A sharp jump in hourly labor costs combined with a drop in work productivity in the first quarter of 1979 to produce a massive increase in unit labor costs, which are certain to create new inflationary pressures, government reports showed yesterday.

Labor costs per unit of production were up 8.8 percent in the first quarter over the first quarter of 1978, a bulge that "is going to be passing through rising prices," according to Commerce Department economist William Cox.

Meanwhile a government index designed to forecast economic trends declinded in March for the third consecutive month - suggesting a slow down but failing to show a conclusive trend, according to the economists who put it together.

Separately, the Agriculture Department said prices that farmers got for raw products dropped one percent in April, the first decline for the monthly index since last November.

The 4.5 percent drop in productivity was the first since the first quarter of 1978, when the economy suffered an identical decline. In the fourth quarter of 1978 productivity had increased at a 1.7 percent annual rate.

According to the Labor Department, the first-quarter drop in productivity reflected the fact that actual output was virtually unchanged-increasing only 0.3 percent-while there was a 5 percent increase in the number of hours work.

But while the yield of goods and services per hour worked was thus sharply reduced, the total compensation per hour of work was up sharply-hence the bulge in the labor cost per unit of output.

Total hourly labor costs-counting wages, fringe benefits and taxes paid by employers-increased at an annual rate of 11.1 percent.

Increases in both the federal minimum wage and Social Security taxes accounted for much of the labor cost increase.

Economists have not been able fully to explain the weak American record on productivity-one of the factors that has disadvantaged American goods seeking to compete in world markets. For 1978 as a whole, productivity increased at only a 0.3 percent rate, smallest since the 1974 recession.

Cox said that "if you could return to more rapid productivity growth, there would be less cost to pass through at the price level. That clearly would help soften the inflation rate."

The composite index of leading indicators is a synthesis of 12 individual economic statistical series published monthly by the Commerce Department. It declined .049 percent in March to a level of 142.3 (1967 equals 100) after declines of 0.42 percent in February and 0.35 percent in January.

But of the 10 indicators available in March, five were up and five were down. And of the five indicators that declined in March, only one declined significantly, while some of the advancing indicators showed surprising strength.

Felicks Tamm, editor of the Commerce Department Business Conditions Digest, which assembles the composite index, rejected the widely circulated view that the three-month decline was a certain sign of recession.

"It is a signal of a slowdown in the economy, but not necessarily a recession," he said. "What we have here is a mixed bag."

Many private economists are skeptical about the recession-predicting qualities of the indicators, noting that the index merely is a summary of previously published data.

In a telephone interview yesterday, former Economic Council chairman Alan Greenspan noted that "not all of the indicators are equally important, or equally important at any given point in the business cycle."

While the index sometimes gives false signals, it is supposed to be more accurate in forecasting downturns than economic recoveries.

Cox said that the index is "consistent with the impression of those who believe there will be a recession." But he added that he thought a recession will be avoided, and he "wouldn't be surprised" if the index turns up next month.

Lyle Gramley, a member of the Council of Economic Advisers, said he does not attach much significance to the leading indicators decline. Gramley forecast that the economy would stay on a path that would match the administration's 2.2 percent real growth target for this year.

Most economists agree that the economy will rebound from the sluggish first quarter, when the real gross national product gained only 0.7 percent. Both Cox and Gramley predicted yesterday that the second quarter would show a gain.Greenspan agrees, and thinks the economy will remain strong in the third quarter.

The question debated among economists is how strong, and for how long. Many see a recession-meaning negative growth for at least six months-beginning late in 1979 or early 1980.

Associated Press reported the following:

Farm prices rose steadily beginning in December, shattering records for four straight months. Particularly because of soaring prices for meat animals and poultry, the climb was a key factor in a sharp boost in retail food prices in the first quarter of this year.

But despite the April decline, farm prices averaged 17 percent higher than a year ago, officials said yesterday. The department's Crop Reporting Board said lower prices for hogs, oranges, eggs, lettuce and milk contributed most to the decline from March to April. CAPTION: Graph, Leading Economic Indicators, The Washington Post