Federal Reserve Chairman Paul A. Volcker met last week with President Reagan for the first time since inauguration week. Apparently the session did little to ease the strain that has developed between the administration and the Fed as the result of outspoken criticism of the central bank's performance this year by some key Reagan officials.

Neithe the White House nor Volcker, who left shortly after the session in the Oval Office for an International Monetary Fund meeting in Africa, would say much about the meeting, which David Stockman, director of the Office of Management and Budget, and several top White House officials also attended. But sources said it did not go well.

Officially, White House spokesman Larry Speakes said only, "Of course we do not favor high interest rates. [But] we realize the Federal Reserve Board has to take certain steps with the money supply in order to make certain economic corrections . . . . We are hopeful that our [economic] program will eliminate the necessity for short-term corrective actions of this type, and that will see a reduction of interest rates once our program gets on stream."

Based on what Volkcer has been saying both publicly and privately, he probably disagreed flatly that adoption of the Reagan economic policy package will end the need for "corrective actions" by the Fed to counter surges in money supply growth, or that interest rates are necessarily going to fall all that far that fast. That kind of fundamental disagreement could sour many a meeting.

Volcker had asked to see Reagan in March just before the president was shot. At that point interest rates were falling from their peak hit at the turn of the year and growth in the money supply was below the Fed's target range. Even then, however, officials such as Treasury Secretary Donald T. Regan and his undersecretary for monetary affairs, Beryl Sprinkel, were pressing the Fed publicly to change its way of doing business in order to make sure money growth did not get out of hand in the future.

In April, the money supply did shoot upward, though it remains even now within the target range once the numbers are adjusted for the effect of allowing interest-bearing checking accounts nationwide as of Jan. 1. When money growth jumped last month, the Fed quickly moved to tighten credit conditions and thereby keep control of the monetary aggregates. But interest rates took off, too. By last week the prime lending rate at some banks hit 20 1/2 percent, only one percentage point below the record of last January. Mortgage rates have reached 18 percent at some institutions, and 13-week Treasury bills brought the highest returns ever, 16.75 percent.

Since tight control of money supply growth is exactly what the administration is demanding of the Fed, one might have expected Reagan officials to stand up and applaud.They did not.

Instead, Sprinkel last month criticized the central bank for allowing excessive fluctuations in the money supply. Those ups and downs, he claimed, were undermining confidence in financial markets that the Fed could or would control the money supply in the longer term. That was why interest rates were rising, not because there was more demand for credit than there was credit available, he argued.

Volcker is known to have resented these attacks, which he believes were unjustified. There is no way to prevent random, short-term fluctuations in the money supply figures, a point acknowledged evey by most monetarists economists, he maintains. The more rigid the attempt to keep the money supply growing along some predetermined path, the more violent will be the ups and downs in short-term interest rates.

The problem in financial markets is not just distrust of the Federal Reserve's intentions, though that is a factor, Volcker believes. The bias at the Fed for the past 30 years has been to be too accommodative, even though the Fed may have been less guilty of that bias than other parts of the government. Now he and other members of the Federal Open Market Committe, which establishes monetary policy for the central bank, say they are putting more discipline in their money supply control efforts to counter that bias.

The markets' real difficulty in Volcker's opinion, is that they have concluded that the demand for credit -- including the added borrowing the federal government will have to do to finance the administration's proposed tax cut -- will collide repeatedly with efforts by the Fed to reduce money growth to slow inflation.

Thus, a smaller tax cut would be enormously helpful to the Fed in trying to achieve lower money growth, Volcker probably told the president. Even with a smaller tax cut, tight money still could continue to sideswipe the markets and the economy from time to time.

None of Volcker's message would hace constituted good news to the administration officials gathered at the White House except his most fundamental point: namely, that the Fed indeed is determined to meet its monetary growth targets. On the other hand Reagan ought to have been receptive to at least part of Volcker's message. Just the week before, he and his cabinet had gotten a briefing from Murray Weidenbaum, chairman of the Council of Economic Advisers, that included a discussion of the relationships between money growth and the economy.

One chart Weidenbaum used in the briefing showed a carefully smoothed path for the most closely watched measure of money, M1-B, which includes currency in circulation and deposits in financial institutions against which checks may be written.

"If you plot [M1-B] weekly or monthly, it would look like Rube Goldberg did it," Weidenbaum remarked last week to reporters, a comment with which Volcker would agree heartily. And of the published weekly numbers that so often cause gyrations in short-term interest rates, the CEA chairman said flatly, "I don't focus on weekly money supply numbers."

