The stock market staged a broad rally Friday, inspired by falling interest rates and hopes for a more generous credit policy at the Federal Reserve.

The Dow Jones average of 30 industrials climbed 44.80 to 2,488.61, cutting its loss for the week to 2.23 points.Advancing issues outnumbered declines by more than 5-to-2 in nationwide trading of New York Stock Exchange-listed stocks, with 1,123 up, 453 down and 428 unchanged.

The Labor Department reported Friday morning that the producer price index of finished goods rose 1.1 percent in October, slightly exceeding advance estimates in the financial world.

But the so-called "core" rate of inflation - excluding food and energy prices - was unchanged from September.

That bolstered hopes that the Federal Reserve would find more leeway to relax its credit policy in the near future, promoting lower interest rates.

On Thursday the Treasury completed a three-day auction of a record $34.25 billion in bonds and notes to a warm reception. Analysts said that gave extra credence to talk of lower rates.

In credit-market activity Friday, prices of long-term government bonds rose about $10 for each $1,000 in face value, lowering their yields to the 8.59 percent-8.62 percent range.

Gainers among the blue chips included General Electric, up 2 at 533/4; International Business Machines, up 23/4 at 1101/4; Philip Morris, up 3/4 at 483/4, and Boeing, up 7/8 at 447/8.

Bank stocks were broadly higher on hopes that falling rates would help heal the industry's finances and shore up the real estate market, to which many banks are heavily committed.

BankAmerica rose 11/4 to 221/4; First Chicago 1 to 15; Chase Manhattan 1/8 to 103/8; J.P. Morgan 11/4 to 401/2, and Manufacturers Hanover 1/4 to 181/4.

In the consumer credit group, Beneficial Corp. gained 11/2 to 39 and Household International 1 to 231/2.

Elsewhere, Russ Berrie & Co. rose 13/8 to 155/8. The company, which markets gift merchandise, reported higher third-quarter profits, raised its quarterly dividend from 10 cents a share to 15 cents a share, and declared an extra dividend of 60 cents a share.

Volume on the floor of the Big Board came to 146.11 million shares, against 155.57 million in the previous session. Nationwide, consolidated volume in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 181.41 million shares.

As measured by Wilshire Associates' index of more than 5,000 actively traded stocks, the market increased $51.69 billion, or 1.80 percent, in value.