Two months have now passed since the July 1 income tax cut that administration officials hoped would spark a recovery. The economy remains extremely weak.

Most analysts believe that there will be some growth in the final quarter of this year, especially after the dramatic improvement in financial markets in the last month. But not only will the upturn be many months later than originally predicted by President Reagan, it likely will be more feeble than most forecasters hoped.

There is considerable uncertainty about just why the economy has performed so dismally this year. Few outsiders shared the administration's official optimism at the beginnning of this year, when Reagan promised that the first signs of recovery were just around the corner. But most believed that the economy would be moving out of recession by the summer at least, especially with the 10 percent income tax cut to help it on the way.

Instead, the latest data suggest that the decline continued through July, and perhaps through August, too. While unemployment held steady last month, the factory work week shrank and so did the number of industrial jobs. Despite the tax cut, consumers have not yet started to buy more and business executives still are cutting back their spending plans.

There is, of course, one very important piece of good news that is bolstering faith in a recovery: Interest rates, particularly short-term rates, have fallen very sharply in recent weeks.

The failure of rates to fall earlier in the year -- despite a weak economy and declining inflation -- was a major factor in prolonging the recession. Although many people had stopped hoping for rates to fall by the time they finally did, earlier this year most forecasters built a rate decline into their projections.

One reason why the drop in interest rates did not come sooner--despite the weak economy and slower inflation--is that private credit demand stayed unexpectedly strong, as businesses apparently borrowed short term to try to stay afloat. This distress borrowing has eased off. One New York economist suggests that at least part of the reason for the slowdown in loans is that banks, increasingly nervous about the risks of lending to weak companies, have started to turn away would-be borrowers, even if they are willing to pay high rates.

Tight money policy also kept the cost of short-term money very high for the first half of the year. Shifts in the relationship between the gross national product and the money supply have made the Federal Reserve's monetary targets even tighter than intended. For some time, Fed Chairman Paul Volcker has made clear that he would not fight too hard to keep money growth within its target range while the economy stayed obviously weak. Much of the growth in the M1 measure of the money supply (currency in circulation and checking accounts) reflected increased saving in interest-earning checkable accounts rather than an increased willingness and ability to spend. Nevertheless, the above-target money growth kept the Federal Reserve from easing its policy for much of this year.

The tight grip of money policy apparently overrode the fiscal boost to the economy that came from July's tax cuts. Now hopes for recovery are centered on money policy. If only rates stay down, then consumers at least may start spending again, analysts hope.

Many believe there is a good chance that short-term rates will hold at close to today's 10 percent level, or even fall somewhat further, and that long rates may edge down, too. But their reasoning often depends on the assumption that the recovery from recession will be very slow, leaving private credit demands still fairly weak for the rest of this year, and on the belief that the Fed is now even more concerned about the state of the economy and the financial system than about adhering closely to its monetary targets.

It is known that senior Fed officials believe it was a happy combination of events in July and August that enabled the Fed to ease its stance in credit markets, bring down the discount rate, and encourage a general decline in rates, while at the same time not exceeding the M1 targets. Money growth slowed sharply earlier this summer, so the Fed was able to respond to increased fears of financial stress and economic weakness without breaching the targets.

But more recently money growth has started back up. Many in the markets now are worrying about a potential bulge in the M1 numbers this week that will be reported at the end of next week. Others believe there could be an October bulge. If this turns out to be the case, the Fed is likely to let M1 overshoot for a while, rather than risk a sharp rise in interest rates by fighting to suppress the bulge. If so, the Fed would be providing further evidence that the money supply targets have not been a reliable guide to policy makers this year.