THE REAGAN administration has now laid out an extraordinarily strong and useful defense of world trade and the principle of open markets. In contrast to the steady drift of the Democrats toward protectionism, the president is sticking with a position that is both traditional and right. He made the case for open trade in his State of the Union address, and the chairman of his Council of Economic Advisers, Martin Feldstein, makes it again in the annual Economic Report.

The rapid expansion of international commerce since World War II has contributed heavily to the rapid rise of standards of living in all of the industrial countries. But that expansion may not be permitted to continue. It is going to take great political skill and stamina to avoid a collapse into a tangle of quotas, discriminatory taxes and buy-American rules that will save a few jobs today at the cost of many more tomorrow.

For the president, the next test will probably be the Houdaille case. Houdaille Industries is a small Florida manufacturer of machine tools. It charges that the American market for certain types of highly sophisticated machine tools is being rapidly captured by its Japanese competitors, organized as a cartel with government support. Houdaille wants the president to suspend the investment tax credit for the purchase of the Japanese machines. The effect would be the same as a 10 percent tariff.

Houdaille's legal case is elegant, immensely ingenious and, in the end, unpersuasive. If Mr. Reagan grants what Houdaille wants, he will have established a deeply damaging precedent that many other industries, particularly in the field of electronics, are eager to use. Suspending the tax credit for imported machine tools would be a clear violation of this country's trade treaties, and the bad example would be immediately followed around the world.

As for the charges of cartels and subsidies, the American electronics industry might usefully reflect on the appearance that it sometimes leaves in other countries. A number of the American companies have, for example, received the blessing of the Justice Department for joint research and development work--not quite a cartel by American standards, but not quite wide-open competition either. Many of these electronics companies will also benefit from the increases in defense spending. Abroad, the U.S. defense budget often looks like the world's richest source of subsidies for high technology.

The administration's purpose, the Economic Report says, is to resist protectionist pressures at home while continuing to urge foreign governments to eliminate their own trade distortions. Just right. Mr. Reagan will have an opportunity to demonstrate it when the Houdaille petition shortly comes to his desk.