Eastern Chairman Frank Borman, in his first public statement on the merger talks between his company and Braniff International Corp., has promised employes that Eastern will take a cautious approach to the negotiations.

"We will proceed only if our study shows conclusively that the merged company will be stronger and more profitable than Eastern alone," Borman said in a letter to employes dated Dec. 29 and obtained today by The Miami Herald.

The letter also warned that 1981 will be another tough year for Eastern, which is the Miami area's largest corporate employer.

The company is expected to post a significant finncial loss for the year just ended, and workers already have been told they will not get back any of the estimated $35 million they contributed to the company under a unique corporate-investment program.

"Nineteen eighty-one looms as a formidable challenge," Borman said. "Unfortunately, the recession will continue. With the prime lending rate at 20 percent, it is difficult to visualize a strong winter travel period.

"We will see the introduction of competition to our [New York-Washington-Boston] air shuttle by New York Air and to our New York-Miami service by Air Florida using DC10s.

In his comments on the possible merger with Braniff, Borman referred to the discussions as representative of one of several "expansion possibilities."

That was another indication that Eastern would remain the predominant partner if any merger should result from the talks, which began last month between Eastern and the financially troubled Braniff.

Borman refused additional comment on the merger today, but company spokesman Jim Ashlock said Borman felt compelled to mention it in his annual message to Eastern's employes.

Earlier this week, officials of Eastern and Braniff said that they had completed their fact-finding missions and were analyzing statistical information that had been collected.

Each side is expected to complete feasibility reports by the middle of this month, at which time senior management official of each airline will decide whether to raise the negotiations to a higher level, spokesmen said.

Most analysts, however, have expressed doubt that the companies could overcome the considerable financial obstacles to a merger.

Braniff, based in Dallas, lost $52 million during the first nine months of 1979 and has long-term debts of at least $700 million. Eastern lost $34.7 million during the same period and has long-term debts of at least $1.2 billion.

In addition, any merger would have to be approved by several U.S. regulatory agencies.

In another development earlier this week, Braniff Chairman Harding L. Lawrence announced his resignation, a factor cited by some analysts as evidence that he was stepping aside to allow Borman to run a merged company.

Other analysts, however, said that if Lawrence thought a merger imminent, he would have delayed his resignation and issued it under more graceful circumstances.