After-tax corporate profits plunged 17 1/2 percent in the first quarter as the recession took a serious toll of the nation's businesses, the Commerce Department reported yesterday.

The drop left profits at a seasonally adjusted annual rate of $118.8 billion, and the decline has been so severe since the recession began last July that a number of economists believe the weak financial position of many businesses will be a drag on the economy even if a recovery begins later this year. In percentage terms, the first quarter plunge was the third largest in the post-war period.

Reduced inventory profits, reflecting the rapid slowing of inflation, was one major cause of the overall profits decline. Profits from current operations, which exclude inventory profits, fell only 7.8 percent to an annual rate of $149.9 billion.

However, first quarter profits from current operations represented only 6.3 percent of national income, a 1.1 percentage point drop from the fourth quarter and the lowest level of the post-war period.

The recession has also hit unincorporated businesses. Proprietors' income from current operations dropped to a $127.7 billion rate in the quarter, down from $135.9 billion in the fourth quarter of 1981. The first quarter figure constituted 5.3 percent of national income, also a post-war low.

On the other hand, net interest payments soared to a $238 billion annual rate, up 19 percent in the last year. In this case, a post-war high was set, both in terms of dollars and as a percentage of national income, which climbed from 9.6 percent in the fourth quarter to 9.9 percent in the first.

Despite the gloomy profits picture, Commerce Secretary Malcolm Baldrige maintained that "the dramatic drop in inflation is laying the groundwork for a sustainable business expansion, which should be accompanied by a strong rebound in corporate profits.

"Meanwhile, some tax relief for corporations is softening the decline in after-tax earnings," Baldrige said in a statement. "The Tax Act of 1981 reduced corporate tax liabilities to the federal government at an annual rate of $8 billion in the first quarter, representing about 16 percent of the total corporate tax bill . . . Tax reductions will become progressively larger in succeeding quarters."

But Lacy Hunt, chief economist of Fidelity Bank of Philadelphia, declared, "The profits figures really indicate the fact that this has been more of a business recession than a consumer recession." The figures indicate that despite last year's tax breaks, "the business sector is not in shape to lead a recovery," he said.

Meanwhile, the Commerce Department also revised the first quarter gross national product figures to show a 4.3 percent rate of decline, after adjustment for inflation, instead of the 3.9 percent drop originally reported. The changes generally indicated that final demand for goods and services was slightly weaker than first estimated while inventory liquidation was not quite as large as was thought. Real GNP also fell at a 4 1/2 percent rate in the fourth quarter.

Prices, as measured by the GNP fixed-weighted price index, increased 5.1 percent in the first quarter, compared with 8.6 percent in the fourth. The swing in the GNP implicit price deflator, which measures price changes for the mix of goods and services actually produced quarter by quarter rather than of a fixed set of goods and services, rose 3 1/2 percent compared with 9 1/2 percent in the previous quarter.

Most of the first quarter drop in profits was attributable to nonfinancial corporations, particularly those in manufacturing. Not only did profits from current operations fall in the aggregate for nonfinancial corporations, but also so did their profit margins.