Public transportation in the United States is finding it does not always pay to be popular. As more Americans leave their automobiles at home and go by bus or rail for local travel, they are straining many transit systems nearly to the breaking point.

Forget the basic economic law of supply and demand. With conventional mass transportation, an increase in riders usually means greater financial losses to be made up by government subsidy. That is because most new ridership comes during the peak commuting hours, forcing transit systems to invest in more employees and equipment which for most of the day runs nearly empty and loses money.

This axiom puts conventional public transit at a crossroads: Should it expand and improve service, as Americans apparently want, and worsen its already shaky financial position? Or should it maintain the status quo, effectively discouraging new passengers?

Taxpayers, urban planners, transit operators, and independent transportation analysts offer various answers. But there is wide agreement that this issue will be the key in determining to what extent public transit grows as a transportation option in the 1980s:

* "Transit in the 1980s has the potential for both boom and bust . . . ," a top federal government transportation official notes.

* "It costs us $1.20 for each new rider we get, and our average fare is 41 cents," says the general manager of one major urban transit system. "Our constituency wants more service, but the more riders we get, the more money we lose. It boils down to a delicate balancing act of never being too far out in front of what the public is willing to pay for."

* "There is a growing perception that the fiscal appetite of public transit is voracious and nearly impossible for elected officials to control," a leading transportation scholar asserts.

* While the strength of support for public transit "at the moment appears quite robust . . . the national mood appears increasingly to be toward the limitation of government expenditures and toward 'balanced budgets,'" a transit analyst at a large research institute warns.

Another way to look at the question of costs is to ask what taxpayers get in return for the growing public subsidy that transit is enjoying.

About 6 million households in US central cities do not have autos, and for many of them urban transit is a necessity for working, shopping, and recreation. For many suburban commuters who work downtown, particularly in older cities like Boston, New York, and Chicago, mass transit is essential, given the cost and shortage of parking facilities in town.

In a broader sense, where mass transit is well planned and well used as an alternative to the automobile, "you get reduced congestion, somewhat less air pollution, and some energy savings," says Anthony Downs, a senior fellow at the Brookings Institution.

Still, transportation analysts point out that a poorly planned and poorly used transit system may offer no social benefits, or at least far fewer than justified by the costs.

For example, studies of the BART (Bay Area Rapid Transit) system in San Francisco contend that given the total cost of building and operating the system , it remains cheaper to drive a car during the peak commute and that overall highway congestion is not much improved, since many BART riders were previously bus patrons. But arguments such as this typically call into question the use of one mode of public transit vs. another -- rail vs. bus, for example -- rather than the basic notion that mass transit can make society more efficient in moving people.

What seems clear from the stacks of studies on the costs and benefits of mass transit is that (1) it is prudent to preserve and upgrade the existing major urban transit systems, which are integral to the survival of many of the nation's largest cities; and (2) in cities with reasonably high population densities and worsening automobile congestion, public transit can help increase the efficiency of the local transportation system. In these cases, analysts say , experience has shown that conventional bus systems and streetcars are generally more successful than heavy-rail systems.

"With rapid rail, the capital cost is so enormous that no matter how well it works, it carries a tremendous built-in subsidy that is almost impossible to recover," says Kenneth Small, an assistant professor of economics at Princeton University.

One response to the worsening financial picture in urban transit has been higher fares. For years, transit operators and the governmental bodies that set their policies have viewed fares as a political hot potato and deliberately kept them low. From 1963 to 1978, for example, the average transit fare in the United States actually declined marginally when adjusted for inflation, according to the American Public Transit Association.

About 90 percent of the nation's transit vehicles are publicly run. They are usually independent, nonprofit authorities established and owned by cities, counties, or regional governments.

Many of these operators now view this pattern of falling fares as a mistake, and in the past two years rate hikes have been widespread. In the future, transit patrons in most cities can likely expect fares to keep rising in tandem with the rate of inflation, analysts agree.

In Atlanta, for example, a 1971 referendum calling for a 1-cent sales tax to support local transit also promised to keep fares at 15 cents for 7 years. The measure passed and the commitment not to increase fares was kept. But the fare policy simply postponed the inevitable, and last year the fare was raised to 25 cents, then, earlier this year, to 50 cents. Those steep increases caused some ill feeling among some local low-income minority groups, feelings that might have been avoided with steady, smaller fare increases.

"You don't build up any credits in this business and there is no point in avoiding fare increases," says Alan F. Kiepper, general manager of the Metropolitan Atlanta Rapid Transit Authority.

In Washington, D.C., the policy is simple: On the new rapid rail subway system, fares rise with the consumer price index, and bus fares increase at half that rate.

Looking ahead, transit analysts expect more aggressive fare policies to bring to a head the issue of how best to protect the poor, elderly, and young central-city residents -- a major share of the transit ridership -- from being immobilized by fares they cannot afford.

