A little steam went out of the nation's economy in December as a sharp drop in automobile output held the monthly rise in industrial production to 0.2 percent, while finished goods prices fell, according to government statistics released yesterday.

The Federal Reserve reported that its index of industrial production increased 0.2 percent last month, after rising 0.4 percent in November and 1.1 percent in October. The index, which measures the output of the nation's factories, mines and utilities, ended the year up 5.2 percent from the previous December.

That was the best annual increase since 1984 and followed a scant 1.1 percent rise in 1986. Analysts attributed the stronger performance last year largely to a jump in the demand for American goods abroad that was spurred by the falling value of the dollar, which makes U.S. exports cheaper in many foreign countries.

But the December figures, and especially the 9 percent drop in the number of auto assemblies, underscored a growing weakness in consumer spending that some forecasters believe could move the economy close to a recession in the first half of this year.

At the same time, the Labor Department said producer prices for finished goods fell 0.3 percent in December after showing no change in November and a 0.2 percent decline in October.

The December drop, primarily due to declines of 1.3 percent in consumer food prices and 1.9 percent in finished energy prices, left finished goods prices 2.2 percent higher than they were a year earlier. During 1986 such prices went down 2.3 percent, largely as a result of sharp drops in energy prices.

A decline in energy, food and feed prices held last month's increase in intermediate materials prices to 0.2 percent, about half the rate of the previous two months, and were responsible for the third drop in four months in crude materials prices.

However, prices of some industrial materials continued to go up rapidly. Copper and aluminum prices soared again and pulp and paper product prices were also strong. On the other hand, some pressure on materials prices eased a bit. Paint materials prices fell 1.3 percent and industrial chemicals prices were up 0.5 percent. Both had risen sharply earlier in the year.

For the entire year, finished consumer food prices fell 0.2 percent. For finished consumer goods other than food, prices were up 3.9 percent. If energy goods were also excluded, finished consumer goods prices rose 2.1 percent.

Prices of capital equipment, which still faces strong competition from imports, rose 0.2 percent in December and 1.3 percent for all of 1987, the Labor Department said.

According to the Fed's report on industrial production, manufacturing output rose 0.2 percent in December, compared to 0.5 percent in November and 1.2 percent in October. The output of consumer durables fell 1.1 percent, which was more than accounted for by the drop in new car assemblies. Production of such goods as appliances and television sets rose during the month.

The output of business equipment fell 0.3 percent, while that of defense and space items rose 0.6 percent. Production of intermediate products was up 0.5 percent and that of materials was up 0.4 percent. Mining production rose 0.2 percent but that of utilities fell 0.4 percent, the Fed said.

In another report pointing to somewhat slower economic growth in coming months, the Commerce Department said manufacturing and retail and wholesale trade inventories rose 0.8 percent in November after a 1.1 percent increase in October. At the end of November, inventories were a seasonally adjusted $695.5 billion.