Most of the nation's major banks sharply boosted their prime lending rate today from 12 1/4 percent to 12 3/4 percent, a bigger-than-expected increase that reflects continued tight monetary policy and a strong demand for business loans.

Despite record high interest rates, analysts say there are a few signs that a credit crunch is developing, a situation in which some borrowers cannot get loans no matter how much they are willing to pay.

But the analysts admit that if the Federal Reserve Board holds to its tight money policies too long, there is a risk of a crunch developing that could turn the coming recession into a serious one.

In fact, one bank official said, the sharp, $1.1 billion jump in loans by New York banks to businesses last week in part might be the result of businesses getting money now in order to avoid being shut out of the market later.

Analysts were not surprised that the prime rate reached 12 3/4 percent. Most now expect the prime rate to go to 13 percent this month, and some expect that the interest banks charge their best corporate customers for a short-term loan could climb above 13 percent before starting to decline.

But observers were surprised by the speed with which banks reached the 12 3/4 percent level, since most institutions have been raising their prime rates in quarter-point increments.

Today had started out much as analysts expected it would. New York's Citibank, the nation's second largest, raised its prime rate from 12 1/4 percent to 12 1/2 percent. That rate was matched by several other major banks, such as New York's Chemical and Manufacturers Hanover and Chicago's Continental Illinois.

Then, however, other major New York banks such as Morgan Guaranty Trust and Bankers Trust leap-frogged Citibank and posted a half-point prime rate rise of 12 3/4 percent.

After that, banks across the country began to announce prime rates of 12 3/4 percent. At the end of the day, Citibank, which at 10 a.m. had the highest prime rate in the country, was among a handful of major banks with a prime rate one quarter point below the norm.

"A 13 percent prime is on the way," said one analyst. "I guess Morgan (Guaranty) said to itself, 'Let's get it over with quickly.'"

A spokesman for Morgan Quaranty said the bank feels that 12 3/4 percent prime rate is "appropriate in view of money costs" and said that business loan demand continues to be strong.

For example, one banker noted, certificates of deposits issued by banks to obtain funds are now carrying interest rates between 11 1/2 percent and 12 percent, while a month ago they carried interest rates of about 10 to 10 1/4 percent.

A month ago the prime rate was 11 3/4 percent, where it was at the start of the summer.

But then, as the Federal Reserve began to tighten monetary policy in an attempt to slow money growth and restrain inflation, interest rates began to rise.

The prime rate hit 12 percent in mid-August, matching the record set during the credit crunch of 1974 and moved to 12 1/4 percent a week later.

The Federal Reserve conducts its monetary policy by buying and selling government securities in the open market, either injecting reserves into the banking system or withdrawing them.

It uses its open market operations to control the federal funds rate, the interest banks charge each other for overnight loans of excess reserve.

The notion is that by raising the federal funds rates, which in turn

The notion is that by raising the federal funds rates, which in turn affect other short-term rates, the central bank makes credit more expensive, discourages borrowing, thereby slowing monetary growth, which in turn puts the brakes on inflation.

"Unfortunately," as one banker noted, "there are hundreds of reasons why inflation is embedded in the system, and if the Fed should hit the brakes to hard there could be a sudden shortage of money in the economy."

That would produce the credit crunch that analysts fear and send the economy into a steep downward spiral.

In the other hand, if the Fed is too loose with its monetary policy, it will continue to feed inflation and push off the nation's day of reckoning with the recession.

"They've (the Federal Reserve Board) got a tough next eight to 10 weeks," another banker said. "If they get through the next few months, then the weakening economy will reduce money growth by itself."

In fact, the nation's credit markets are in a state that is typical of an early recession.

As demand for good falls off, companies find themselves accumulating inventories involuntarily. That means they made products with the expectation of selling them and cannot. To finance these inventories, companies have to borrow from banks or other sources.

At some point, when the company realizes that it is not selling products as fast as it once was, the company cuts back its production.

That's when layoffs begin and the effect of a recession begins to be felt in the economy.

At the same time, that is when demand for credit begins to slacken: as laid-off consumers borrow less to finance new purchases and as companies reduce their borrowing because they are no longer adding to their inventory.

The trick, for the Fed, is to make credit expensive enough to discourage companies from borrowing too much without making it so expensive that companies slash production sharply (because of the cost of carrying needed inventories) and hold off on making capital investments.

One banker said that three forces are at work encouraging business loan demand, but that it is impossible now to determine how to rank these forces:

A continuing volume of loans to finance acquisition of one company by another.

A new surge of borrowing by business to finance growing inventories and to replace declining cash flow.

An increase in short-term borrowing because of the high-cost of lon-term funds. In other words, businesses think long-term interest rates (those on loans for say three years or more) will drop soon and rather than be locked in to high interest rates for a long time, the companies are taking out loans for a few months and will switch to longer-term borrowing when those rates fall.