Ronald Reagan campaigned coast to coast this year promising to reduce the burden of federal spending for every American. Now a new government study suggests that this promise has already been fulfilled -- under Jimmy Carter.

A tabulation of government expenditures compiled by the Advisory Commission on Intergovernmental Relations shows that per capita government spending in "constant" dollars -- that is, with the figures adjusted for inflation -- began to decline in the last two years of Carter's presidency, reversing an upward trend that goes back at least 50 years.

In constant 1967 dollars, the commission's preliminary figures for total government spending in calendar year 1979 show that government at all levels spent $1,580 for every man, woman and child in the United States. The study estimates that in such constant dollars total spending per capita will drop to $1,540 for 1980.

The commission measured local, state and federal spending over the past half century, beginning in 1929, when the three governmental levels combined spent the 1967 equivalent of $163 per capita. The per capita spending figure went up steadily thereafter through 1978, when it peaked at $1,605.

The commission's report, "Significant Features of Fiscal Federalism," also shows that the western states -- Reagan's political base and the home of the strongest anti-Washington fervor -- have taken more money from Washington relative to taxes paid than any other region.

The commission's economists compiled an index comparing the amount of money each state sends to Washington in taxes to the amount of federal spending in the state. A state that got back exactly what it paid in would have a rating of 1.0; if the rating is higher than that, the state is taking more out of the federal government than it is paying in.

The District of Columbia, with a rating of 3.23, turned out to be the biggest "taker" under this formula. But the mideast region, including D.C., had a rating of 0.99, meaning the mideast states -- Delaware, Maryland, New Jersey, New York and Pennsylvania -- pay the federal government more than they receive. The Great Lakes region had a rating of 0.74. For the plains states, the rating was 0.98.

Meanwhile, the Rocky Mountain states were "takers," with a rating of 1.10, and the Far West states took even more, for a figure of 1.13 Alaska, where the people are perhaps most outspoken of all in their disdain for Washington, received $1.82 in federal funds for every $1.00 of federal taxes paid. The government is a major employer and major landowner in Alaska.

Figures showing the drop in total percapita government spending indicate that the only area where government spending is rising is in federal spending for defense, an area where Reagan has promised to spend even more when he takes over the White House next January.

Federal spending on domestic programs -- a total that includes Social Security and other transfer payments -- peaked in 1978, fell sharply last year and will fall again in 1980, the commission said. Expenditures by state and local governments follow the same pattern. But federal defense spending, after dropping in 1978-1979, will hit an all-time this year.

The figures on per-capita spending show that the amount of money local, state and federal governments spend in rising at a slightly slower rate than the increase in population. In straight dollar terms, however, government spending continues to climb, according to the commission's tabulations.

In 1980 dollars, the cost of government in the United States this year will be $848 billion. That breaks down to $580 billion in federal spending, $151 billion in expenditures by the 50 state governments and $117 billion spent by counties, cities and other local governmental units.

If the recent rates of spending increase and inflation continues, the total cost of government in the United States will pass the $1 trillion mark in 1982.

The Advisory Commission on Intergovernmental Relations is a federally funded, 26-member group with representatives from federal, state and local government, as well as three "public" members. Its chairman, one of the public members appointed by President Carter, is former New York City mayor Abraham D. Beame.