THE ASTOUNDING drop in the unemployment rate last month is heartening. It is also totally unexpected. The children born at the peak of the post-war, baby boom are now 18, and most of them graduated from high school last month. Despite the enormous wave of young people flooding into the labor markets, more people found jobs from May to June than started looking. The unemployment rate dropped from 6.1 percent to 5.7 percent in that one month. Over the past year, employment has risen by some 4 million jobs, a phenomenal increase. With the very large numbers of women now working for wages, the ratio of jobs to population in June was the highest in the country's history.

The strange thing is that it's happening at a time when the American economy is not growing very fast. Last week, the administration revised downward its estimates of current growth. It now believes the gross national product will expand only about 4.1 percent this year. There is - or, more accurately, there was - an economists' rule of thumb suggesting that a growth rate of 4 per cent is necessary merely to keep unemployment from rising. But the growth rate since the beginning of the year has been hardly better than 4 percent and, after the brief spring spurt, seems clearly to be falling. Yet the statistic show hundreds of thousands of new jobs in June alone.

There is a warning in this pattern. The country is evidently closer than the administration, or most other people, would have thought to the point at which a tight labor market begins to generate inflationary wage increases. There are many different measures of unemployment - among blacks it is twice as prevalent as among whites, and among black teen-agers the rate is still 37 percent. But for the population as a whole, unemployment is low enough to give the White House a new cause for worry: Any error on the side of too rapid economic expansion threatens to fan up immediate wage inflation, on top of the present unacceptably high rate.

This decline in the unemployment figures strengthens the hand of the people who consider inflation to be far the greater danger. Above all, it strengthens the Federal Reserve Board, which has been raising interest rates as a brake. The administration is likely to respond by becoming more cautions than ever.

Perhaps the economy is entering a period of growth that will be slow, compared with the hypertonic 1960s. Perhaps it will also continue to behave like an economy in which labor is plentiful but capital is scarcer than it used to be. In the past, Americans pressed relentlessly for higher productivity through investment in labor-saving equipment and, when growth flattened, the result was rising unemployment. But the present figures suggest that companies currently are hiring people to do work that otherwise a new machine might do.

If that trend continues, the effect of prolonged low growth might be earnings and standards of living that are now nearly static. The burdens of low economic growth would be shared by almost everybody in that kind of an economy, instead of being forcused mainly on an unfortunate few who lost jobs. A triumph of democratic planning, you could say - except for the embarrassing circumstance that nobody planned it, or even foresaw it.