The nation's industrial production grew a healthy 0.5 percent in August, a pace consistent with the administration's prediction that the overall economy will grow between 3.5 and 4 percent for the rest of the year.

Output of business equipment grew sharply last month, while production of consumer goods barely increased at all, according to the Federal Reserve Board.

For the last several months, consumer spending has levelled off and most of the boost to the economy has come from business investment and construction - both residential and heavy industrial.

At the same time, the Fed reported that factories operated at 84.8 percent capacity in August, the highest rate in 47 months. The August report marked the seventh consecutive month that capacity utilization has increased. The August rate was the highest since October 1974.

In another development, Citibank, New York's largest, raised the interest it charges its best corporate customers for a short-term loan from 9.25 percent to 9.5 percent. Citibank's lead was quickly followed by many major banks including Chase Manhattan, Morgan Guaranty Trust, Continental Illinois of Chicago, and Irving Trust.

The climb in the so-called prime rate reflects both continuing strong demand for bank credit and moves by the Federal Reserve Board to raise short-term interest rates in an effort to fight inflation and shore up the international dollar.

Although the Fed has been raising short-term rates (through its buying and selling of government securities in the open market) with tacit White House approval, many administration economists say privately that they are concerned that continued increases in interest rates could shoke off the continuing economic expansion.

But so far, although the economy has slowed from the torrid growth of the second quarter, there is not evidence that higher interest rates are impeding the 42-month-old recovery.

Treasury Secretary W. Michael Blumenthal said recently that there is no chance the nation will face a recession for the rest of Carter's first term.

And the steady growth in production of business equipment as reported by the Federal Reserve Board yesterday seems to confirm that businesses are taking up some of the slack left by consumer spending.

Retail sales have been disappointing for the last several months and that is reflected in the production of consumer goods. Output of consumer goods fell in both May and June and barely rose in July and August, the Federal Reserve Board reported.

Business equipment production, on the other hand, rose 1.1 percent last month and in July and rose 1 percent in June.

One government economist cautioned that business spending cannot continue to out-pace consumer spending for a long period of time before businesses begin to worry and retrench a bit.

In fact, much of the heavy production of business equipment reflects orders placed months ago. In recent months, new orders for business equipment have slowed appreciably.

The Commerce Department also reported that business inventories rose $1.7 billion in July. But economists agree that there is no large backlog of unsold goods sitting in warehouse that might convince companies to slow down their accumulation of stocks, which would quickly translate into a decline in production.

The ratio of inventories-to-sales, at 1.41, is well below the level economists regard as dangerous.

The 1974 recession was triggered when companies found themselves with huge inventories and a sudden slowing of demand. Their moves to bring their stocks more in line with sales resulted in massive layoffs.

"We've all been expecting and eager to see business investment pick up relative to consumer spending," said William Cox, deputy chief economist of the Commerce Department. He said the overall increases in the industrial production index for the last three months - it rose a revised 0.7 percent in both June and July - suggest that the industrial sector of the economy might be even stronger than the administration had thought.

As a rule of thumb, economists say the overall economy must grow about 3.5 to 4 percent a year to keep unemployment (now 5.9 percent) from rising. Industrial production is about one-third of the total economy.

Cox said, "We were too preoccupied with retail sales - which have not been very satisfactory - and we over-looked the strength that is coming from housing, heavy construction and the investment sector."