The government's latest offer to the Professional Air Traffic Controllers Organization was billed as a $10 million increase over its previous offer, but administration officials concede that the package would have cost the government $15 million less over the course of the contract.

The last administration proposal was a benefits-only package that would have started a $20 million a year and risen to $50 million in the last of its three years. The earlier proposal was for a 42-month contract that would have given the controllers $40 million a year in the first two years, and another $40 million for the last 18 months of the contract.

In effect, the first pact, offered June 22 and subsequently rejected by 95.3 percent of PATCO's nearly 15,000 members, was a "front-loaded" deal in which the inital increase carried through each year of the life of the agreement. At the end of the 42-month contract, PATCO members would have had a $40 million higher "base," meaning that they would have been able to enter their next contract negotiations receiving $40 million more annually than they had been getting in 1981.

The administration's second proposal was a "back-loaded" deal calling for progressive increases over a three-year period. Controllers would have gotten $20 million worth of benefits in the first year, $35 million in the second year and $50 million in the third year.

By the administration's reasoning, the second proposal would have given the controllers the advantage of a $10 million higher "base" in entering their next contract negotiations.

But in dollar terms, the second offer was worth $15 million less than the first offer. A $20 million-$35million-$50million arrangement adds up to only $105 million. The straight $40 million-$40 million-$40 million offer added up to $120 million.

"The back-loading arrangement was better for the government because the bigger money would have repeated itself at the end of the contract, rather than at the beginning," said Kenneth E. Moffett, the acting director of the Federal Mediation and Conciliation Service who vainly tried to wring an agreement out of the two sides before the strike began yesterday morning.

"But it really didn't matter," Moffett told reporters early yesterday."The government could have added $40 million, or even $20 million and it would not have been enough to bridge the gap."

Moffett said the gap was so wide and that the sides were so intractable in their positions that they did not even discuss the controllers' demands for a shorter workweek and a more generous retirement plan before negotiations broke down shortly before 2:30 a.m. yesterday.

"Most of those things were left off the table," Moffett said.