Bethlehem Steel Corp., the nation's biggest steel maker, announced yesterday it will boost prices about 5.5 per cent Feb. 1. If followed by the rest of the industry, the increase could reduce benefits steel producers will get from the administration's import relief program.

Although only one smaller producer has announced price increases - Wheeling Pittsburg Steel Corp. said Sunday it would raise prices 7 per cent - if previous patterns hold, other major steel makers will follow Bethlehem's lead shortly.

U.S. Steel Corp., the nation's biggest producer, said yesterday it was "studying" the situation, but U.S. Steel has said several times in recent months that price increases are needed for domestic steel makers.

Carter administration officials were careful to avoid a major confrontation with Bethlehem or other steel companies yesterday. When steel makers announced a boost last summer, Charles L. Schultze, chairman of the Council of Economic Advisers, called reporters into his office to denounce the increases.

Barry Bosworth, director of the Council on Wage and Price Stability, did characterize the 7 per cent Wheeling-Pittsburg increase - which will likely be lowered - as "awfully big."

But at the same time, officials such as Bosworth and White House spokesman Jody Powell noted that steel companies have faced rising costs and that some price increases had been expected.

Officials noted, however, that the more the industry raises its prices the less help it will get from the new reference price system the Treasury is developing to sheild American producers from unfair foreign competition. (Details on Page D10)

Under that program, foreign steel imports that come in below the reference price trigger an accelerated Treasury proceeding to determine whether the steel is being sold below cost, or dumped, which is illegal under the nation's trade law.

The reference price is based on the costs of production of the Japanese, reportedly the world's most efficient steel producers. The administration hopes to have its reference prices in hand by the end of month.

Only if American producers sell their steel at prices near the refernce price can they expect to get much relief. The reference price system is designed to cut steel that is being sold below cost.

America steel users will buy foreign steel if it is substantially cheaper than American steel, but not if differentials are small - like between $10 and $15 a ton. However, price increases such as Bethlehem's are likely to increas the differentials.

American steel companies have long maintained that they can produce steel more cheaply than any country but Japan and that when Japanese shipping costs are added in, American steel becomes competitive in the U.S. market with Japanese steeL, too.

In announcing the price increase, Bethlehem cited sharply rising costs of raw materials and labor. In the third quarter of this year, the steel maker reported a loss of $477 million, the largest quarterly loss ever posted by a U.S. industrial company.

Bethlehem plans to boost prices an average of 5.5 per cent Feb. 1 on a wide range of products, including hot and cold rooled sheets, which are used primarily in making automobiles and other consumer items such as refrigerators, washers and dryers. The company will raise prices March 1 by a similar amount in construction, and on tin mill products, used to make food and beverage containers.

Ironically, the 5.5 per cent boost on most steel prices is due to take effect or the same day that administration planners have set as their target for putting into action the import relief program.

Bethlehem contacted the Council of Economic Advisers before making the announcement, but a council spokesman said the agency had no comment on the increase.

In announcing the boost, Bethlehem took note of the administration's steel-aid program, which includes "among its objectives" the reference price system designed to shelter American producers from unfair competition.

"This system, if property designed and vigorously enforced, should go a long way toward easing the adverse effects of unfair trade practices while maintaining the free flow of trade between nations. However, the details have not yet been announced and it could take up to six months to determined whether the system is effective," Bethlehem said in a statement.