Lower interest rates raise inflation concerns. Last week was particularly busy for the nation's central bank. The Fed helped stabilize shaky financial markets with injections of cash. And while the short-term outlook is bright, the Fed now has to consider the possibility of an overheated economy.

How do you extinguish a financial firestorm? The answer, the Federal Reserve Board decided last week, was to douse the financial markets with money.

Through transactions in the money markets, the Fed helped to slash interest rates, leading several banks to lower their prime lending rate. At the same time, it reassured the markets that it would stand behind banks or brokers who needed short-term funds.

The result was a dramatic rally in the bond markets, driving interest rates sharply lower. The widely watched 30-year Treasury bond declined in yield from 10.25 percent two weeks ago to 9.09 percent on Friday. Falling rates eventually calmed investors and helped stabilize the stock market after its most traumatic week since 1929.

While the Fed's actions seemed to be the only positive option available, investors will now try to assess the economic impact of the central bank's actions.

The Fed hacked down interest rates during a time of relatively strong economic activity as shown by statistics released last week. On Friday, the government reported that the nation's gross national product grew at 3.8 percent in the July-September period. Detroit automakers, meanwhile, reported that sales of new cars in mid-October were up 4.1 percent over a year ago - the first increase since August.

This bright economic news prompted Robert Ortner, undersecretary of commerce, to wonder ``whether the stock market pertains to this particular economy, or what economy it's looking at.''

The danger of lowering interest rates during an economic upswing is the possibility of stimulating inflation.

``It doesn't have to,'' says Georges Rocourt, chief economist with Mercantile-Safe Deposit & Trust Company in Baltimore. ``It depends on the way the Fed handles it.''

Fortunately for the Federal Reserve Board, there are no overt signs of inflation. On Friday, the government reported that the consumer price index rose by only 0.2 percent in September.

Even so, there are problems with providing a lot of liquidity during a time when a lot of extra funds are sloshing around in the stock markets of the world. The classic definition of inflation is too much money chasing too few goods.

The good news for the Fed is that it may not have to play the role of the cavalry coming to the rescue much longer.

President Reagan meets with congressional leaders this week to try to resolve their budget dispute. The politicians need to slice only $23 billion from the budget. But there is sentiment that both foreign investors and Wall Street would like to see deeper cuts. Further cuts would help to remove the government as a borrower, bringing interest rates down.

At the same time, Mr. Ortner noted that it is not likely the economy will continue to grow like it did in the third quarter. He points to the likelihood that consumer spending will tail off. This will be noticeable in retail sales, especially during the holidays.

Many economists don't believe the stock market drop will be felt in the nation's malls. ``It will not be reflected in a decline in general business,'' said John Templeton, on an appearence Friday on PBS's ``Wall Street Week.''

One sign that a slowdown is taking place will be an indication that the public is saving more. Last quarter, however, the savings rate was only 3 percent, compared with an average of 6 percent over the past 10 years. After watching the stock market drop, and economists mumble about possible recessions or depressions, the public is likely to respond by increasing its savings rate.

Despite the Fed's calming actions, important questions remain for the economy and the financial markets:

Will the President and Congress reach a significant accord on reducing the budget deficit?

Will foreign investors be enticed back into the US financial markets?

Will the central banks continue to prop the dollar up?

What will be the inflationary impact of the Fed's actions and what will happen when the Fed reabsorbs the funds it injected this week.