President Carter issued a sobering economic report yesterday warning that the average American's standard of living will improve only slowly for years to come.

The White House outlook now is for gains in real incomes only half as large -- or less -- than the 3 percent annual increase that once was considered the norm.

In 1979, with the economy held down deliberately to fight inflation, any improvement in living standards will be tiny.

The traditional visionary economic goals announced by most presidents were missing from Carter's report. In it, the president declared, "My economic and budgetary program deals forthrightly with the economic realities we face today."

The political reality means a growing struggle over how to divide an economic pie that is growing more slowly, a struggle that began this week with the release of Carter's fiscal 1980 budget. Black leaders, spokesmen for the elderly, and representatives of cities have denounced efforts by Carter to reduce the federal deficit by trimming programs that aid their constituencies.

Nevertheless, Carter emphasized in the report, "The task now confronting us is to manage an economy operating at close to its capacity" -- adding with a nod to his critics, "to sustain prosperity and extend its benefits more widely among our citizens."

The principal reason for this new slower-growth view of the future, according to the report, is the very slow growth of productivity -- the volume of goods and services produced for each hour Americans work.

Without faster growth of productivity, the period of "austerity" Carter has launched will continue indefinitely.

"The disappointing performance of productivity, the related sharp drop in unemployment, and the acceleration of inflation brought the economy" to a point in 1978, the report said, that policy had to "switch from efforts to strengthen growth in economic activity to measures that restrain inflation."

"Reducing inflation," it continued, "must be the top priority of economic policy in 1979."

Lowering the estimates of how fast productivity is likely to grow in the future also means lowering assumptions about how much the economy could produce if there were full employment. New calculations show that the economy's output last year was only about 2 1/2 percent below it s potential. In other words, the recovery from the 1974-75 recession was largely complieted.

When productivity gains were large, employers could step up production without adding more workers. But last year, with the gains small -- less than I percent for the year -- more employes were needed to increase production.

In the first quarter of 1978, even though unemployment was still above 6 percent, new workers were being hired so fast that wage rates, and thus inflation, were pushed up, according to the report.

"The evidence suggests that under current labor market conditions, the danger of accelerating wages begins to mount as the rate of unemployment falls significantly below 6 percent. During 1978 the unemployment rate moved into the top of the range," it said.

And the report added, "pressures associated with the speed of the decline in unemployment were an important source of increased wage inflation."

In short, it concluded, "A further reduction of the unemployment rate during 1979 would run some rusk of generating excess demand and creating inflationary pressures in labor markets."

The report forecasts gross national product growth, adjusted for inflation, of only 2.2 percent this year and 3.2 percent next yeat, compared to 4.3 percent last year. The forecast assumes there will be a marked slowdown in expansion in the second half of the year, but no actual decline and therefore no recession.

"In case you hadn't noticed," Carter's chief economic adviser Charles Schultze noted wryly at a briefing on the report, "out economic forecast for the growth in GNP is somewhat more optimistic than many private forecasters." The private forecasters, as well as the Congressional Budget Office, expect a recession.

That optimism did not really extend to the productivity problem, however. The economc report said productivity increase had slowed in virtually every industry in America.The causes are "complex," and include a lower rate of investment by business, "a dramatic shift in the age-sex composition of employment," and "increased economic and social regulation."

More young workers, as well as women, are taking jobs taan in the past, and both groups have lower productivity than more experienced workers genreally, the report said.Increased regulation, such as pollution control and safety requirements, may have but productivity by 3.3 of a percentage point, it added.

"Let's face it," said Schultze, "nobody had any magic buttons to push on productivity. There are a lot of things about what has happened that we don't fully understand.

"All over the world, the rate of growth of productivity has fallen off in the past five years. Productivity growth means change. It means doing innovative things, different things. The confidence of people in the future, their ability to look at a stable future, has been shaken by the events of the last five to seven years."

More research and development spending, more investment, lower inflation -- "all those things contribute to turning that productivity experience around and getting it improving" -- Schultze declared.

The hard economic realities described by Carter and his economists were at odds with the goals of last yeat's Humphrey-Hawkins Full Employment and Balanced Growth Act.

That law requires that the president, this year, show economic projections for growth and inflation that would achieve a 4 percent unemployment rate and a 3 percent rate of inflation in 1983. Those projections were included in the report.

For 1979 and 1980 the figures are forecasts. In 1980, for instance, unemployment is forecast at 6.2 percent and inflation at a 6.4 percent rate. In the following three years, the Humphrey-Hawkins goals require a rapid, simultaneous reduction of both.

"By any criterion," said the report, "these are very ambitious goals." Added Schultze, with the sort of modesty that marked the entire report, "We need to learn a lot more and do a lot more to get there."