Despite the fanfare over the resumption of normal relations with the Peoples Republic of China -- and the supposed business bonanza that this holds open for U.S. and other Western countries -- a continuing, even accelerating, boom on Taiwan may be one of the surprise stories of the next five or 10 years.

At least, that's the hope of many Carter administration officials who believe that the changed political status of Taiwan vis-a-vis the U.S. should not prevent the continued growth of what has been one of the most dynamic economies in Asia.

As Secretary of State Cyrus Vance put it to a group of American businessmen last month, "Taiwan will continue to prosper. It is now our eighth largest trading partner, and there will be no change in the way. private business is conducted with Taiwan."

In fact, many administration officials think that once things settle down, Taiwan will be in a unique position to reap benefits from the expansion of the People's Republic's trade with the rest of the world.

Frank Weil, assistant secretary of Commerce for trade affairs, said in an interview: "I think there's a good chance that the Chinese on Taiwan are going to play an important role in the normalization and industrialization process in Asia."

For the immediate future, Taiwan has such a long lead that it will be many years before the PRC catches up to it, American businessmen agree. "In the most crass sense, the current and immediate opportunities are in Taiwan, and no one is going to give them up," said an American corporate executive. Or, as Raymond C.F. Chen, president of Ford Lio Ho Motor Co., told a reporter in Taipei; "This is a bird in the hand; the mainland is two in the bush,"

In fact, from the perspective of the Taiwanese business community, the competitive threat of the moment is not the PRC, but Korea, which is chipping away at Taiwanese export markets in the same way that Taiwan was cutting into Japan's business a few years ago.

The spectacular growth of the Taiwanese economy, with a population of only 17 million against the PRC's one billion, is one of the success stories of Southeast Asia. With Japan as a model, Taiwan has developed its electronics, textiles, metals and machinery industries, and has boosted its standard of living to the point where its per capita gross national product is the third highest in Asia. Cheap labor and massive financial investment have been the keys.

At about $1,100, the Taiwanese gross national product per capita income now is almost three times that of the PRC's $400. Moreover, as a recent study of the Overseas Development Council here points out, Taiwan at the same time has enjoyed a relatively high quality of life.

As measured by the ODC, an index of the quality of life in Taiwan stood at 87 (on a scale of 0 to 100), while that for the PRC was only 71. For example, life expectancy at birth is now 70 years in Taiwan and 65 in the PRC. The Taiwanese record compares favorably with those of wealthier Middle East countries and European nations with more sizable economies -- and is substantially better than that of Mexico, which has a similar per capita income.

Taiwan's foreign trade amounted to $23.3 billion last year, which is about 15 percent greater than the PRC's $19.5 billion, and business interests in Taipei predict that Taiwan's foreign trade will hit $80 billion by 1985.

United States-Taiwan trade last year was nearly $7.5 billion, or about one-third of the Taiwanese total, with U.S. imports of $5.1 billion, and sales of $2.3 billion, for an American deficit of $2.8 billion. (Total U.S.-Taiwan trade, by the way, was about 7 times U.S.-PRC trade.)

The American stake in Taiwan is substantial, at $516 million in direct investment in 278 different projects in electronics, chemicals, food processing, metals, textiles, footwear and other industries. In addition, according to the U.S. Treasury, private U.S. banks had $4.1 billion in loans outstanding as of June 30, and the Export-Import Bank had extended a net amount of $1.8 billion in credits at the end of last year. World Bank investments in Taiwan are about $250 million.

But Walter Hoadley, executive vice president and chief enonomist of the Bank of America, said in a telephone interview that the Taiwanese are "realistic, hard-working and pragmatic people" who know that somewhere down the line their economy will face competition from the massive economic potential of one billion people on the mainland. And they will have to depend on their internal strength, not outside investment, to do it.

Hoadley noted the typical Asian concentration on "time, patience and face," and suggested the Taiwanese will focus attention in the next few years on accelerating their economic advance. "When you get right down to it, Taiwan's ultimate bargaining power (on its political status) with the PRC could depend on it outperforming the mainland," he said.

Weil and other U.S. government officials put much store in the fact that PRC Vice Premier Teng Hsiao-p/ing gave some interviewers -- including U.S. Sen. John Glenn (D-Ohio) -- the feeling just before Teng's visit to the United States that the PRC might be content to allow Taiwan to develop a relationship analagous to the close ties the PRC maintains with Hong Kong and Macao. Peking could make the usual noises about its rights to the various territories while continuing to milk the economic relationships with offmainland outposts.

Hoadley thinks that the notion of Taiwan as a sort of Hong Kong is completely realistic. Much, of course, depends on Taiwan's willingness to sublimate its disappointment and anger over being "dumped" by the United States to concentrate on solidifying business and commercial relationships that will make it politically and economically stronger.

Asian scholars believe that will require Taiwan to avoid any rash action such as a unilateral declaration of independence and fulfillment of promises by the United States to shun a military relationship with the PRC, while maintaining Taiwan's defensive military strength.

Washington Post correspondent Jay Mathews noted in a Hong Kong dispatch on Dec. 21 that Taiwan already has begun to increase underground trade and foreign contacts with mainland China that even might lead to formal negotiations in the distant future.

The PRC sold Taiwan about $25 million worth of goods through Hong Kong in the first six months of 1978, mostly mainland herbs highly prized in Taiwan. This semisecret trade doesn't include a large volume of goods being smuggled between Taiwan and the mainland.

Since normalization between the U.S. and the PRC was announced, wall posters have appeared in Peking suggesting exchanges of mail and tourist visits between families on the mainland and Taiwan.

Even before normalization, the PRC sent delegates to a scientific conference in Tokyo, at which representatives from Taiwan were also present. Later, the PRC didn't object, as they would have in past years, to a Thai airlines request to make stops in Taipei as well as Peking.

Another clue of potentially great significance for Taiwan's furture came in Teng's interview with Time magazine published Jan. 29. In that, Teng said not only that Taiwan might maintain some armed forces of its own but that," As for trade and commerce with foreign countries, they can continue."

That would seem to answer the question raised by some skeptics of whether the PRC might seek to blackball business enterpreneurs from the West who also choose to maintain their relationships with Taiwan.

In fact, this has not happened to businessmen who earlier in the game did exactly what the U.S. has done -- extended diplomatic recognition to the PRC while maintaining full relations with Taiwan in everything except the formal diplomatic sense.

Thus, Japan's trade with Taiwan has grown 233 percent since Japan normalized its relations with the PRC. Australia's grew by 370 percent; and Canada's, by 539 percent.

So far, Taiwan has played it cool. The government has not leaped to embrace any of Teng's overtures. But after the initial shock and outrage at American recognition of the PRC, things have settled down. President Chiang Ching-kuo seems to be steering away from any provocation that would lead Peking to boycott companies doing business with Taiwan. And as American officials point out, after first saying no, Taiwan is going along with the nongovernmental "institute" formula that replaces the former diplomatic relationships. If it all works out, for American businessmen it could be the best of two worlds.