Productivity at the nation's private businesses other than farms rose at a strong 3.4 percent annual rate in the first quarter, but the gain was not enough to offset a sharp decline in the previous quarter, the Labor Department reported yesterday.

The increase in the productivity measure -- the output of goods and services per hour worked -- was the result of an increase in output at a 4 percent rate coupled with a rise in hours worked at a 0.6 percent rate.

Productivity fell at a 4.1 percent rate in the fourth quarter of 1985.

After a rapid increase in 1983 when the current economic expansion began, productivity growth has disappointed many analysts who had hoped a combination of tax incentives and lower inflation would keep it growing by 2 percent or more a year. Instead, output per hour has been essentially flat recently, with the level of productivity in the first quarter virtually unchanged from its level two years earlier.

In fact, productivity gains since the beginning of 1981 have averaged just over 0.7 percent a year, up from the 0.5 percent annual gains in the previous five years.

The sizable increase in productivity in the first quarter was greater than the rise in compensation per hour, so that unit labor costs declined at a 1 percent rate. However, unit labor costs had gone up at a 7.6 percent rate in the fourth quarter, and still were up 3.1 percent from the first quarter of 1985, the report said.

Historically, changes in unit labor costs have been tied closely to changes in consumer prices.

"Productivity growth continues to lag expectations, especially in the nonmanufacturing sectors, which are becoming a more significant part of overall economic activity," said economist Lawrence Chimerine of Chase Econometrics in a report sent to clients last week.

"Thus, even with a decelerating pattern of wage increases, unit labor costs are likely to continue to grow at the recent 3 percent to 4 percent average rate. This could, in fact, accelerate further if wage restraint eases in many industries during the next several years," he said in suggesting that inflation will return at least to the 3 to 4 percent range this year.

The Labor Department report said compensation per hour -- which includes employer contributions to social insurance and other benefit programs as well as wages and salaries -- rose at a 2.4 percent rate in the first quarter, the slowest rise since the third quarter of 1983. Consumer prices rose even more slowly during the quarter, so that real compensation increased at a 0.9 percent annual rate.

Since the first quarter of last year, real compensation in the nonfarm business sector has not changed. It is up about 2.5 percent in the past five years, but up not at all during the course of the past decade.

When farms are included, productivity rose at a 2.3 percent rate in the first quarter and unit labor costs fell at a more modest 0.6 percent rate.

In manufacturing -- which typically has faster rates of productivity growth than the service sector -- -- productivity was up 2.6 percent in the past year, while the entire nonfarm business sector, of which it is a part, had no productivity growth. That means productivity in the service sector fell significantly.