Interest rates will be crucial in determining what happens to the economy in the next few months.

But as most anaylsts have been wrong so far this year in their predictions of rate movements, they are cautious in their forecasts for the rest of the year. Economists have also been surprised by the resilience of the economy in the face of record high rates.

The prime rate now seems to be edging down from its summer highs, but bankers are not yet convinced that the decline will continue. So far this year the cost of money has soared higher, and stayed high longer, than almost any economist expected. Meanwhile, however, the economy, far from collapsing under the impact, has performed more strongly than most predicted.

Although there are now clear signs that the pace of the economy is slowing, the downturn has come later, and is less severe than many forecasters predicted. Most are now expecting a further slight contraction in real output this quarter, followed by a turnaround at the end of this year or the beginning of next.

But the more optimistic ones who expect the economy to pick up in the last quarter, such as Otto Eckstein of Data Resources Inc., generally caution that if interest rates remain very high, recovery could be delayed.

The administration, of course, has been forecasting a sharp fall in rates for several months. This, in combination with the tax cuts effective next month, will revitalize the economy and lead to steady growth next year and beyond, officials say.

But other analysts, such as Charles L. Schultze, former adviser to President Jimmy Carter, expect interest rates to stay relatively high and to put a brake on the economy throughout this administration.

If the Federal Reserve's tight-money policy continues to hold interest rates high, the economy may be unable to recover strongly, they argue. The restraint on money and credit will inhibit business expansion, as well as consumer demand for houses, autos and other goods typically bought on credit.

These tight-money policies are Reagan's main weapon against inflation, although they are actually the responsibility of the Federal Reserve. The administration predicts that inflation will drop significantly this year and through 1984. The latest official forecast shows consumer prices up 8.6 percent in the fourth quarter from a year ago, compared with a rise of 12.6 percent in the previous 12 months.

Many analysts share the official optimism about this year's inflation rate. Despite a sudden return to double-digit inflation in July's CPI, there has been a marked slowing of price increases since Reagan took office. Few expect the July number to amount to more than a temporary blip.

But much of this year's improvement has come from special factors, which may not continue to restrain price rises. A slumping oil market and weak food prices have contributed importantly to the cooling of inflation, while a very strong dollar has also helped by cutting the cost of imported goods. Although the benefit from cheaper oil may go on, food prices have already started to turn up, and many believe the dollar has peaked.

A sustained slowing of prices can come only if wage increases are cut. Labor costs are by far the biggest component of total costs, so price rises cannot diverge for too long from the underlying rate of wage inflation.

Next year is a major bargaining year, with several key wage contracts up for renegotiation. These will indicate how successful Reagan can be in holding down the price spiral in 1982 and later years. Many experts doubt there will be a sharp reduction in wage raises in next year's contracts, particularly if the administration's growth predictions are fulfilled. Workers are unlikely to moderate their wage demands at a time when output is rising and firms are stepping up their demand for labor.

This underlines a central problem for the president. From the outset he has been criticized for espousing policies that pull in opposite directions: tax cuts for growth and tight money to fight inflation.

The summer slump in bond markets - which shows little sign of easing - could be a symptom of the conflict implicit in Reagan's economic plan. Despite the slowing of inflation, the Federal Reserve's extremely tight rein on the money supply and Wall Street's fears of a huge federal deficit have kept interest rates sky high.

Tax cuts are about to set fiscal policy on a more expansionary path, but the Federal Reserve has promised to continue its extreme tight-money policy.

Schultze predicts the result of such a clash between fiscal and money policy will be sustained high interest rates, even if inflation comes down somewhat. Although this may prevent the economy from growing very rapidly, he believes there probably can be some expansion of output and employment even with high rates. "Neither utopia nor disaster" was how he characterized the likely outcome.

What if the administration succeeds in finding more spending cuts this fall, to make good its promises of narrowing the deficit? This may help cheer up the markets, although they are not impressed with the size of cuts so far being talked about. But at the same time, deeper spending cuts will slow the economy and offset the stimulative effects of the tax cut.

Recent experience has made clear the underlying strength and resilience of the economy. Several analysts say this year's slowdown is not a true recession because there have been no sudden slumps in business orders or employment, despite some decline of output. In addition, while some sectors have declined, others, such as energy, have boomed.

But, as administration officials now seem to be admitting, there cannot be a strong recovery as long as interest rates stay high. The big question is whether rates can remain high without toppling the economy into a more serious recession.