Driven by decontrolled energy prices and the first wholesale food price increase in four months, the producer price index jumped 1.3 percent in March, the most since last summer, the Labor Department reported yesterday.

On an annual basis, that increase in the cost of finished goods works out to an inflation rate of just over 16 percent.

But there were signs that increases later this year may be smaller.

Many economists believe economic activity has begun to decline or is about to do so, which could help ease inflation.

The department reported yesterday that the nation's employment rate remained unchanged at 7.3 percent in March, a high rate by historical standards.

And the number of people employed, as measured by the survey of business payrolls, failed to grow in March for the first time since last June.

At 7.3 percent, the unemployment rate has changed little over the last three months. In March, the rate for adult men edged downward by 0.1 percentage point to 5.9 percent. The rate for adult women went the other way, rising 0.1 percentage point to 6.6 percent. The rate for teen-agers fell from 19.3 percent in February to 19.1 percent last month.

The largest change was in the umemployment rate for blacks which rose sharply from 13.1 percent to 13.7 percent.

Part of the increase in the price index for finished goods, as well as the 1.1 percent rise in the companion index for intermediate goods, was a result of large increases in the cost of refined petroleum products. These came in turn from President Reagan's decision to strip away federal price controls on domestic crude oil, and the continued pass-through of Organization of Petroleum Exporting Countries' price hikes.

However, most of those increases actually occurred in February, since changes in prices of refined products enter the index with a one-month lag, the department said.

For instance, the energy component of the finished goods index rose 6.1 percent last month. That includes a 7.5 percent increase in the price of gasoline charged by a refiner. Similarly, the same component of the intermediate goods index -- which covers the cost of, say, heating oil to businesses -- rose 4.3 percent.

But the energy component of the crude materials price index, which includes changes in crude oil prices that go into the index with no lag, rose only 0.3 percent in March.

All this suggests, analysts said, that energy prices will not have nearly as much impact on the producer price indices in coming months.

Janet Norwood, commissioner of labor statistics, told Congress' Joint Economic Committee that a large decline in the length of the average factory work week in February was reversed in March.

But at 40.0 hours, the work week is slightly less than it was in December, another indication that the economy may be set for a decline, analysts noted.

Townsend-Greenspan & Co., the economic consulting firm headed by economist Alan Greenspan, recently told its clients that the gross national product declined slightly in February after adjustment for inflation.

Lawrence Chimerine of Chase Econometrics sees much the same pattern developing. The economy is beginning to weaken again, he said.

"We are in the midst of a period of stagnation rather than a 'normal' business cycle," he said. "This stagnation has resulted from the combination of weak real incomes, high debt burdens, depleted savings, and high interest rates, which have prevented any sustained improvement in household spending and have kept new housing activity sharply below potential demand."

That same stagnation has caused declines in the prices of many raw materials in the last three months. An index of crude materials prices other than for energy has fallen more than 7 percent in the last three months, the Labor Department said. The movement of such prices often is a harbinger of changes in the overall economy.

The 0.8 percent increase in consumer food prices in March was the largest since last August. Prices for pork, fresh fruits, vegetables and fish all rose. The cost of beef and veal continued to fall, but by less than in February.

Finished goods prices rose 10.5 percent in the year ending in March.