Major banks boosted the prime lending rate by one-half point to 11.5 percent yesterday, the highest in four years, and just below the record 12 percent peak that many market observers now predict will be exceeded soon.

The increase in the prime rate - the cost of borrowing for a bank's biggest and best customers - was initiated by Citibank of New York, and quickly followed by other major U.S. banks even though a one-half point jump is unusual.

It was the second prime rate increase in two weeks, and Citibank's 14the boost since Jan. 1, when the rate stood at 7 3/4 percent.

Rates for consumer loans and for home mortgages are not linked directly to the prime rate. But those rates, like all others, have already moved up sharply in response to Federal Reserve board policy - backed by the Carter administration - to tighten credit markets in an effort to reduce inflation and protect the U.S. dollar.

Meanwhile, the Carter administration put its stamp of approval on an average 3.2 percent price increase by U.S. Steel Corp. as "consistent" with its new wage-price guidelines program. Another bit of good news was an offer by the American Association of Railroads to cut proposed freight rate increases by 12 percent. The scaled-down rate boost would be 6.5 percent. (See Page C9).

Daniel J. Callahan, president of the Riggs National Bank of Washington (which maintained an 11 percent prime rate yesterday) said that "this type of interest rate environment puts pressure on the banks to become more qualitative in their loans."

He said Riggs would "look at consumer loans much more closely," but noted that the bank does not always try to charge the highest rate obtainable "if the relationship is a good one."

He also pointed out that banks here and in many states have a legal maximum on consumer installment loan interest - around 11.5 percent. Many banks are still making auto and home mortage loans at 10 percent, but on a highly selective basis.

Some Businessmen and economists are concerned that the steep rise in interest rates will result in a recession next year. Arthur M. Okum, a former chairman of the Council of Economic Advisers, in a recent commentary for the American Security Bank predicted higher interest rates, and said that "history wants us that when the monetary brakes do take hold, they typically grab abruptly rather than working gradually."

Administration officials have said they recognize the risk of recession but hope that the impact of higher interest rates will be lessened through availability of a new 26-week "money market" certificate. These certificates enable savings institutions to keep pace with interest paid on competing investments.

This has slowed the outflow from savings institutions that normally takes place during a tight money period, and has maintained a flow of money - at high interest rates for housing construction.

The bank prime rate reached record 12 percent during the 1974-75 recession, when there was a true-monetary "crunch" - a period when loans were hard to get even at high rates.

So far, although there has been a strong demand by business for credit, an actual crunch has not developed. But the soaring level of business borrowing, especially in New York, has escalated the effort by banks to secure new sources of funds by paying higher rates. In turn, this helps push up the prime rate.

Thus, large New York banks competing for deposits are reportedly offering 11 to 11.5 percent or more for six-month certificates of deposits, and 10.8 percent for 90-day CDs. Interest rates have also risen in the Euro-dollar market.

A New York money market expert, Henry Kaufman of Salmon Brothers, said that banks have been pushed to increase the rate of their return by their own higher costs for money, by increased reserve requirements as well as by soaring business demand.

As for commercial loans to business, he observed that the total for all reporting banks in the country from Jan. 1 through Nov. 15 of this year had amounted to $13.8 billion, compared with only $6.5 billion in the comparable period in 1977.

Kaufman said he thinks that the prime rate will "significantly exceed" 12 percent, and that high-grade corporate bond yields will move into "the 10 to 11 percent range." Most observers agree that yesterday's 11.5 percent figure eventually will be exceeded, but have not yet predicted a rate over 12 percent.

The big business demand for money reflects three related developments.

First, economic activity continues high, including housing construction, insulated against the normally ravaging effects of high interest rates by the new, 26-week certificates.

Second, business has been borrowing more than it needs now in anticipation that it will have to pay even higher rates in the next six to nine months.

Third, some observers believe that a share of the anticipatory borrowing is based on fear that the Federal Reserve may later establish credit controls, keyed to past borrowing averages. In an interview last week, Federal Reserve Chairman William G. Miller denied that such a move is contemplated. But market men, who have seen reversals of policy before, continue to be edgy about that prospect.

The Fed's high interest rate policy - reflected in a 1 percent point boost in the discount rate to 9.5 percent on Nov. 1 and a series of sharp increases, in the federal funds rate - is a matter of daily concern to money markets.

The discount rate is the rate at which member banks borrow from the Fed. The federal funds rate, which is established by the Fed, is the over night borrowing rate at which banks lend money to one another. This rate largely determines the level of short-term interest rates.

The actual federal funds rate is announced only after a 30-day delay, but observers yesterday believed they saw signs that the Fed had inched its target up 9 7/8 percent from 9 3/4 per cent. Analysts said, however, that factors other than the federal funds rate had caused yesterday's move by the banks.

Treasury bill rates were also up sharply, and since savings institutions' 26-week certificates are tied to the Treasury bill rate, it is likely that the yield on such certificates will rise again. In turn; that will add pressure on mortgage rates.