The economy plunged deeper into recession last month as industrial output fell 2.1 percent, but there was good news on inflation, with producer prices for finished goods rising 0.3 percent for the month.

The gloomy report on production from the Federal Reserve, combined with one from the Commerce Department that the level of business inventories continued to rise in November, indicated that the recession is not about to end, analysts said.

Additional cuts in production, and more layoffs, will be needed to bring down inventories in the wake of falling sales.

The output of consumer goods fell 1.9 percent in December as production of automobiles, appliances and furniture continued to be reduced. Auto assemblies fell 4 percent to an annual rate of 4.6 million units. Production of business equipment decreased 1.2 percent, while output of defense and space equipment rose moderately.

During 1981 producer prices for finished goods rose 7 percent, compared with 11.7 percent in 1980 and 12.6 percent in 1979.

Producer prices for consumer foods climbed a slight 0.1 percent for the month, but the increase followed three straight monthly declines. Prices for other consumer goods rose 0.2 percent after two months of large gains. Natural gas prices increased a sharp 3.6 percent. Home heating oil prices went up 1.2 percent, while gasoline prices dropped 0.3 percent.

Meanwhile, the Federal Reserve also reported that the nation's money supply rose by $9.8 billion to $450.2 billion in the week ended Jan. 6, the largest one-week jump in history.

Bond prices fell sharply in late trading yesterday after the announcement. Market analysts had been expecting a much smaller increase in the M-1 money supply, which includes currency in circulation and checking deposits at financial institutions.

"This is very damaging news for both the bond and stock markets," David M. Jones of Aubrey G. Lanston & Co. said. "The Fed will be attempting to lean against this unexpectedly large jump and that will mean more pressure on bank reserve positions and higher money-market interest rates."

Long-term interest rates have been rising since the middle of November despite the continuing drop in economic activity, leading some economists to question whether there will be a recovery later this year as the Reagan administration and most private forecasters have been predicting.

Economist Alan Greenspan of Townsend-Greenspan & Co. said yesterday's news, coupled with other recent information about the flow of orders to business, "suggests the economy is not about to turn around right away." But he added, "The good news is that there is a significant trend toward disinflation."

In New York Thursday President Reagan said the recession could end "faster than expected," though a White House spokesman later said the administration forecast of a recovery beginning in the spring has not changed.

The December numbers left the index of industrial production 6.9 pecent below its peak in July, the month the recession began, the Federal Reserve said. It is 4.7 percent below its level of a year earlier, when the recovery from the 1980 recession was under way.

The largest decline last month, 4.2 percent, came in durable goods, such as autos. Output of construction supplies fell 2.2 percent, and that of basic materials dropped 3.2 percent.

Producer prices for intermediate materials and components rose 0.4 percent, about the same as the month before. The index for crude materials for further processing, which is quite sensitive to economic conditions, fell 1.3 percent, the fifth consecutive monthly decline.

The level of business inventories went up $3.5 billion in November, almost as much as the revised figure for October, $3.6 billion. Stocks of manufacturers rose by $1.1 billion, of retailers by $400 million, and of merchant wholesalers by $1.9 billion.