Incredible as it may seem, the federal government is expected to save money if it pays the annual Social Security cost-of-living increase due Jan. 3, 1987, and to lose money if it doesn't.

How can the government save money by paying an increase between $1.7 billion and $3.7 billion for the year?

Under the law, a "cost of living adjustment" (COLA) is made each January only if the consumer price index (CPI) in the previous fiscal year (or since the last time a COLA was paid) rose 3 percent or more. Because the 1986 inflation rate is not expected to hit 3 percent, the COLA would not be paid in 1987 under existing law.

But Congress and the administration are expected to approve legislation allowing it to be paid anyway at the actual inflation rate for 1986, probably between 0.9 percent and 1.9 percent.

Social Security actuaries, in studies released by COLA advocate Sen. John Heinz (R-Pa.), calculate that under current economic projections, paying the COLA would leave the government financially better off in the long run than not paying it.

According to Heinz's figures, paying a 0.9 percent COLA beginning Jan. 3, 1987, would produce a net profit to the government of $1.7 billion after five years. And paying a 1.9 percent COLA would start producing a small net savings after about six years.

One reason for the paradox is that whenever a COLA is skipped for a year, new retirees automatically receive a "windfall" increase the next time it is paid, reflecting the total increase in the CPI since the last raise. If no COLA is paid in a year during which the CPI rises only 2 percent, and then the CPI rises 3 percent the next year, the COLA payable at the start of the subsequent year is 5 percent.

The "windfall" occurs because people who become entitled to Social Security in the year preceding the catchup increase -- about 3 million people -- receive the full 5 percent increase, even though they have not been on the rolls long enough for their benefits to have lost 5 percent in purchasing power. They would not receive the 2 percent catchup portion of the 5 percent if a COLA had been paid the preceding year.

The initial windfall raises costs for these recipients' benefits as long as they live, because all subsequent COLA increases are paid on top of the higher basic benefit achieved from the initial windfall.

A second reason that paying the COLA saves money is that whenever the COLA is skipped, the Social Security "wage base" -- the amount of salary on which the Social Security tax is levied, now $42,000 -- is frozen for the year instead of rising automatically to keep pace with wage increases. So paying the COLA allows more revenues from the tax -- a boon to the treasury if not to the wage-earner.

Moreover, whenever the COLA is not paid, the premium Social Security retirees pay for Medicare -- now $15.50 a month -- is frozen for the year. So paying the COLA allows more revenues from this source.

According to five-year projections, if the cost of living rose 0.9 percent in 1986, and the 1987 COLA were paid despite not reaching the 3 percent trigger, the government's extra COLA payments on 1987 Social Security benefits would be about $1.7 billion over the five years. It would also pay out $200 million for 1987 COLAs on Supplemental Security Income and other benefits tied to Social Security.

On the other hand, it would avoid $300 million in extra costs over the five years by eliminating the windfall, and would garner about $1.7 billion in extra revenue through the 1987 wage-base increase and $1.7 billion through the Medicare premium increase.

The bottom line? Paying the COLA would produce a net gain over five years of about $1.7 billion.

If the CPI increased 1.9 percent in 1986 (higher than many now expect) and a 1.9 percent COLA were paid in 1987, the figures are less favorable for the first five years, but turn favorable at six. Social Security, SSI, and other COLA outlays would total $4.1 billion over five years.

The offsetting windfall savings and added wage-base and Medicare premium revenues would be $4 billion over the five years -- a tiny net loss. But savings from eliminating the windfall would continue for many years after that, and starting in the sixth year, would produce a net gain over the total period.