Businessmen appear to be losing confidence in the economy, telling the Commerce Department they plan to cut back sharply their spending in plants and equipment during the first six months of 1979.

But consumers continued to show their willingness to take on debt to finance their purchases in October, although their net borrowing increase was smaller than in September, according to figures released yesterday by the Federal Reserve Board.

The $3.12 billion increase in consumer credit in October was a healthy one, although less than the $3.68 billion rise in September

Some analysts are becoming worried that consumers are going so far into debt, that repayments could become a burden forcing a sharp retrenchment in spending by consumers. As a result, some economists say, a gradual slowing in consumer borrowing is the best thing that could happen to the economy.

Many economists, both in and out of the administration, are concerned that an economic slowdown will occur next year as consumers slow their spending.

Administration officials say, however, that the economy will continue to grow in 1979, although at a slower pace than in 1978, which is now expected to be about 3.5 percent.

Strong consumer spending and consumer willingness to go into debt to finance that spending has been the backbone of the 45-month-old economic expansion.

If business projections about capital spending are correct, then investment in plants and equipment would not be able to pick up the slack should consumers suddenly decide to start repaying their debts.

According to a Commerce Department survey of companies, businessmen plan to increase capital spending from 3.1 percent in the third quarter to 3.8 percent in the current quarter, but cut that spending back early next year.

In a survey conducted during late October and November by the Commerce Department, businesses said they expect to increase spending by only 1.3 percent during the first three months of 1979 and by 2.7 percent during the second quarter.

When inflation is fractured in, the department said, "virtually no change in real spending is indicated from the second half of 1978 to the first half of 1979."

By contrast, real spending on plants and equipment is expected to rise 4.5 percent in 1978. It rose 6.5 percent in 1977.

If the consumer should stop spending and business forecasts prove accurate -- sometimes businesses actually spend more or less than they anticipate -- little help can be expected from other sectors in the economy to propel the expansion.

The housing sector is expected to slow in 1979 as a result of higher interest rates and higher prices on new homes, while businesses are unlikely to order large quantities of goods for their inventories.

The Federal Reserve Board said the increase in consumer debt works out to an annual rate of increase of 14 percent, compared with 17 percent in the third quarter as a whole and 21 percent in the second quarter.

The slight "slackening of growth was evident in all" types of consumer credit, the Fed said, from auto loans to revolving loans such as department store and gasoline credit.