THE SUBURBS' STAKE IN CITIES

''YOU can't build a wall around a city - we all are one.'' As Pittsburgh Mayor Richard Caliguiri sees it, major cities and their suburbs stand or fall together. He says he's convinced that more suburbanites will move back to the city as they realize they did not leave urban problems behind and that areawide, metropolitan government is on the way. ''There's no doubt in my mind that economic necessity will dictate it before the turn of the century.''

In the meantime, he says, suburbanites must do more to support the city services and facilities they use than the maximum $10 per-capita annual charge now allowed under Pennsylvania law. Mayor Caliguiri insists he has just as much garbage to collect, fire and police services to provide, and bridges and roads to maintain as when his city had 200,000 more residents.

That kind of steady demand for services in the face of rising costs and shrinking revenues poses a growing dilemma for all of the large older cities of the Midwest and the Northeast.

Most urban experts say metropolitan government could help but won't come. Suburbs strongly oppose the added tax burden. And some city halls would rather go broke than yield authority. ''It will happen only if the suburbs become convinced that if the city goes down, they will be losers, too,'' says Roosevelt University urbanologist Pierre deVise.

Much more likely is the continued spinoff of city functions - from waste-water treatment to museum management - to the county or state. Most states now pick up the nonfederal share of welfare. The state of New York has taken over many of New York City's court, hospital, and university expenses.

''The states are getting stronger and stronger vis-a-vis the cities, and they will increasingly play an equalizing role,'' says John Shannon, assistant director of the Washington-based Advisory Commission on Intergovernmental Relations.

In some cases where there is a common area interest, special districts may be formed. The St. Louis region, which resoundingly defeated a metropolitan government proposal in 1961, recently set up a new zoo-museum district, and is talking about setting up another for economic development.

More than half the states now limit city authority to raise taxes. Many cities, claiming they have the responsibilities of New Federalism without the dollars to go with them, are pushing hard to remove those limits.

But many urban experts argue that only more federal help can really make a difference to the adjusting economies of the most troubled industrial cities.

Cleveland State University's Paul R. Porter, co-editor of ''Rebuilding America's Cities: Roads to Recovery,'' argues that some kind of government-supported jobs program and temporary aid along the lines of a ''Marshall Plan'' is vital. ''Without such help these cities won't even make it through the transition,'' says this former assistant administrator of the Marshall Plan.

Urban sociologist Philip Morris Hauser, professor emeritus of the University of Chicago, argues that the federal war on poverty did not try to do enough in a comprehensive way and that only massive federal help now, including a full-employment policy, can successfully rescue the large older industrial cities. ''And there's no doubt in my mind,'' Dr. Hauser says, ''that the additional revenues would represent the most enlightened kind of investment - that in the human being - with the greatest possible return.''

''The key to saving our cities is getting the people in them to be employable and employed - everybody benefits with everybody working,'' agrees John E.Jacob, president of the National Urban League. ''People say that government spending isn't the desirable way, but the job is too big for the private sector alone. And whether we like it or not, our cities have to be repaired and rebuilt. It's not make-work.''

The case may be strong for more federal help - particularly for federalizing the urban welfare burden - but many proponents admit that the prospects are limited regardless of who moves into the Oval Office. ''Anyone who thinks there is going to be fiscal salvation for the cities from Washington over the next 10 years is dreaming,'' says Donald Haider, a former Chicago budget director. The 1983 federal deficit alone was $24 billion more than all taxes collected by state governments that year, Mr. Shannon notes.

But many say Washington must at least think through its responsibility to cities and set some priorities. ''We definitely need a national policy for dealing with displaced employees - we haven't really explored what we should be doing,'' says Alan Beals, executive director of the National League of Cities.

One reassuring note for those concerned about the financial health of the industrial big cities: A strong mix of fiscal and accounting safeguards have been added since New York's troubles in the mid-1970s. The more professional approach may not preclude other close calls. But Mr. Haider, now a professor at Northwestern, insists it removes most of the ''mystery'' and ensures advance warning. ''A revolution has been going on beneath the surface in cities in the adoption of technology, management by objective, and strategic planning that's every bit as good as what's going on in the private sector,'' says Mr. Beals.

Although recovery of the large industrial cities depends in part on how well the economy of the region rallies, urban enthusiasts insist that with enough vision, effort, and time the cities of the Midwest and Northeast will make it.

''I'm constantly reminded that within our federal system there is tremendous diversity and a capacity for regeneration,'' Shannon notes. ''There are self-correcting forces at work.''