West Germany is running short of children - and with the birth rate heading down at a steady rate, some demographers have glumly warned that the West Germans' preference for prosperity over progeny could lead them to extinction.

While no one seriously believes that the West Germans will disappear, the effect of declining reproduction on population threatens to become a serious problem, with potentially far-reaching effects on politics, social patterns and economic stability.

Ironically, Communist East Germany - cut off from the West by walls, ideology and post-war politics - is confronted with the same worrisome problem. Despite some progress in the last year, the East German birth rate is still the lowest of any country in Communist Eastern Europe.

But the West German situation is far more acute. West Germany's birth rate is the lowest of any major country in the world, according to the Ministry for Youth, Health and Family Affairs.

If the steep decline of recent years continues, officials calculate that West Germany's current population of 61.3 million will be cut almost in half by the year 2052 and sink to 20 million 100 years from now.

Fewer young West Germans mean fewer workers to pay the higher taxes that must be levied to support a retirement population with some of the Western world's most generous benefits. The federal bank has already noted the potential effect of the population decline on future economic growth.

Unstated but also present is unease over the future makeup if West Germany's still largely homogeneous population. Included in today's population figures in West Germany are almost 4 million foreign workers and their families who live here and are having babies much more frequently than the Germans.

Every second child born today in Frankfurt and evert third born in Munich are born to non-German parents.

Shifting social values, pill, women's movements and general affluence have had their impact on birth rates in many developed countries, Germany, both East and West, the effect has been so great that population is declining rather than just rising more slowly.

In England and Austria, population held roughly even in the years from 1973 through 1977.In France, Italy and the Netherlands it went up slightly.

But in West Germany, the population dropped by 650,000, and the birth rate of roughly 9.8 per 1,000 population is well below the rates of those countries and that of the United States, where it is 13.6 per 1,000.

This has raised the question of whether there is something specifically German about what is happening here.

The answer, in the view of West German specialists, is "yes." West German society today is not as "pro-children-oriented as other countries," says Helmut Buerger of the family ministry. "It is not that German parents do not love their children like all other parents," he says, but rather that "the climate for children is not so good" in the society as a whole.

"It's not a simple matter," says sociologist Helga Gripp of the Social Science Institute of West Germany's Evangelical Church, "but part of it has to do with the political, economic and ideologial situation of West German capitalism. The aims of the society primarily are prosperity and materialism and children are not very opportune for this. They are seen as hindering people from further developing themselves.

The Bonn government has, in fact, been candid in acknowledging that something has gone wrong. A government report on the subject made in response to inquiries from parliamentarians identifies the "limited friendly attitudes of the scoiety" toward children as a factor along with an increase in the number of women entering careers, the "orientation toward wealth and ambition of young couples, and the competition between happiness with children - who can be obstacles to a higher income - and the other fulfillments of marriage."

The number of childless couples is increasing, and about half of those with one child do not want more, the report said.

On the surface, West Germany does not seem especially unfriendly to children. But there is a degree of what Gripp calls "hostility to children" - a feeling that they are a nuisance - visible in the behavior of neighbors toward the children of others or to whatever ruffles the still generally orderly ways of the older generation.

What to do about it is another matter. Schemes to pay people to mavry and produce large families raise hackles in West Germany because they smack of the bonuses and medals awarded by Hitler to those who increased the Aryan flock.

Bonn ministry officials do not think that giving more money to West Germans, already reasonably well-off financially, will help. But that is what the big and conservative state of Bavaria will start doing on July 1.

Marriages have dropped 27 percent, divorces have increased more than 100 percent and births have dropped 50 percent in Bavaria since the mid 1960s.

From now on, however, couples can get a low-cost, seven-year loan of $2,500 when they marry and the same amount when their first child is born. The sweetener, however, is that the state allows the couple to keep large chunks of that money free when additional children are born.

The federal government, however, has not yet figured out what to do, although several plans are being developed as part of the international "year of the child" next year. Still, officials believe the solution lies in improved public attitudes rather than money.

The Bavarians actually have followed East Germany's example.

East Germany, whose post-war population of more than 19 million was reduced to about 17 million as people fled west before the walls went up in 1981, has also suffered from a low birth rate that is just slightly higher than West Germany's.

Since 1973, the population has dropped to somewhere under 16.8 million, and East Germany is the only Soviet-bloc country with a declining population. This is something of a stigma for such states, where increasing the population is accepted policy, and for East Germany in particular, because it has staked much on a young generation that does not know a time when the country was not under Soviet domination.