The surprise bid this week of the huge West German chemical company, Bayer AG to buy Indiana-based Miles Laboratories is just the tip of a planned $700 million expansion by the German firm into the U.S.

Officials at Bayer headquarters in "in addition" to the offer, estimated at Leverkusen, West Germany, say that about $215 million, to buy Miles, the firm plans to invest another half-a-billion dollars in the U.S. over the next five years.

"The American market for chemicals and pharmaceuticals is simply the best in the world, and it is necessary to invest in the U.S. if you want to sell your products there," a company official said.

The purchase offer is also part of a plan to make the German firm a major force in the U.S. market. Bayer through its existing U.S. subsidiaries, already does slightly more than $1 billion a year in sales in the U.S.

Bayer still manufactures its famous aspirin in Europe, although it lost the rights to the U.S. patent after World War I when the giant I. G. Farben industry combine was seized by the Allies. Bayer cannot market or manufacture any product in the U.S. with its own name, since that is a trademark held by the Sterling Drug Co., which makes Bayer aspirin for the American market.

Bayer AG also owns Cutter Laboratoes in the U.S., its major subsidiary in the pharmaceutical market. Cutter showed a loss in 1974, but was profitable by 1976.

Miles, which is most famous for its production of Alka-Seltzer, had sales of just under $450 million last year. Cutter's sales were $163 million.

Aside from aiming at a bigger slice of the market, the firm undoubtedly is being influenced by the same economic factors that are causing more and more German firms to seek investments in the U.S.

Those factors include steadily rising labor costs here, a Deutsch mark that has risen steadily in value against the dollar, and shrinkage of export markets caused by lingering recession.

In 1976, hourly labor costs in West Germany exceeded those in the U.S., economic institutes here have reported. The West German mark gained roughly 36 per cent in value against the sixteen major world currencies in the past since the end of 1972. German investment in the U.S. - most dramatically symbolized by the decision of Volkswagen to open a U.S. plant - has also risen by about 140 per cent over roughly the same period.

A Justice Department spokesman said yesterday that either the department's antitrust division or the Federal Trade Commission would examine Bayer AG's merger proposal to determine the likely effects of such a move on drug industry competition. He said, however, that the agencies haven't decided which one should handle the inquiry.

Bayer, with almost $9 billion in sales internationally last year, is already the fourth largest chemical company in the world in terms of revenues. Yet the West German chemical industry itself is so large that Bayer ranks as only the third largest in Germany behind Hoechst and BASF.

While the offer to buy Miles was being made, Bayer chairman Dr. Herbert Gruenewald was in New Martinsville. W.Va., at ground breaking ceremonies for a fifth million iron oxide plant - reportedy the largest in the U.S. - of the firm's Mobay Chemical Co. subsidiary.

At that ceremony, Gruenwald said the factors that led the firm to investing in the U.S. were proximity to the market, a high caliber labor force and enlightened political leadership that welcomes investment.

In Leverkusen, officials say Bayer's total new investment plan for the next five years call for spending roughly $750 million annually over the next five years. About sixty per cent of that would go into the firm's sprawling West German plants. The remaining forty per cent would be invested overseas, with the U.S. as the prime investment area. Other expansions are planned in Belgium, Italy, France and Spain, officials said.

Yesterday, Owens Corning Fiberglas Corp. of Toledo, Ohio, said it has entered a joint venture with Bayer to manufacture and market glass fiber insulation materials in Western Europe.