As seen through Japanese eyes, the great steel export war of 1977 boils down to a single, simple assertion Japan built the better mousetrap.

The better mousetrap is a modern integrated and highly efficient steel industry which can produce steel products ship them to the United States, and market them at costs lower that those charged by American companies.

"We have been very wise in our investments," one company official said this week. "We concentrated our investments in the most effective way. Your companies did not."

That, of course, is not the view of American manufacturers who have mounted a forceful campaign to keep Japanese steel out and who insist their Asian competitors behave unfairly. They picture a Japanese industry "dumping" its products at prices below cost to seize an even larger share of the market and benefitting from a government patronage unthinkable in the United States.

The truth is buried somewhere in the real cost documents which only economists would understand if they could get access to them, which they cannot. Mounds of reports are churned out to justify both points of view.

Whether it's a better mousetrap or a case of vicious underselling, the six Japanese giants led by Nippon Steel have become the world's most proficient exporters. This year, they'll send 34 million tons abroad - about 7.6 million tons to the United States - to keep afloat an industry whose home markets are sagging badly. Without exports, the industry would almost collapse. In the past 10 years, two-thirds of that industry's growth has been through exports. Both the U.S. and Canadian industries are suffering as a result.

To hear the Japanese tell it, the success story results from their own marvelous capacity for planning efficiently - coupled, they like to add with a smile, with a big dose of borrowed American technology.

They built thrir huge new steel mills from scratch in the "green fields," as they put it after the war, using all the latest techniques from abroad. The plants are fully integrated, meaning that iron ore and coal roll off ships at one end and finished steel products roll out the other in an almost continuous process.

In contrast, they say, the American steel plant is old and awkwardly dispersed. "You go to Cleveland and you see one thing being done in one place," a Japanese steel official said. "Then they transport it all over to another place to have something else done." It is very wasteful."

On the surface, a lot of facts justify Japan's claim to superiority through modernization. In the past 15 years, nine huge plants have been built from scratch here with the most productive cost-cutting equipment. Only one was built in the U.S. Some American plants date from the 1890s.

United States plants trail Japan's in construction of the more efficient basic oxygen furnaces to replace the old open-hearth furnaces. Eighty per cent of Japan's steel is produced from the oxygen furnances compared with 63 per cent of American steel. "That is enough of a gap to make a very big difference," said an American economist based here.

The end result, say the Japanese, is plants which turn out steel cheaper, with higher productivity and lower real costs than any in the U.S. except for one built by Bethlehem Steel.

That view is supported in most respects by the investment firm of Merrill Lynch in a devestating analysis that portrayed America's industry creaking along like an old Model T alongside Japan's sleek new limousine.

Direct labor productivity in a Japanese plant is 50 per cent greater than in an American one, the study concluded, and the average Japanese steel employee produces 410 tons per year while the U.S. employee produces only 250. In 1976, the Merrill Lynch analysis found, the overall cost of producing steel in Japan was 30 per cent less than in the United States. Modernization had made the difference.

"Comparing facilities of similar size, age, and product mix, we believe that United States plants are just as efficient as their counterparts in Japan," the report said.

"The problem is that we have only one major plant in the country that can be called modern, while in Japan there are few plants that are not modern."

Comparing costs is tricky. The U.S. anti-dumping law, used recently against five big Japanese exporters, requires that an 8 per cent profit must be calculated as one of the fixed costs of doing business in determining whether a foreign company is selling below cost. None of the Japanese firms, by their accounting, comes anywhere close to 8 per cent (3 per cent is the highest industrywide profit in recent years). It is "absurd," one official complained, to tack on an 8 per cent profit in deciding what Japanese costs should be and then accuse them of dumping.

American firms counter with the charge that much of Japan's competitive edge stems from the intimate relationship between that country's steel corporations and the government. And although direct subsidies and overt protection are rare, it is true that Japan's mills have traditionally benefitted from favors and shelters not tendered American companies.

Government sheltering of big steel dates back to the 1950s when the postwar governments deliberately set about creating a dynamic industry to revive the war-torn economy. Government and business sat down and planned the future together. Through the powerful Bank of Japan, the government made sure steel had all the credit it needed. Even now, 80 per cent of Japanese steel's investment capital comes from commercial banks which are very responsive to direction by the central bank.

The cozy cooperation continues today. Every Monday, top steel executives sit down to lunch with an official of the Ministry of International Trade and Industry.

"They will discuss how to cope with important problems, such as exports," said one industry official. "It doesn't mean that we always agree with the government's suggestions - we often disagree with MITI on whether there should be quantitative restrictions on our exports to the United States. We wanted them and the government did not. But it is usually profitable to have those meetings."

Each quarter of the year, MITI issues what it calls "guideposts" for production levels in the ensuing three months for the big six companies. The executives almost always decide to go along with what MITI recommends and taper their production schedules accordingly. Although the industry insists it is fiercely competitive in home markets, observers believe there is an unwritten understanding of what share of the market each firm can have.

Japan's steel companies also benefit from tax privileges, including one which permits them to establish "special reserves" in fat years to tide them over the lean ones. The reserves are not subject to national taxes.

Until recently, the government-guided success story of Japanese steel seemed destined to continue indefinitely. But the recession has introduced a most unpleasant chapter. With the domestic markets saturated, the mills are operating far under capacity.

Some companies have stopped paying dividends. The traditional lifetime employment patterns prevent them from laying off workers, as American plants have done, and so the fixed costs remain high even in recession. If exports are curbed in the U.S. and elsewhere, the mighty post-war giant will shrivel quickly.

In typical Japanese consensus fashion, government and industry have arrived at a shared conclusion: accept restrictions on their exports to America if the U.S. industries will stop waving the hated anti-dumping club at their heads. The Japanese firms feel they never can win in the American courts as the law is written and interpreted now. Industry and MITI have indicated they will reduce exports to the U.S. from 7.6 million tons a year to less than 6 million in a program of voluntary restraint.