The ultimate success of Metro from a financial point of view depends on its ability to attract riders. Just how many riders will it attract is a subject of substantial debate and depends in part on how high Metro keeps its fare.

Peat, Marwick, Mitchell & Co. just completed a new study for the Metro board that estimates an annual ridership for the combined bus and subway system of 365 million by 1990.

That figure is 8.5 percent lower than the 400 million that Peats, Marwick estimated in another study just a year ago. The differences have to do with such things as the adequacy of the feeder bus network in Prince George's County and housing densities west of Vienna.

Some federal officials and other critics who are watching Metro closely believe that potential ridership may be overestimated by as much as 40 to 50 percent.

They point to assumptions made in those estimates that they do not think will hold water. Included are assumptions that downtown parking charges will increase generally with inflation and that full market value will be charged for 39,000 federally controlled parking spaces that presently are free or highly subsidized for their users.

In the past few years, the Washington area's explosive growth rate has slowed to about half of what it was in the 1960s, when the Metro subway routes were originally laid out. At the same time there has been an equally dramatic increase in the number of people who commute to Washington from long distances - Fredericksburg, Harpers Ferry, Frederick, Clavert County. If those commuters are to be served by transit, they are going to have to drive to the station because the line will never reach them.

What are the implications of these trends?

The answer depends partly on fares.

One of the things Peat, Marwick rediscovered for the region was that a full, 100-mile Metro system would be cheaper to operate, and thus would have lower deficits, than a full-bus system providing equivalent service.That finding was in large part responsible for the recommendation from the regional task force that all of Metro be completed. Until it is completed, the system will be less efficient and interim deficits will be proportionately higher.

Assume that all of Metro is in place by 1990. Assume a ridership of 400 million annually, bus and rail combined. The total operating deficit for the region in inflated dollars will be $90.7 million, almost $10 million less than it is today in 1978 dollars.

One important fact is missing from the preceding paragraph. That is the key assumption that, between now and 1990, Metro will have increased its fares annually at a rate approximately the increase in the cost of living generally. The recent history of Metro suggests that is wishful thinking.

In fact, over recent years Metro's fares have increased at only about half the cost of living. If that pattern continues, by 1990 Metro's combined bus and rail deficit will total $301.6 million, assuming 400 million riders. If 1990 ridership is really 365 million, according to the latest Peat Marwick estimates, the deficit would be $328.6 million.

Another study by a task force of the Washington Center for Metropolitan Studies, suggests that the deficit could reach as much as $500 million or $600 million a year in inflated dollars given a 20-percent cut in projected ridership of 400 million.

The key ingredient is fares. There is a raging debate on whether high fares drive away transit riders or whether low fares attract people to transit. A substantial body of academic opinion suggests that the quality of service, not the price of the ride, is the determining factor in rush-hour ridership.

Therefore, the line of argument goes, Metro might as well charge high fares because they do not hurt ridership and they reduce the burden on the general taxpayer to operate the transit system.

That argument has be espoused in this area most vigorously by Joseph S. Wholey, current chairman of the Metro board and a member and past chairman of the Arlington County Board. "The average rush-hour Metro commuter has a higher family income than the average metropolitan area resident," Wholey said in an interview. "Therefore the average rush-hour commuter is being subsidized by a poorer person."

Douglas N. Schneider, director of the District's Department of Transportation, believes in low fares and vigorously represents that position in Metro board deliberately. "We've got to look at what we're doing here," Schneider says repeatedly. "That fare is too high, and people are going away."

Indeed, there was a big drop in Northern Virginia bus ridership in March 1977 when fares went up and an increase in the number of cars crossing the bridges into Washington. Schneider points to those facts when arguing with Wholey.

Schneider is also concerned that D.C.'s relatively high number of transit dependents - people who cannot afford cars - requires the District government to keep fares at a low level as a matter of social justice.

Wholey does not believe in starving the poor, but suggests that high fares be charged and that subsidies be provided to the individuals who need them.

The idea of making a poor person stand in line of quality for a low-fare card offends Schneider and many D.C. politicians. "There is no reason a person whould be stigmatized for being poor," Council member Jerry A. Moore said.

The arguments does not appear to be near resolution.