Argentina's new president will inherit a nation on the brink of economic collapse

Inflation is raging along and reaching new and dizzy heights in Argentina. One report this past week put it at 945 percent a year. Another report estimates that $35 billion left the country from 1976 to the present ''without justification.'' That amount is almost equal to Argentina's $ 40 billion foreign debt - a debt that more than one Argentine thinks is unserviceable given the economic conditions here.

And between now and Dec. 31, a scant two months, unemployment is expected to rise to 17 percent, according to yet another report. New business bankruptcies and industrial cutbacks are the culprits in this unemployment tally which now is 15 percent ''and climbing,'' in the words of the report.

All this and more have Argentina at the brink of economic collapse - a sad outcome for what was once one of the richest nations in Latin America.

And it is this economically bankrupt nation that Argentina's first civilian president in seven years will inherit when he takes office later this year.

Although the results are not in at this writing, the election Sunday was largely a race between two men: Peronista candidate Italo Argentino Luder and Radical candidate Raul Alfonsin.

There is a soberness on the part of both. In the final days of the campaign, Mr. Luder spoke of the ''economic traumas'' of the nation being ''far more serious than anyone realized.'' Mr. Alfonsin said, ''No matter who wins, the victory dance will be played out against the worst economic crisis in Argentina's history.''

If the two candidates are somber, so is the nation as a whole. As Argentina stumbled steadily toward election day, Argentines as a people seem to have lost their self-confidence.

It will take all the talents of either Luder or Alfonsin - and then some - to alter this mood and turn the country around. But there is little certainty that either can really do the job needed.

Waiting in the wings is a badly shattered and demoralized military. Recovering from its bitter defeat in an ill-timed war with Britain over the Falkland Islands last year, the military after seven turbulent years of rule was preoccupied with promotions and retirements, and the benefits that go with both.

But no one here can be sure the military will not want to be back in power again soon. In fact, one of the newest generals said privately over the weekend, ''If the civilians make a wrong move, you can be sure we will be back to straighten things out.''

But their track record of straightening things out is poor. This latest seven-year run of military government has, by most standards, been a disaster. The Argentine economy is in the worst shape it has ever been in. And most of the Argentine people are contemptuous of the armed forces.

Still the threat of a military comeback is something that neither Luder nor Alonfsin - or their advisers - cannot overlook. Although some of his supporters have spoken out against the military with derisive language that only a year ago would have clamped them in jail, Luder has been moderate. He called on the nation this past week to recognize that the military is not alone to blame for the ''economic disaster through which we are stumbling.

''We are all responsible and we must now get together and act responsibly.''

At the same time, both Luder and Alfonsin must respond to a growing national clamor for sharp boosts in wages and salaries eroded by hyperinflation, which hurts family budgets as it does the national budget.

But any new round of wage increases - and there will undoubtedly have to be some increases - would simply fuel the inflationary fires all over again.

The winner in Sunday's vote will soon have to grapple with this dilemma. Exactly when he takes over is not clear since there is talk in military circles of perhaps leaving office as early as November 15, allowing the civilians to wind up the calendar year and to share some of the blame for 1983's economic mess.

But beyond the immediate mess is an important question here of just how Argentina with its rich economic potential has allowed itself to slump into ''an economic basket case,'' as the newspaper La Voz put it.

The problem goes back 50 years or so to a time when Argentina's conservative rural political leaders failed to respond to the growing urban, industrial needs of the country.

That leadership was swept aside as an obscure army colonel, Juan Domingo Peron, emerged on the scene and mobilized the urban masses, setting up the Peronista movement over which Luder now reigns. Successive civilian and military governments over the past 30 years have grappled with the tensions and frustrations that ensued and, as J. Iglesias Rouco, the columnist for La Prensa, puts it, ''simply misruled.''

Whether Luder or Alfonsin, whatever their personal desires may be, can change this pattern remains to be seen. In fact, there is not too much hope that the new president will be able to control the economy or to control the military.