For people who think the Japanese economy is as solid as the Rock of Gibraltar, it may come as somewhat of a shock to learn how relatively little the yen is worth. It traded yesterday for 268 to the dollar -- which economists figure is between 20 and 40 percent less than it should.

This disparity is not an arcane matter for international economists. It has practical applications that vitally affect the balance of trade between the United States and Japan, it adds one more irritant to trade relations between Washington and Tokyo, and it threatens the ability of American companies to compete successfully here and abroad with the Japanese.

Ford Motor Co. Chairman Philip Caldwell estimated that the undervalued yen gives Japanese manufacturers "a windfall advantage" of $900 a car and $100 on a ton of steel. For American companies such as Caterpillar Tractor Co., which sells almost 60 percent of its giant earth-moving machines in foreign markets, the cost is figured in millions of dollars a year. One Caterpillar official estimated that its major Japanese competitor, Komatsu, has as much as a $20,000 price advantage on a $100,000 tractor because of the yen-dollar differential.

In a telephone interview, Caldwell called the undervalued yen "just a huge subsidy on exports from Japan to the United States and a huge penalty on exports to Japan from the United States. "When both are competing for markets in a third country, "the U.S. producer is at a huge disadvantage," he continued.

Caldwell was careful not to blame the "out-of-whack" weakness of the yen on manipulation by the Japanese government, as some business leaders have charged privately, or on a widely held view that the Japanese government is not doing all it could to strengthen the yen.

But he did say that the yen is behaving "just the opposite of what one would expect" considering Japan's high productivity, favorable trade balance, rate of savings and success in controlling inflation. Moreover, the yen has continued its decline in the face of the drop in U.S. interest rates that should have strengthed it.

To some economists, however, the Japanese economy is not as strong as it appears, and these underlying weaknesses keep the value of the yen down in relation to the dollar.

"In fact, what has kept the dollar-yen relation from tracking conventional wisdom is a reappraisal of the Japanese economy," said Brookings Institution economist Lawrence J. Krause. "Both foreign and domestic investors now believe Japan may be a very-slow-growth country . . . with very high savings and nothing to invest in at home."

As a result, Japanese are investing overseas and foreign investors are now pulling their money out, he continued. The outflow of yen during the first 10 months of the year has been estimated at $20 billion.

Former Assistant Treasury Secretary C. Fred Bergsten, now director of the Institute for International Economics here, recommends that Japan return to its policy of two years ago by placing a six-month moratorium on certain capital outflows and manipulate its capital acounts to attract money. "It is imperative to get the yen quickly under 200 to the dollar," he said.

The Reagan administration is trying to pressure Japan to ease its barriers to American imports just when the caretaker government established following the resignation of Prime Minister Zenko Suzuki feels most vulnerable politically and economically and least able to compromise on trade policy.

Yet American business pressures mount on the Reagan administration to force a strengthening of the yen. Late last month, nine top business leaders met at the White House with top Reagan aides to underscore their concern. They received apparent sympathy from such administration officials as Trade Representative William Brock, Treasury Secretary Donald Regan and Secretary of State George Shultz -- but no promises of help.