Industrial production fell another 0.5 percent in August as auto companies and makers of business equipment slashed output in the face of falling sales, the Federal Reserve Board reported yesterday.

It was the 11th drop in the past 13 months for the index, which measures production of the nation's factories, mines and utilities, and it indicated that recovery from the recession has not begun.

Undersecretary of Commerce Robert G. Dederick called the report "disappointing," adding, "the recovery has not taken hold as yet." Dederick maintained that the recent personal tax cut, surging stock prices and declines in interest rates ought to spark a turnaround "in the autumn."

The August drop left industrial production 10.2 percent lower than it was a year earlier and no higher than it was in May 1977.

With companies rapidly reducing investment plans, the production of business equipment has slumped and last month was 18 percent lower than in July of last year. In the 1974-75 recession, it fell only 14.2 percent, the Federal Reserve said.

Automakers, encouraged by higher sales in late spring, optimistically increased production in June and July, only to see sales fall again and dealer inventories climb sharply. To try to reduce those inventories, the companies cut auto assemblies in August by 16 percent to an annual rate of just 5.5 million units.

Car sales, however, have stayed low and inventories high, suggesting additional cuts in auto production in the fourth quarter, analysts said. In the first 10 days of September, sales were running 29 percent lower than a year ago and were at the lowest level since 1967.

Donald H. Straszheim of Wharton Econometric Forecasting Associates said, "There is almost no good news" in the industrial production report. "Since retail sales were so bad in August it's probably fortunate that production was, too. Otherwise there would have been a big buildup of unwanted inventories."

Straszheim said Wharton was in the process of revising downward its forecast for the remainder of 1982 because of the continued declines in production and the consumer's unwillingness to buy even in the wake of the large tax cut in July.

"Clearly, people haven't reacted to the tax cut as expected," Straszheim declared. "High unemployment seems to outrank the tax cut. People are scared."

Earlier this week, the Conference Board, a business research group, reported that consumer confidence dropped substantially in August after four consecutive monthly increases, and that a record proportion of the households questioned in its monthly survey -- 58.3 percent -- complained that jobs were hard to get.

On the basis of later information, the Federal Reserve revised upward by 0.2 percentage points the change in the production index for both June and July. That left June with a 0.5 percent decline and July with a 0.1 percent increase.

The defense and space category of products showed a healthy increase, 0.8 percent, for August, and even that was slightly less than the 1.1 percent rise the month before.

Output of construction supplies rose 0.2 percent, the third consecutive monthly increase. However, that category remained down 14.2 percent compared with August 1981. Production of basic materials was unchanged from July to August, but output in primary metals fell again. Output of steel, copper and other metals now stands nearly 29 percent lower than it was in 1967, the base year for the industrial production index