With everyone else, local governments in the Washington area are trying to sort through the consequences of the budget decisions made by the president and Congress earlier this year.

The direct effects on individuals are easily seen: fewer student loans for families with children in college, fewer federal jobs and reduced cost-of-living increases for current employees and retirees. The list goes on and on.

Other budget changes are not as obvious. There will be substantial reductions in many local services because, contrary to common belief, many of those services are paid for with federal tax dollars, even though they are provided and administered locally. For example, Arlington County offers a program for the frail elderly at its Madison Center. The average age of those using the center is 83. Typically, they live in the homes of their children who work. Their grandchildren are in school or are themselves grown and living elsewhere. Last year, the federal government provided more than 50 percent of the total cost of the program. Without this money or some substitute, the center will not operate.

At the other end of the age spectrum, federal money now helps support child care programs by providing assistance to families whose income is under $10,000. While the program will survive, federal support will be provided only for a family whose income is under $5,000. Typically, in Arlington, those losing eligibility would be one-parent families where the parent works full-time.

The budget cuts do not decide the fate of the programs now federally funded. They merely shift the responsibility for deciding whether to fund them from the president's desk to ours, in local government. As a general principle, we welcome this return of responsibility. We believe better decisions result when they are made by those in closest touch with the community. Many of the most useful programs are those that originate in the neighborhood, both through government and non-profit voluntary agencies. But no thHOing is free. If the local community wants to continue a program such as the Madison Center, it will have to provide the money.

Preliminary information supplied to Arlington by state and federal authorities projects a reduction of at least $700,000 in federal funds for human service programs alone in fiscal year 1982. Further reductions are expected in the course of the next year in an amount now unknown. We know only that health services provided to the elderly in their homes will be cut 25 percent, as will family planning money. Further state and federal cuts in county health and mental health funds are anticipated.

Impact aid, which provided the Arlington school system with $929,000 in fiscal year 1981, will be reduced subsntially. However, until federal regulations are written allocating reductions among various categories of students, the total loss is unknown. One-half? One-third?

Federal support for the operating costs of public transportation is being reduced this year, with further cuts planned for later years. The fate of Legal Services and the funding it provides to local legal aid offices are still up in the air. Recisions of money already appropriated are being discussed.

The cutback in Arlington's human services funds represents only the first-year cut. In subsequent fiscal years, the state, facing reduced statewide totals, intends to revise its allocation formula, giving a greater share to jurisdictions with heavier welfare case loads. For relatively high-income Northern Virginia, this will mean further cuts. Federal cuts in future years are likely to accelerate this trend. More federal programs will be converted to block grants, giving the state an augmented role in regulation-writing and establishment of priorities. Experience has shown that decisions made in Richmond are not likely to favor Northern Virginia.

Fortunately, Arlington's fiscal year 1982 budget includes a contingency fund to help deal with the immediate problem. But the hard decisions are yet to be made. In future years, programs previously funded by the federal government will have to compete with other local programs for limited resources. No one wants to raise taxes. Efficiencies and administrative savings only carry one so far.

Arlington has the good fortune to have a steadily increasing tax base as new buildings keep going up, but no one expects new development to carry the full burden. Moreover, while a sterile row of office buildings improves the tax base, it does not contribute to an attractive or vital community.

So the federal budget will force some tough choices. Most people want services continued, but no one wants taxes increased, and new development will not provide an easy out. This essential dilemma will face local government throughout the 1980s. It is perhaps the toughest tangle of issues we face.

The president has turned the decision on continued funding of these programs over to local government. The buck does not stop in the Oval Office. It stops in the local courthouse.