If someone were casting for the part of international money man, Anthony M. Solomon, undersecretary of Treasury for monetary affairs, would be a logical choice. Although he is engaging in private, and the international money markets provide -- to those who play them -- their own form of high drama, Solomon in public displays a dry deadpan manner that coincides perfectly with the popular view of international monetary affairs as an esoteric subject too technical to be understood or to matter.

Solomon was at his best last week at the traditional Washington press briefing that precedes the annual meetings of the International Monetary Fund and World Bank, being held in Belgrade. He methodically dispensed statistics and coughed up obscure answers to obscure questions. It was the calming, clinical style of a physician whose very detachment is designed to instill confidence that things are under control.

Actually, they aren't. Even by Soloman's estimates, economic growth in the industrialized nations -- hurt by a 60 percent increase in oil prices and a further rise in non-energy inflation -- will slow both this year and next, though the slump does not yet appear to approach the size of the 1974-75 recession. Most of the slowdown is occurring in the United States, Germany and Japan are actually expanding faster in 1979 than 1978. If the Treasury Department's estimates are correct, their growth will slacken only modestly next year.

It is decidedly a mixed picture; neither as tranquil as Solomon's manner suggests, nor as turbulent as the recent stampede for gold implies. But, technical as all this monetary business seems, it does matter. The question that hangs over the Belgrade meetings -- and will not be settled there -- is whether things will get much better in the 1980s or whether the 1970s slowdown will evolve into a more pervasive stagnation. The economic diplomacy being increasingly practiced by Solomon and his colleagues will help resolve that issue.

The theme of this diplomacy has now become abundantly clear; currency stability. No one knows the cost of restoring faith in paper currencies, but it is not the mindless objective -- undertaken blindly as an unquestioned good -- that it sometimes seems.

In the past 20 years, the world economy has become far more integrated than most people appreciate, and yet business across borders -- trade, tourism and investment is conducted in a multitude of different currencies whose values are constantly fluctuating in relation to each other. The broad notion is that these fluctuations, by creating immense uncertainty about future costs and prices, destroy confidence and discourage investment in internationally-oriented interprises on whose vitality everyone depends.

Thus, in this view, to foster stability is to create a foundation for renewed growth to which instability and uncertainty are implacably opposed. This is a commonsense idea with a great deal of superficial appeal, but it is unclear how it will work out in practice.

What we are talking about here are relative rates of inflation, which is the main (though not exclusive) source of instability between curriencies. If inflation in the United States is reducing the dollar's value twice as rapidly as inflation in Germany is reducing the mark's -- which is roughly the case -- then, sooner or later, the exchange rate between the two currencies (business, government central banks and wealthy individuals) perceive this, their efforts to anticipate the change by shifting their funds into strong currencies (or gold) can magnify and multiply exchange rate fluctuations.

Such currency shifting has clearly hurt the dollar in the past 18 months, though no one really knows just how much. Since 1976, according to the annual report of the International Monetary Fund, dollars have declined from about four-fifths of the official foreign exchange reserves of countries to almost three-quarters. These funds moved primarily into German marks, Swiss francs and Japanese yen.

Preventing these movements is no mean task. Neither is it simply a technical matter. If the U.S. inflation rate is twice Germany's, one way for the United States to prevent shifts out of dollar investments is to keep interest rates high. Thus, the commitment undertaken last November by the United States to stabilize the dollar against other currencies, particularly the mark, inevitably entails a protracted anti-inflationary policy, including relatively high interest rates, unless the Germans are willing to let their inflation rate drift upward.

They aren't, and there's the rub. It's no secret that the Germans seek to impose their brand of stability not only on the United States but also on their partners in the European Community through the European Monetary System. This is a sophisticated scheme for keeping the European currencies linked together that creates the same pressures to adjust interest rates to compensate for different inflation levels.

The danger is that anti-inflationary policies that flow from a slavish devotion to exchange rate harmony will induce precisely the stagnation and instability that everyone seeks to avoid. A protracted period of slow growth or no growth -- meaning higher unemployment -- risks the political uncertainty and increased protectionism that also suffocate confidence and investment.

No one knows the way. Just last week, currencies within the European Monetary System were realigned slightly (the mark was raised 2 per cent against most currencies) and the dollar was permitted to drop against the mark, indicating that countries believe they can't adhere too rigidly to perfect currency stability without creating intolerable domestic pressures.

We are, in short, walking the fine line between instability induced by excessive deflation. Our basic sources of instability are many: oil scarity, our once exaggerated expectations of the future and current reluctance to adjust to new realities. But a constant theme of twentieth century economic history is the danger that we may aggravate our underlying problems through an international monetary system that is either too repressive or too permissive. Technical though it may seem, that's what this economic diplomacy is all about.