similarly strong rise next year as well. However, some privete forecasters expect outlays to rise less rapidly in 1979.

Business spending on new plant and equipment has figured more importantly in economic forecasts in recent months in the face of an apparent tapering-off in consumer spending.

Analysts say business investment now must pick up and fill the gap or the economy may slow more than is considered desirable. Capital outlays rose by 6.5 percent in 1977.

Yesterday's report showed non-manufacturing industries plan to boost their spending by 4.7 per cent, while key manufacturing firms plan a 6 per cent jump - both slightly below last year's increases.

The new survey was compiled using an estimate of 7 per cent for the estimated inflation rate, instead of the less-realistic rate 5.3 percent rate employed in the earlier sampling.

Before adjustment for inflation, the increase would work out to be 12.3 percent, to a new level of $151.1 billion.