The US Department of Transportation is studying the feasibility of programs of direct subsidy to Americans with low incomes who depend on public transit. Most analysts who have explored this idea say its major drawbacks are the complexity of administering such a program on a national scale and the problem of verifying and setting standards for those who would qualify for transit aid.

George E. Gray, chief of mass transportation at the California Department of Transportation, says a better approach might be for already established social welfare programs to reimburse transit operators for the fare subsidy they provide users who cannot afford more.

One clear incentive to keep fares rising at least at the same pace as the inflation in operating costs is the public's insistence that service not deteriorate. Many transit operators in all parts of the country have had to hold frequent public hearings on proposed fare increases in the past few years. They are nearly unanimous in their assessment that riders are more concerned about the quality of service than marginal increases in fares.

After months of community hearings in the New York metropolitan area, John Simpson of the Metropolitan Transportation Authority, which is the regional policymaking agency, concluded, "No one believes service should be cut."

New York City's fiscal problems have magnified what happens to an urban transit system when financial constraints cause service to deteriorate. In the mid-1970s, as inflation rapidly raised the cost of operating the New York bus and rail system, the transit authority's budget was kept essentially flat. Nonessential maintenance and personnel training were reduced sharply.

Today, as a result, on-time performance is down, and public hostility is increasingly evident in growing vandalism and abuse of the subway cars and buses.

"It's a long road back up the hill" to stabilizing the quality of service, says Steven K. Kauffman, general manager of the New York City Transit Authority. And as New York plays catch-up on maintenance, Mr. Kauffman is concerned that this could divert attention and funds from expanding the system to meet the transit needs of the city in the next 20 years. New York already accounts for roughly one-third of the daily US ridership on public transit.

In Chicago, where some 90 percent of the area residents coming downtown to shop or work each day use mass transit, there is also concern that the system is not being adequately maintained. While insisting that enough money is being spent to keep the Chicago rail and bus system safe, Harold H. Geissenheimer, general operations manager at the Chicago Transit Authority, warns that "orderly replacement of the system requires much more than we are spending."

The result, he says, is that the city's rail system, particularly the elevated "loop" that circles downtown, has a "turn-of-the-century look" that does little to entice new riders.

The worsening financial plight of the nation's public transit industry is evident in two developments since 1972: While ridership has increased, the combined net operating deficit of operators nationwide has been rising by an average annual rate of nearly 20 percent, according to an analysis by Michael A. Kemp, a senior research associate at the Urban Institute.

To the rescue have come federal, state, and local governments. They now provide more than half the money it takes to keep the nation's public transit systems operating. The rest comes from fares.

Major federal involvement in public transit began in 1964 with legislation that permitted capital grants for new equipment and facilities. Such grants amounted to $51 million in 1965 and required operators to meet one-third of the cost of projects with local funds. Today, capital grants from the federal government require only a 20 percent local contribution, and they are budgeted at $3.3 billion for fiscal year 1981.

Since 1974 the federal government has also been providing operating assistance to help transit systems meet day-to-day expenses. Operating subsidies have grown from $300 million six years ago to more than $1 billion in fiscal 1981.

Theodore C. Lutz, administrator of the Urban Mass Transportation Administration, says the level of federal investment is warranted when one considers that the nation's urban transit service was near collapse when government involvement began in the 1960s. And, he maintains, "the alternative to this investment was not so hot: more freeways, congestion, and pollution."

Still, most analysts agree that the rapid growth of federal assistance to public transit in the 1970s will not be matched in the '80s.

Sen. Harrison A. Williams Jr. (D) of New Jersey, a longtime advocate of public transportation and the architect of many of the funding bills that have funneled more aid to it, warns that the "fragile coalition supporting urban transportation in recent years is rapidly changing." It is being altered by more fiscal conservatism in Congress, and could jeopardize any major increases in federal transit aid in the coming years, he says.

President-elect Ronald Reagan has said little to indicate his views on government aid to public transit, but his clear preference for a reduced federal role in local affairs could mean fewer dollars for transit. California's Mr. Gray, who also served in transportation during Mr. Reagan's tenure as governor, speculates that Reagan "will tend to see if the private sector can take care of more of the cities' transit needs before encouraging more government involvement."

One sign that federal dollars for public transportation may grow more scarce is reflected in the heightened sense of competition for federal subsidies among transit operators. As this goes to press, Congress was considering a major transit authorization bill that would alter the formula for awarding operating grants. It would be based on the amount of service provided. The current system is based instead on an urban area's population and density.

The net effect of such a formula change would be to shift more money to the large, already established transit systems at the expense of cities where public transportation is a relatively minor component of local travel.

With tax subsidies expected to become more scarce, transportation analysts predict that transit operators will be forced to make existing systems run more efficiently and to explore new, more cost-effective kinds of paratransit service.

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