If it could manage to do so, the Reagan administration would avoid a discussion next month at the Williamsburg economic summit of any new commitments to international management of the global economy. But it's likely to be forced into it, anyway.

The last economic summit, in Versailles, started to crumble almost as soon as it ended when Europe and the United States failed to agree on how to handle the trade security nexus with the Russians. Soon after that, a highly touted ministerial meeting in Geneva of the General Agreement on Tariffs and Trade (called, supposedly, to wind down protectionism) was a total fiasco.

This bit of recent history in mind, Secretary of Treasury Donald T. Regan and Trade Ambassador William Brock have invited their fellow finance and trade ministers of the summit countries to sit down in Paris, May 10 and 11, to discuss the interlinks between trade and financial policy.

This will be a first: In some of the invited countries, the trade and finance ministers barely talk to each other. At the failed GATT meeting in Geneva, the exchange-rate problem wasn't even an agenda item. And the International Monetary Fund, when it lends money, pushes the debt-ridden countries to reduce imports. But when they reduce imports, that cuts somebody else's exports, diminishing world economic growth.

The logic for greater international cooperation is creating relentless pressures for some success. The main stumbling block is the fixation of some ideologues in the Reagan administration against a greater role for government, and for a total reliance on free markets. And there is a lot of plain old chauvinism mixed in here: To traditionalists, "talking the dollar down" is almost antipatriotic, because a strong currency means a strong nation and a strong economy.

And no one can deny that part of the strength of the U.S. dollar is a belief that, uniquely, America is a safe haven in times of world stress.

But as former West German chancellor Helmut Schmidt recently told a private session of equally distinguished world citizens in Tokyo, a decision to "leave everything to the free market" is "too classic."

He proposed that the United States, Japan, and the European Community create a stabilization fund to minimize currency fluctuations. And although it attracted little attention here, New York Federal Reserve Bank President Anthony Solomon told a Swiss business audience on April 8 that the Williamsburg summit may actually produce a modest agreement on limited intervention in world currency markets.

There is no doubt that the extraordinary strength of the U.S. dollar has created enormous problems for the rest of the world. There also should be little argument, at this point, that the dollar is strong in part because interest rates are high, and interest rates are high because of the huge budget deficit.

Sony Corp. President Akio Morita snaps: "The yen-dollar rate has moved at least 20 percent in a year. I can't run my business on that basis." Morita and some other international businessmen would like a more fixed-rate relationship.

But pragmatists don't expect to go back to the old Bretton Woods system based on gold. They are looking for some way of reducing exchange rate instability--in effect, preventing the undisciplined foreign exchange markets from overshooting real values in either direction.

Some, such as Economic Council Chairman Martin S. Feldstein, would argue that this can't be done and shouldn't be tried. And, in fact, since the world went off the Bretton Woods' fixed dollar-gold standard in 1971, reformers have sought in vain for some way to "manage" floating rates.

But this is a gut issue. In plain language, what happens to exchange rates affects jobs.

If the German mark or the Japanese yen are in fact too cheap compared with the dollar, then American manufacturers are going to find it difficult to compete. There's a fine line to draw here: Regardless of the exchange rate, some manufacturers will be unable to compete, because their products don't match up, qualitatively. So the appeal for exchange-rate stability can be a disguise for protectionism.

But to come back to Morita's point, it's hard to see why it took 278 yen to buy one dollar on Nov. 1, 1982, and only 227 yen on Jan. 10, 1983. Something seems screwy there. The "underlying" economic factors, to which free-market devotees like to point, couldn't have changed that much in 10 short weeks.

These problems defy easy solution--and there won't be any tailor-made answers at Paris or Williamsburg. But talking about them as an interconnected puzzle for the world economy is a small step forward--especially for the Reagan administration.