In the 10 years since Metro took over the region's transit system, the Washington area has failed to solve what key officials describe as the transit authority's most serious problem: soaring deficits.

When Metro acquired the area's faltering, privately owned bus companies in early 1973, the firms' losses amounted to about $1 million a year. Since then, the gap between revenues and expenses has widened steadily, aggravated by the 1976 opening of Metro's multibillion-dollar subway system. Subsidies paid by local governments to keep the bus and rail systems running have doubled since 1980 and are considered likely to exceed $200 million next year.

Far outpacing inflation, the deficit is expected to climb by more than 20 percent in the current fiscal year and to double again by 1988. Without broad cutbacks in bus service, reductions in unionized employes' wages or other sweeping changes, some officials say, the increases in transit costs will probably outstrip inflation until the 1990s and possibly for the rest of this century.

"It's one of the great mysteries that's confronting us now--how we're going to cope with this," says Philip M. Dearborn, vice president of the Greater Washington Research Center and a specialist in local government finances. Adds Thomas M. Downs, District of Columbia transportation chief, "We're gaining a rail system, but it's costing us a fortune."

Amid long-standing disagreements about how to bridge the deepening fiscal chasm, officials are calling for steep annual increases in bus and subway fares, new taxes to underwrite transit expenses and stiff cost-cutting measures. Yesterday, most minimum bus and subway fares rose 10 cents.

"We're talking about big bucks--50 percent increases in the proportion of Metro's costs paid by the rider," says Anton S. Gardner, Arlington County's fiscal analysis chief. While it is unclear how high the fares would have to be to reach Arlington's goal, the increases would be sizable. Fares now provide less than half the money needed to run the transit system. Arlington wants them set high enough to cover nearly 75 percent of Metro's costs.

Richard S. Page, who recently announced his resignation after four years as Metro's general manager, has cited the rising costs as Metro's "No. 1 problem" and voiced fears about putting off the day of fiscal reckoning. "That's what worries me. I'd hate to see the transit service face a real crisis," Page said in an interview.

Though Metro's finances form a labyrinthine jigsaw puzzle, its staggering deficits stem from two fundamental causes. First, most of its current costs rise with inflation. Wages paid to bus drivers, subway operators, mechanics and other employes are tied to the Consumer Price Index through cost-of-living clauses in union contracts. Other major costs--for diesel fuel, electric power and spare parts--have shot up faster than inflation.

Second, Metro continues to add new costs by expanding its rail network, a process expected to last at least until the 1990s. Since the subway system runs at a deficit, more service usually leads to bigger losses. Although bus service has been thinned out along routes where rail service has started, the subway system is growing faster than the bus system shrinks.

The deficits have mounted as the number of passengers using the transit system dropped. Ridership peaked in 1980 after the nation's gasoline crisis and is expected to continue to decline during the next fiscal year, partly because of reluctance by some to pay rising fares.

Nevertheless, Metro officials predict that the number of passengers will start climbing again in fiscal 1985.

Regional officials are currently seeking to pare the transit agency's proposed $384 million operating budget for the next fiscal year, which starts July 1. Tentative cuts would leave an expected $206 million gap for financially pressed local governments to fill by drawing on their own revenues from real estate, income and other taxes.

Recent declines in inflation have eased Metro's financial pressures, allowing officials to reduce their forecasts for wages, fuel and other costs by millions of dollars. Nevertheless, the chief administrative officers of major suburban governments recently proposed stiff hiring curbs to help cut Metro's budget by $34 million. And D.C. Mayor Marion Barry expressed dismay at Metro's request for $7.7 million more than the District had offered to pay.

The severity of Metro's deficit problems has been widely recognized for several years. Page pointed to the issue on the very day he was hired as Metro's general manager in March 1979. "What Metro needs--and everybody knows it--is a firm source of dedicated tax revenue to cover the deficits ," Page said at the time. "Passing the hat among local governments has worked, but it has made life extremely difficult."

Local governments have taken some steps in recent years to try to shore up Metro's finances. Montgomery County has added 19 cents to its real estate tax rate and set aside the increased revenue to underwrite Metro and other transit costs. Montgomery and Prince George's County also benefit from subsidies paid from Maryland's statewide transportation fund.

However, federal subsidies for transit operations here and across the nation have been reduced under pressure from the Reagan administration, which wants to end the payments. Local governments' budgets have increasingly been squeezed. And the Metro system's troubles have been compounded, Metro officials contend, by the Reagan administration's refusal to finance expansion of the planned subway system as rapidly as regional officials have urged.

The General Accounting Office is among government and private agencies that have issued recent warnings about Metro's deficits. In a January report, the congressional auditing agency termed Metro's forecasts "overly optimistic," described its deficits as "burdensome to local jurisdictions" and urged periodic reviews. Mounting subsidies "have far outstripped even the fast-rising Consumer Price Index," GAO said, pointing to a near-tripling between 1976 and 1981.

A study prepared last summer for the Greater Washington Research Center by three Urban Institute researchers predicted that Metro's deficits would rise by an average of 20 percent a year during the next five years. "We envisage that over the next few years financial pressures will increasingly drive Metro to contemplate and carry out both service reductions and fare increases," the study said.

A 1981 report for Metro by two consulting firms, Peat, Marwick, Mitchell & Co. and JHK & Associates, predicted that Metro's deficits would reach $446 million by 1990, about three times last year's amount. If the figures were adjusted to eliminate the impact of inflation, Metro's deficits would still rise by 43 percent, the consultants said.

Attempts to reduce the deficits have repeatedly encountered opposition. Arlington is not alone in advocating big fare increases. The Northern Virginia Transportation Commission has proposed raising fares steadily during the next 10 years with the aim of financing two-thirds of Metro's costs from fares and other nongovernment revenues. Page has suggested setting fares high enough to cover about half the costs.

Today fares and revenues--from parking fees, advertising charges and other sources--provide only 46 percent of the money Metro spends on bus and rail service. But many officials argue that any steep rise in fares would drive away riders and jeopardize low-income passengers who are most dependent on public transportation. A recent fare increase was adopted by Metro's board of directors only after protracted disagreements, and it fell short of the agency's initial proposals.

Page and others have long urged local governments to establish special taxes--on sales, employment, earnings or other sources--to help subsidize Metro. But many transit specialists express doubt that Washington-area governments with widely divergent views will ever agree on such a tax. Some officials warn, moreover, that new tax revenues might initially fuel excessive growth in Metro outlays and eventually lead to renewed deficits.

Metro's past efforts to hold down wages by seeking changes in union contracts have been largely thwarted in labor negotiations and arbitrators' rulings. Talks recently began on a new labor contract with no initial sign of a softening in union demands. Either side may invoke binding arbitration by asserting that the negotiations have reached an impasse.

Attempts by Metro officials to decrease bus service on what they consider lightly traveled and unneeded routes have frequently foundered amid protests from riders and opposition by local governments that must assent to changes. Complaints by state, county and city officials about what they describe as excessive staffing, salaries and expenses at Metro headquarters have been rejected by Metro officials.

The rising deficits may foreshadow a transit crisis, said Fairfax County Supervisor Joseph Alexander, a longtime Metro board member and chairman of its budget committee. "In the next three or four years it may come to that . . . . A disaster may come along."