The nation's largest steelmaker yesterday reported more than a 50 percent increase in earnings for the first quarter, but profits for the second-largest steel producer dropped by about the same percentage.

First-quarter net income for U.S. Steel Corp. was $270.9 million ($3.06 a share) up from $126 million ($1.45). Sales were $3.4 billion, up from $3.2 billion. Steel shipments fell 6 percent from 4.9 million tons to 4.6 million tons. Production dropped 7.1 percent to 6.9 million tons.

But in Wilmington, Bethlehem Steel Corp. stockholders braced for the bad news. The firm reported a 52.3 percent drop in first-quarter net income from $54.4 million ($1.25 a share) to $25.9 million (59 cents); revenues were $1,858 billion, compared with $1,929 billion last year. Steel shipments dropped 7.7 percent from 3.3 million tons to 3.1 million tons. Raw steel produced dropped 10.4 percent from 4.6 million tons to 4. 1 million tons.

Bethlehem Chairman Donald H. Trautlein, in his address to stockholders at the company's annual meeting, blamed costs that exceeded sales and lower production and shipment levels for the decline.

"There were some encouraging signs during the first quarter that business conditions may be improving," such as a spurt of new-car sales in March, moderating interest rates and confidence spurred by President Reagan's announcement of his economic recovery program, Trautlein said.

"Our expectations for the year as a whole have also improved," Trautlein continued. But he added, "Of course, a long coal strike by the United Mine Workers could change these expectations." Bethlehem has extensive coal-mining operations that it is considering selling or putting to better use, Trautlein said.

"For the longer term, we are cautiously optimistic that confidence in the future business climate will continue to grow and that the steel industry will benefit," Trautlein said. "The major uncertainties are the measure of success that will be enjoyedby the administration's economic policies and the future level of inflation. However, our expectation is that positive changes will gradually occur for business."

In Pittsburgh, meanwhile, U.S. Steel Chairman David M. Roderick said, "The first-quarter results provide an excellent beginning for U.S. Steel and indicate improved results from those attained in 1980."

"Income improvements over last year's first quarter reflect continued strong demand from energy-related market, performance improvements, particularly in steel, higher interest income due to increased cash availability and gains from disposition of underutilized assets."

Trautlein said Bethlehem Steel is conducting evaluations of its major product lines and facilties to determine how the company can operate best. For example, the company is studying the best markets for its coal reserves considering the scarcity and rising cost of oil and gas, Trautlein said. So far, the company has decided to develop and mine its own coal properties.