President Carter recommended yesterday that the federal government spend slightly more than half a trillion dollars next fiscal year.

Nearly half a billion of those dollars will come here -- an average of more than $2,500 a citizen.

In that respect, this friendly industrial city is typical. Americans are accustomed to thinking of the federal budget as a burden. For many, it is a source of income as well.

Some of the federal money will show up here as Ed Finkel's wages. Finkel works on the gasket line at Fort Wayne Truck Parts, and the Army buys about $200,000 of those gaskets a year for jeeps.

Some federal money also will help to pay for Bill Whetsel's spinal treatments at the Veterans' Hospital here. Pauline Holmes' railroad retirement check is in the budget, too, as are Barker Davie's witness fees, the Medicaid reimbursements that come to Clarence Haynes' pharmacy and the interest on paper carrier Billy Hartman's $37.50 U.S. savings bond.

The commission for Art Amt's "ethnic sculpture" may be somewhere in the budget, too, but that hasn't been settled yet.

Economists look on the federal budget in part as a redistributive device. The government sucks up money from the public in taxes, then disgorges it as expenditures.

The largest portion of that money -- a little more than 40 percent -- is sent straight to individuals in the form of "transfer payments," benefits of various kinds.

About 8 percent is interest on the federal debt, and about 15 percent goes out in grants to state and local governments for various purposes.

The rest -- about 33 percent -- is for direct federal purchases of goods and services: the money the government spends as employer and consumer.

Those national ratios are not precisely matched in federal spending here. Among other things, Fort Wayne is long on defense contractors and short on big banks that buy federal securities.

Still, the 185,000 residents of Fort Wayne receive income from the government under an astounding variety of federal programs. If you follow the bouncing budget dollar through this fairly typical city, you can find a real person earning income from almost every line item.

In fiscal 1977 more than 100 federal offices spent money in Fort Wayne. They bought everything from infrared radiometers and laser diodes to sewer pipe, paper clips and $177,000 worth of high-energy candy bars.

A look at the spending data raises some tantalizing mysteries: How did the State Department spend $139,000 in Fort Wayne? Why did the Tennessee Valley Authority spend $247,000 here? Which federal agency paid for the city's full-time, salaried pantomime artist?

The biggest federal spender here is the Pentagon. A single Magnavox plant in the new industrial park sells about $120 million worth of weaponry to the government annually. Jack Schrey, the Magnavox division head, says he will ship about 200,000 sonobuoys -- small, floating submarine detectors -- to the Navy in fiscal 1980.

Other big defense contractors include ITT and International Harvester (Harvester, it turns out, also sells equipment to TVA). And then there is Fort Wayne Truck Parts, a little factory at the edge of a junk yard that makes gaskets, mufflers, flanges and air brakes for Army vehicles.

Finkel, a 47-year-old foreman with a broad belly and a broader smile, knows how much the plant relies on the government. "You remember that year that Ford shifted $12 billion out of Army's budget?" he asked. "I figured out on my calculator -- that cost this plant about $1 million. We were laying guys off like crazy."

The second biggest chunk of Fort Wayne's federal money is the flood of benefit checks, flowing mainly to the elderly. This includes federal workers' pensions and Social Security and a large amount -- more than $6 million annually -- in Railorad Retirement checks to people like Pauline Holmes, a stout, stern woman who was employed as a clerk in the years when Fort Wayne was a busy rail hub.

Federal benefits come in kind as well as in cash. Whetsel, a 56-year-old carpenter who looks and talks like James Cagney, gets free nerve treatments at the VA hospital for the injury he suffered when the Japanese bombed his paratroop battalion on New Guinea in 1942.

He also gets $43 a month from the Veterans Administration as a disability allowance.

The Department of Health, Education and Welfare provides Fort Wayne residents with millions of dollars worth of in-kind aid through Medicare and Medicaid.

One of the big winners in the latter category is Clarence Haynes, proprietor of a small pharmacy in a low-income neighborhood. Haynes, a soft-spoken man who wears wirerimmed glasses and a huge gold watch ringed with diamonds, said he gets about $110,000 from Washington each year for filing Medicaid prescriptions.

Recognizing its dependence on federal grants, Fort Wayne has a full-time grants specialist, William S. Latz, with an office right down the hall from the mayor, to see that the city maximizes its potential take from Washington.

Latz, a wry and thoughful man, scored a coup last year when he convinced the federal government to help pay for restoring the town's old city hall, a gingerbread palace that has been vacant for nine years.

"You've got to catch the current wind," Latz said. "Used to be that helping blacks was the big thing in federal grants. Then it was energy conservation. Right now its historic preservation.

"Six months from now, history will probably be blah, but at the moment it's absolutely King Tut stuff. So we got $350,000 to preserve our historic city hall."

In fiscal 1980, Latz may have a tougher challenge. A community organizer named Art Amt, concerned because the city's public statutes all commemorate whites (Gen. Anthony Wayne, who fought here, and Johnny Appleseed, who died here, are favorite subjects), asked Latz to find some federal money for a statute honoring blacks' struggle for freedom.

Here as elsewhere, grants under the Comprehensive Employment and Training Act (CETA) are important benefits for the unemployed. Fort Wayne has hundreds of CETA grantees, who get about $8,700 annually for jobs that range from digging ditches to staging pantomime performances.

The federal government also spends money here for its own operations. Although the VA hospital is the only major federal installation, the area has nearly 1,000 federal employes (not counting mailmen).

Regulatory agencies, such as the Interstate Commerce Commission and the Labor Department's wage and hour division, have inspectors in town. The presence of the Gladieux Oil Co.'s refinery requires the presence of Phil Wilson, an amiable Energy Department auditor, who makes sure pricing regulations are obeyed.

Fort Wayne has the usual run of federal crimes, requiring judges, prosecutors and special agents of the FBI. About a dozen times a year, the government presents a $30 check to Barker Davie, a local chemist, as his fee for testifying about his analysis of the substances seized from narcotics dealers.

The government's calculation of its total spending here shows Washington sends Fort Wayne more than $2,500 per year for every man, woman and child in town.

The government does not calculate the tax burden on particular geographic areas, but a private organization, the Tax Foundation Inc., does.

Its data show that the total burden of federal income and excise taxes in Allen County -- Fort Wayne and environs -- is about $1,710 per person (the figure is probably higher in the city itself).

Because tax revenues, on a national basis, do not equal expenditures, the government has to borrow money. It pays about $16 million annually in interest to individuals and institutions in Fort Wayne.

Among the recipients in fiscal 1980 will be Billy Hartman, a freckle-faced sixth-grader who bought a savings bond last year. President Carter's $532 billion budget for fiscal 1980 will include $1.58 for Billy Hartman.