Output at the nation's factories, utilities and mines was unchanged last month, the Federal Reserve Board said yesterday, while other government reports showed the growth of consumer credit slowing and inventories increasing.

The reports continued the recent pattern of economic indicators that point toward slower growth at a time when the Reagan administration is claiming that the ballooning federal budget deficits can be reduced by spending curbs and anticipated high growth.

Many economists and even some Republican politicians maintain that economic growth will not be strong enough next year to close the budget gap, and insist that a tax increase will be necessary to bring deficits down.

Economists said one of the main reasons that industrial production did not improve in October was the impact of the Canadian automobile strike against General Motors Corp. this fall, which affected the company's U.S. operations.

However, economists also said that the Federal Reserve's report reflected weakness in production of business equipment, indicating lower rates of capital spending next year and much slower economic growth.

Industrial production had declined 0.5 percent in September, the first drop after 21 consecutive monthly increases, and rose only 0.1 percent in August, the Federal Reserve said.

In a separate report, the Fed said consumer installment credit outstanding grew by $4.28 billion in September, following gains of $6.0 billion in August and $7.11 billion in July. The annual rate of growth in consumer credit was 16.25 percent in the third quarter, compared with the 24 percent rate in the second quarter, the Fed said, further confirming economists' suggestions that the economy is slowing down.

In another report, the Commerce Department said that inventories of U.S. businesses rose 0.6 percent in September following a 0.9 percent rise in August, suggesting that businesses' stocks are accumulating faster than they can sell them.

It was because of the growing inventories in September that output at factories declined in October, economists said.

"The inventories numbers really are saying the economy is slowing down faster than most people anticipated," said Steven Wood, an economist with Chase Econometrics.

"Inventories are up not because retailers or manufacturers want them to go up, but sales have slowed."

Wood said that based on recent economic statistics, it appeared that third-quarter economic growth would probably be revised downward from a 2.7 percent rate of expansion to between 1.5 percent and 2 percent. The rate previously was revised downward by the government from an estimated 3.6 percent.

Robert Ortner, Commerce Department chief economist, gave a more optimistic view of the statistics.

Ortner said the figures did indicate the economy had slowed, but he said the industrial production figures were dominated by the impact of the automobile strike in Canada and a 25 percent reduction in coal production.

Ortner said sales and production of automobiles should improve soon and that consumer spending for cars should increase as more cars become available and interest rates continue to decline.

"I think we'll see a healthy increase in production," Ortner said. "Consumers will be getting back on track."

However, Ortner said the fourth quarter probably will be sluggish.

Output of durable consumer goods declined 0.1 percent in October, and production of nondurable consumer goods rose 0.3 percent, the Federal Reserve said.

"In October, parts shortages caused by the Canadian auto strike held car output to an annual rate of 7.0 million units; light truck production decreased substantially," the Fed said.

Auto production in September had been at an annual rate of 6.9 million units.

Output of business equipment rose a modest 0.3 percent in October, following an increase of 0.1 percent in September. Wood called those increases "weak."

"This sort of indicates . . . capital spending for the next year will be significantly less, which means economic activity will be much more moderate" next year, he said.

A lot of the economic growth this year was attributed not just to strong consumer spending but a boom in purchases of capital equipment.

"If there's significantly slower capital spending," that would lead to modest economic growth next year, no higher than 3 percent, Wood said.

The Reagan administration is banking on economic growth of 4 percent to bring down the rate of unemployment, increase incomes and generate more tax revenue to reduce the deficit.

The Commerce Department said that business stocks equaled 1.37 months of sales in September, an increase from 1.35 months of sales in August.

Business sales in September declined 0.5 percent following a 0.1 percent decline the month before.