Inflation and unemployment both increased in October as the nation continued the long, slow struggle out of recession.

The Labor Department reported yesterday that rising food prices and the cost of new cars pushed the Producer Price Index up 0.8 percent, while unemployment edged up 0.1 percentage point to 7.6 percent.

The October price increases were a sharp turnaround from September when wholesale prices actually declined 0.2 percent. The Carter administration has been predicting sharp increases in food prices throughout the remainder of the year.

Janet Norwood, commissioner of the Bureau of Labor Statistics, said the October statistics were "quite consistent" with other economic indicators at this stage of the recovery, which she described as "quite slow and relatively weak."

Although the economy has shown signs of recovering from this year's recession, Norwood said the beginning of the recovery has yet to be pinpointed. She also noted that the nation probably will have a higher inflation rate at the end of the slowdown than it did when the recession began, in keeping with earlier recession periods.

In other economic developments yesterday, the Federal Reserve Board reported an increase in consumer credit in September -- the first major rise in consumer borrowing since the start of credit controls last March. The Fed also reported a drop in the nation's money supply for the week ending Oct. 29.

The amount of consumer credit rose 6.7 percent in September, with increases reported in all borrowing categories. Despite the rise in consumer credit, the level of borrowing in September -- $20.7 billion -- was well below the record level of $28.63 billion in September 1979. The Federal Reserve Board lifted its credit controls program last summer.

The money supply report for the final week in October showed both M1-A and M1-B down $700 million.

The October unemployment report basically showed the overall jobless picture unchanged since the start of summer. Within the broad unemployment picture, however, there were several changes in the types of unemployment. The jobless rate for adult males, for example, dropped from 6.7 percent to 6.4 percent, the lowest level for this category since April.

The unemployment rate for adult women, on the other hand, rose from 6.1 percent to 6.8 percent during the same period. Teenage unemployment rose nearly a full percentage point in October from 17.5 percent to 18.4 percent. Unemployment for black teenagers remained more than twice as high as unemployment for white teenagers, with blacks at 14.3 percent and and whites at 6.7 percent.

On the wholesale price front, Norwood took some encouragement from the fact that while the October increase was large, it was not as large as the increases in July and August when producer prices rose 1.5 percent a month.

But Norwood also warned that the continued acceleration in semifinished materials could prove troublesome in future months. This category has been rising at the rate of about 0.8 percent a month for the last several months. "Price movements in these products should be watched carefully in the coming months for indication of a possible change in trend," she said.

Wholesale prices have been rising at an annual rate of 12.4 percent through the first 10 months of the year and show signs of possible acceleration in the months ahead. This is basically the same pattern that unfolded in 1979.

The Producer Price Index, which replaced the Wholesale Price Index several years ago, includes three basic categories: finished goods, intermediate goods and raw materials. Prices in the intermediate and raw-material categories have been rising rapidly in recent months.