President Reagan, having flunked a test of his free-trade policy when it came to Japanese autos, faces another crucial desision -- this time over shoes.

Reagan will have to dedcide the future of Orderly Marketing Agreements (OMAs) -- which for the past three years have placed restrictive quotas on show imports from Taiwan and South Korea -- well before the expire at the end of June.

In sanctioning a "voluntary" quota on Japanese cars, the president departed from his hong-held commitement to free-trade principles, although he felt "guilty" about it, he told a private session of his outside economic advisers. Like some of his predecdssors, he fell pray to political pressure that in the end will not help the auto industry -- but will add to inflation.

Now, the president had another tough one to deal with and, as economist Tom St. Maxens of trade representative Bill Brock's off puts it, The International Trade Commission has put us in a real pickle." The ITC, after studying the domestic industry's plea for continued protection suggested keeping restrictions on Taiwanese imports for another two-years, except for so-called "athletic footwear." But the ITC would free South Korea from all restraints.

Naturally, this proposal has sent the Taiwanese through the roof, screaming that the ITC proposal is discriminatory. They have asked the Reagan administration to let the OMA quotas exprire for both countries and to replace them with an "antisurge" device to counter any unexpected serious competition for domestic manufacturers.

Meanwhile, a bipartisan group of 10 members of the House of Represenatives -- led by Speaker Thomas P. (Tip) O'Neill (D-Mass.) -- representing a cluster of shoeproducing states had been pressing Brock to extend the OMAs on both countries for another three years. The American Footwear Industries Association also is supporting that demand.

It would be extremely tough for the Reagan administration to reapply the OMAs to South Korea, thus being even tougher than the ITC. Equally, it would be difficult, if not unacceptable practice, for the United States to apply a unilateral trade barrier against Taiwan. Hence, the "pickle" described at the Brock office.

But there's a way out: The American Importers Association, the American Retail Federation and the Volume Footwear Retailers of America -- which claims to sell half of all the shoes sold at retail in this country -- all are begging Reagan to follow his free-trade instincts and abandon the OMAs completely.

What does Reagan do in this situation? One earnestly hopes he dosen't fall for the quick-fix lure of voluntary quotas or ""orderly" marketing agreements. As Stanford University lecturer David Yoffee pointed out in The Wall Street Journal on May 18, these leaky agreements don't work. For example, when the OMA was established, Taiwan and other entreprenuers established production facilities in four other places -- Hong Kong, the Phillipines, Singapore and Thailand -- to make cheap footwear for export to the United States. So while shoe exports from Taiwan fell from 166 million to 144 million pairs for 1977 to 1980, exports from the other four zoomed from under 10 million to over 40 million.

"In part," said a brief of the Volume Footwear dealers before the ITC, "the imports from the 'New Four' represent a replacement of the imports that otherwise would have come from Taiwan in the absence of the OMA." (When the United States slapped an OMA on Japanese color TVs 10 years ago, Taiwan and South Korea stepped in and claimed the business. In all probability, some of the sales of Toyota and Datsun now will lose to the "voluntary" quota will be picked up by Volkeswagon, Renault and Fiat, rather than by U.S. companies.)

But the footwear OMAs did reduce the availability of cheap shoes and did raise the general price level. Faced with a quota, the foreign exporter naturally upgrades the distribution of what he sells. In the three years from 1977 to 1980, according to U.S. government figures, the average unit value of Taiwan shoes more than doubled -- from $2.08 a pair to $4.31. The Korean average increased from $3.91 to $7.09. These are all "landed," or wholesale, prices, which get multiplied before customers try the shoes on in the store.

The ITC decided that South Korea, which exports mostly athletic shoes, is no threat to U.S. producers, Who are in good shape, with respectable profit margins. But it was also concluded that, if unrestricted, Taiwan's producers of regular shoes could give the industry here trouble. Together, Taiwan and South Korea last year had 50 percent of the U.S. show import business, against 61 percent before the OMAs were slapped on.

William Kay Daines, executive vice-president of the American Retail Federation, says the domestic footwear industry "has done extremely well in this three-year period they've had the OMAs. But the end result is the exclusion of a lot of low-end goods, especially women's and children's shoes.

"That happened in the first week after the OMAs were put in, and it's continued since then. The retailers who deal in volume in this type of footwear are of the firm opinion that if you terminated both the Taiwan and Korean OMAs, you would have a substantial increase in imports from Taiwan, but a substantial decrease in imports from other developing nations. Taiwan [shoes] for the money right now are the best buy," Daines said.

The shoe retailers concede that a return to a free market would likely see a growth of imports from 365 million pairs to 400 million pairs in 1984, mostly in women's and children's vinyl sandals, children's cheaper shoes and athletic-type footwear, with the domestic industry retaining 52 percent of the market. Much of the "New Four" business would revert to Taiwan, which produces a more reliable shoe.

Unless the domestic industry is able to show conclusively that it can't tolerate that small margin of additional competition, the president should junk the OMAs. As Stanford's Yoffee observes, no industry ever has been successfully weaned from this kind of protection.

Here it is, 25 years after the first restrictions to prop up the domestic textile industry were enforced, and we're still at it -- the big sophisticated United States, squabbling with the most backward nations of Asia over little bits of cloth. If we don't kick the habit, we'll be protecting the U.S. shoe industry into the 21st century.