American consumers took on $2.52 billion more in new installment debt in November than they paid off, with a surge in auto loans helping to reverse the previous month's credit decline, government figures indicated yesterday.

The November increase in borrowing was the largest since the $2.98 billion surge in September 1981 when the current recession was only two months old.

Since then, borrowers generally have scaled back. In two months consumers even reduced the amount of outstanding credit despite the increase in prices and population.

Outstanding loans for autos expanded $1.82 billion in November after shrinking $78 million in October.

Meanwhile, major banks across the country cut their prime lending rate by one-half point to 11 percent yesterday, trimming the cost of business borrowing to its lowest level in 2 1/2 years.

Economists predicted that the Federal Reserve's aggressive efforts to pull the economy out of the recession by easing credit could lead to another drop in the prime rate to 10 1/2 percent, or even 10 percent, in the next few weeks.

President Reagan hailed the prime rate reductions as "good news" and said "it will be particularly important in the housing and automobile field."

Chase Manhattan, the nation's third-largest bank, had led the move to an 11 percent prime on Dec. 28, but no other major banks followed until yesterday when fifth-ranked Morgan Guaranty Trust of New York cut its prime and the rest of the industry followed.

Other major banks reducing their prime rate to 11 percent included Bank of America, No. 2-ranked Citibank, Continental Illinois, First National Bank of Chicago, Manufacturers Hanover, First National Bank of Boston, Mellon Bank of Pittsburgh, Crocker Bank, Chemical Bank, Security Pacific and Irving Trust.

Discounting the effect of the auto loans, which tend to move up or down sharply in line with special deals, private analyst Ted Gibson said the report on consumer credit seemed to show a continuation of "a very gradual restoration of confidence by the consumer."

The next few months' credit reports should show "pretty much more of the same," said Gibson, an economist with Crocker National Bank in San Francisco. "It indicates a slow but steady recovery when you add in housing, which is picking up."

In all, consumers took on $31.6 billion in new installment debt in November, up 12.6 percent from October. They paid off $29.1 billion in old debt, up 2 1/2 percent.

Through November of 1982, consumer credit grew only 2.4 percent. Consumer credit grew 6 3/4 percent during all of 1981.

Aside from car loans, outstanding installment debt for:

Revolving credit such as charge cards issued by banks and gasoline stations rose $107 million.

Mobile home loans increased $40 million.

Other credit such as cash loans from banks, credit unions, and savings and loan associations gained $560 million.