President Carter and his newly revamped economic team are facing a policymaking box in their efforts to steer the economy through the 1980 elections. The dilemma: How to cope with the coming recession without exacerbating inflation and provoking another slide in the dollar.

Although Carter has calmed some market jitters with his nomination of Paul A. Volcker, former undersecretary of the Treasury for monetary affairs, as chairman of the Federal Reserve Board, the fact is that the problems are no less serious now than before the president began his reshuffling.

Indeed, many experts believe that, if anything, the nomination of Volcker is likely to make it tougher for the White House to achieve its goals. Volcker, who is more sensitive to the dollar's troubles than outgoing Fed chief G. William Miller, may keep monetary policy tighter than his predecessor would have.

The predicament is a frustrating one. In previous years, when a president feared the prospect of a coming recession, the first thing he would do would be to stimulate the economy. In 1977, for example, Carter proposed a major cut in income taxes and a big new job-creation program. Congress approved them both.

This time, however, inflation is so virulent that even many liberals fear that additional stimulus would heighten the wage-price spiral. Both Carter and Congress have urged caution on the tax-cut front. And some analysts argue that any cut should involve Social Security taxes, which would be less inflationary.

The problem is, what can be done without exacerbating inflation? The answer, until recently, was to let monetary policy do the job. Both Miller and ousted Treasury secretary W. Michael Blumenthal favored holding fiscal policy steady and banking on the Fed to ease credit if the recession proved deep.

But, as the past month's events have demonstrated so graphically, the Fed itself may be prevented from playing that role because of its duty to defend the dollar, which is proving particularly vulnerable in the face of worsening conditions here.

As a result, although the central bank normally would have continued policy intact, or even eased credit some, at the start of a recession, the Fed found itself actually raising interest rates again two weeks ago - in part to bolster the dollar, which has declined because of nervousness over the Cabinet shakeup.

The rescue action was necessary because of the vicious cycle that links the dollar, inflation here and recession. Any prolonged slide in the dollar's value seriously adds to the wage-price spiral here at home and eventually serves to worsen the recession. Carter could only go along.

At the same time, however, every time the Fed riases interest rates, it worsens short-term prospects for growth. Part of the reason for t e current forecast of a mild recession is the belief that the central bank will keep money tight. Turning the screws more tightly could deepen the slump.

Nor is the widely hailed appointment of Volcker - and the shift of Miller to replace Blumenthal at Treasury - likely to alter the president's dilemma. Although Volcker is no right-wing hard-liner, he is by experience more attuned to the dollar's needs than Miller, and presumably would move in its defense more quickly.

Although Volcker tried to minimize these differences during a press conference Wednesday, he has voted several times in the Fed's policymaking Open Market Committee to tighten - or at least not to ease - money and credit policies when Miller endorsed the more liberal stance.

What that's apt to mean is that the Fed - in which Volcker already has had some influence as president of the New York Federal Reserve Bank - is now all the more likely to look after the dollar's needs before it tends to the president's political requirements. And that only tightens the box.

Ironically, Carter's own performance virtually forced him to pick a conservative Fed chief as Miller's successor. The countless policy wafflings of the past 2 1/2 years, combined with his abrupt firing of Blumenthal last week, raised new fears that the White House would "politicize" economic policy.

The appointment of Volcker served to allay some of those apprehensions - perhaps more than some White House aides may prefer. Whatever his policies, the betting is that Volcker will be tough and independent enough to keep the White House Georgians in their place.

And Miller is described by Fed insiders as deceptively complaisant-seeming. Although the new Treasury secretary is likely to appear to be a "team player" in his public appearances, colleagues say he's a tough in-fighter when he's backed into a corner. White House staffers are expected to be no match.

Still, although Carter may have landed on his feet with his new Fed and Treasury appointments, his team has its work cut out and already is behind schedule in tackling the administration's growing list of serious economic problems.

While Carter has been reshuffling his economic policymaking team, there's been no one to make decisions on what changes to make in the wobbling wage-price guidelines program. The White House must cement plans soon if it hopes to meet its Aug. 1 deadline for asking public comment on them.

And there's still the question of what to do about fiscal policy for 1980 - to hold out without new stimulus, as Carter now says he wants to do, or to go for further stimulus, as most outsiders expect the administration will decide as the election draws closer.

To top it off, one of the key members of the president's economic policy team is ill and unable to help in the planning. Charles L. Schultze, chairman of the Council of Economic Advisers, is recuperating from a liver ailment and may not be back at the office for several weeks.

For all the adverse reaction to the firing of Blumenthal, it seems clear that Carter has overcome much of the recent nervousness about whom he would name to his new team. But, just as policy has not changed as a result of the shakeup, neither has Carter's dilemma. CAPTION: Picture, Paul A. Volcker...nomination calms markets. AP