The economy is now contracting sharply after a slight rise in the third quarter of the year, official statistics revealed yesterday. Commerce Department projections show the gross national product in the final quarter of this year falling at an annual rate of 5.4 percent, sources said yesterday.

Meanwhile the Department released a revised set of figures for the third quarter GNP that showed a rise of 1.4 percent in real GNP, after adjusting for inflation, instead of the last reported 0.6 percent increase. The upward revision was due partly to a better-than-expected overseas trade performance, and partly to a greater buildup in business inventories.

Despite the better-than-expected performance in the third quarter, the latest evidence shows a significant and widespread recession taking hold in the last months of this year. Assistant Commerce Secretary Robert Dederick said the Bureau of Economic Analysis predicts "that real GNP will be down substantially" in the final quarter of this year.

He and other economists agree that the recession has broadened out so that it is hitting much more than just the housing and auto industries.

"We have seen the classic phenomenon that initial weakening in consumer-related sectors finally worked its way into the business sector" so that the economic weakness is now "rather widespread," he said.

The administration is forecasting a rapid improvement in the economy in 1982, after a further decline in GNP in the first few months of the year. Most private forecasters expect the recession to bottom out sometime in the late spring, but Otto Eckstein of Data Resources Inc. commented yesterday, "We shouldn't get so excited about the turn-up now, because there's really no sign of it yet . . . The economy is getting sicker."

Record high interest rates last summer, when the money supply was growing below its target range and credit demand remained strong, pushed the economy into recession. Since then the Federal Reserve has succeeded in speeding money growth, although many market participants believe that the central bank may not want to ease further. Interest rates fell sharply for several weeks, but the decline has recently halted.

The Fed announced yesterday that M1B, which includes cash and all checking accounts at banks and other financial institutions, grew by $800 million in the week ending Dec. 9 to reach $440.6 billion. The previous week the money supply on this measure had expanded sharply. In the four weeks ending Dec. 9, M1B was up 4.9 percent at an annual rate from three months earlier.[Money tables, F9. TABLE OMITTED]

Dederick said there was strong evidence that the recession is holding down prices, and that there would be a significant slowdown in the wider inflation measure for the fourth quarter. The GNP deflator, which shows how prices across the whole economy changed, was up by 9.9 percent in the third quarter, the revised GNP report said.