A $20 billion trade gap with the United States is the new Nakasone Cabinet's most vexing international problem. ''What measures will you take concretely to dissolve trade frictions between the United States and Japan?'' Foreign Minister Shintaro Abe was asked during a series of post-election interviews with local news media.
''With a presidential election looming in the United States,'' the lanky foreign minister replied, ''it is urgent to find concrete solutions for problems such as agricultural products, procurement by the Nippon Telephone & Telegraph Corporation, and the yen-dollar exchange rate.'' Mr. Abe, who has been kept on as foreign minister in the new Cabinet, said he expected to visit Washington toward the end of January to discuss these problems as well as the international situation as a whole.
Mr. Nakasone retained Mr. Abe in order to show the continuity of his administration's foreign policy. But his ability to make the kind of concessions Washington wants has been reduced by the results of the Dec. 18 election, in which the Liberal Democrats lost their majority and regained it only with the addition of nine independents and an alliance with the small New Liberal Club.
President Reagan refrained from asking his good friend ''Yasu'' Nakasone for trade concessions during his November visit to Japan, not wanting to embarrass the ruling Liberal-Democrats during an election campaign.
Now the shoe is on the other foot. The Japanese election campaign officially lasted only two weeks. The American presidential election campaign will be going on for most of next year. The continuing flood of Japanese goods into the American market, as well as what most Americans see as the unfairly closed nature of the Japanese market, are certain to be election issues. It is President Reagan who needs specific evidence that Japan is restraining its own exports to the US while doing everything to increase imports from the US.
When Mr. Abe spoke of agricultural products, he meant principally beef and citrus fruits. Washington has been pressing Japan for years to import substantially larger quantities of both items from the US, and eventually to free imports altogether. Japan is, in fact, one of the world's largest importers of American agricultural products, but on beef, citrus fruits, and certain other items Tokyo has long had detailed restrictions to protect Japanese growers. The present quota is 30,800 tons of high grade beef and 82,000 tons of citrus fruits.
Cattle raisers and orchardists account for only a fraction of employment and income in Japan. But their collective political clout, exercised on legislators from rural constituencies, outweighs that of giant manufacturers who would like to eliminate this source of Japanese-American trade friction but whose influence is felt more by bureaucrats in the central ministries than by rice-roots politicians.
Procurement by Nippon Telephone & Telegraph is another sensitive issue. This public corporation opened up bidding on procurement to non-Japanese suppliers some years ago after constant prodding from Washington. But the US remains dissatisfied with the amount of purchases NTT has actually made from American companies.
The current yen-dollar exchange rate amounts to a 25 percent subsidy on Japanese exports to the US and an equivalent penalty on American exports to Japan, American trade experts say. The yen currently fluctuates between 232 and 236 to the dollar. Japanese money specialists agree the yen is undervalued relative to the dollar, but they blame high American interest rates rather than any deliberate low-yen policy by Japan.