BUDGET CUTS sometimes cost more than

they save. One current example is the drastic reduction the administration has proposed in the cultural exchanges--especially the programs that send American scholars abroad to teach and bring young foreigners here to see the United States firsthand.

Congress established these ventures immediately after World War II, and many of the young people who came here on those grants in the early years are now senior figures in the political and business life of their own countries. Americans on rotating fellowships have taught for a generation in the universities of nearly every country on earth, including some not particularly friendly to the United States and not otherwise inclined to allow their people much contact with Americans. Young Americans who went abroad to study in years past are now the specialists who serve, among others, the government itself.

The benefits are the sort that do not lend themselves to simple measurement in terms of dollars. But there are few people working in these fields who do not believe that the cumulative effects on attitudes abroad have been profound.

The House of Representatives passed last week the Reagan administration's revised budget for the State Department and the International Communications Agency. It cuts the money for the Fulbright academic exchanges and for the visitor programs by more than half. Fulbright exchanges --running since 1946, and named after the former senator from Arkansas--currently operate in 120 countries. Under this budget, they would continue in only 59.

The situation in the Senate appears to be a little less bleak. Sen. Lowell P. Weicker has persuaded the Appropriations Committee to uphold the present funding with a modest increase, not quite covering the rate of inflation. That bill is scheduled to come to the Senate floor within a few days. It would provide $101.6 million for international educational and cultural affairs this year--compared with $50.3 million in the House bill.

It is ironic that the Reagan administration, with its intense concern for this country's standing abroad and its extreme sensitivity to every aspect of international competition, should insist on nearly destroying this highly successful campaign of persuasion. The amounts of money are not large, the visibility is great and the results are demonstrable. In its preoccupation with military power, the administration is in danger of neglecting other kinds of influence that serve the national interest less dramatically and certainly less expensively, but not necessarily less usefully.