Unfortunately, financial market analysts do, as they try to guess the immediate course of interest rates. Regularly, the markets perversely respond to an increase in the weekly money supply by increasing interest rates. Normally, the effect of having a greater supply of money available to meet the demand for credit ought to cause the "price" of money -- the interest rate charged -- to fall. But the markets look beyond that supply-demand relationship in anticipation that the Fed will have to tighten credit conditions to keep the money supply from getting out of hand. Since that tightening ultimately would boost interest rates anyway, the markets just skip the intervening step.

Monetarist economists, including the dean of them all, Milton Friedman, maintain that increasing money supply growth can boost economic growth briefly at best while quickly leading to higher inflation. Because of the sensitivity of interest rates to inflation, Friedman has declared, "High interest rates are a sign that money has been easy, low interest rates are a sign that money has been tight."

The U.S. economy certainly has been marked in recent years by relatively easy money, high inflation and high interest rates.Somehow a shift toward tighter money has not yet produced low interest rates. The reason, officials such as Sprinkel argue, is that markets do not believe money will stay tight.

The question really is whether Friedman's dictum necessarily applies during a transition period from an inflation-prone economy with easy money to one of much lower inflation. Expectations of future inflation seem to change only slowly and many economic relationships are marked by actual or implicit long-term contracts that will not be adjusted overnight. Thus, a dose of tight money may not immediately lower inflation.

In such a case, the growth of total spending in the economy -- which is another way of saying the gross national product -- still can be limited by slower growth of money. But the GNP has both a real component and an inflation component and, in the short run, the impact of the monetary restraint may fall much more heavily on real economic activity than on inflation.

At present, inflation is still high albeit declining somewhat. And real economic activity stubbornly keeps expanding, although there, too, at a lesser pace. With the underlying demand for credit still fairly strong, an upward blip in the money supply such as occurred in April sent interest rates soaring.

It is still not very clear why the blip occurred, or what its magnitude really is. For instance, those weekly figures for M1-B, which the markets watch so closely, bounce around and they get revised. The current accepted figures for each week for the periof from Jan. 1 to April 29 represent changes from the originally reported figures by a much as plus $1.1 billion to minus $2.8 million. Many of the changes were the result of new seasonal adjustments.

Monthly figures are less volatile but hardly steady. In a debate recently at Ohio State University between two Federal Reserve officials and two monetarist economists, one of the latter, Robert Rasche of Michigan State University, said that even if the Fed followed to the letter all of the monetarist prescriptions for controlling the money supply the central bank probably still could not guarantee hitting its targets. The Fed could not count on coming closer than within one percent of its target on an annual basis with wider and wider deviations for shorter periods.

Moreover, Rasche and his partner in the debate, Allen Meltzer of Carnegie-Mellon Institute, agreed that deviations from the chosen money supply path for a quarter or more would have little impact on inflation or economic activity if growth were brought back on track speedily. A massive study by the Fed of monetary developments in 1980 reached the same conclusion.

Then why all the fuss? Meltzer put it this way: "We don't care what happens month to month. If the Fed had credibility . . . then you could say that . . . is an aberation. The reason we are so concerned about what is an arcane issue is . . . that we want to reestablish that credibility."

So the monetarists, and the Reagan administration, are seeking some changes in operating techniques -- as opposed to monetary growth targets -- at the Fed to try to smooth out even month-to-month variations which, except for purposes of credibility, do not matter economically, and at some cost in greater interest rate volatility.

"Exactly how much volatlity we would get is hard to say," Rasche told the audience that packed the OSU auditorium for the debate. "Most of the evidence comes from econometric models," but such tight control could "produce volatility that is scary." Nevertheless, that remains the monetarist objective.

In fact, the Federal Reserve moved with great alacrity in April to clamp down on money growth by reducing the availability of reserves, which must rise hand in hand with deposits, to the banking system. M1-B remained well within its target range in April, as the accompanying chart shows.

The administration, however, had to suggest that the Fed was at fault anyway. Otherwise, it wouldd have had to acknowledge that financial markets might not respond to the Reagan economic program as the administration has predicted confidently, that the combination of tight money, tax cuts, nondefense budget cuts and defense spending increases, and regulatory retrenchment might not produce simultaneously lower inflation, faster economic expansion and much lower interest rates.

Late in the week, even Sprinkel seemed to be conceding that possibility. In Gabon at the same IMF meeting as Volcker, Sprinkel was reported to be saying that interest rates would not fall significantly in the near future and would remain fairly high at least until next year.