Stock prices fell sharply today as new inflation worries and market declines in Tokyo and London set a gloomy mood for Wall Street. The Dow Jones average of 30 industrials tumbled 44.16 points to 2,716.51 by noontime in New York. Losers outnumbered gainers by about 8 to 1 in nationwide trading of New York Stock Exchange-listed issues, with 173 up, 1,394 down and 301 unchanged. The Labor Department reported that the producer price index of finished goods rose 0.7 percent in December, exceeding most advance estimates for that measure of inflationary pressures. The index finished 1989 with an increase of 4.8 percent, its biggest in eight years. Analysts said the news dealt an abrupt setback to hopes on Wall Street for any further moves soon by the Federal Reserve to relax its credit policy and encourage lower interest rates. Stock traders also were absorbing word of overnight declines in the Japanese and British markets, where interest-rate and inflation worries have also been weighing down enthusiasm lately. Among actively traded blue chips, General Electric dropped 1 to 63}; Exxon ~ to 48&lsqb;; International Business Machines 1 to 98~; Coca-Cola 1| to 74}, and Philip Morris ~ to 39&lsqb;. Precious-metals stocks, which have been rallying of late along with the price of gold, bucked the downtrend. Homestake Mining gained &rsqb; to 22&lsqb;; ASA Ltd. 1&lsqb; to 62&rsqb;, and Newmont Gold &rsqb; to 54}. The NYSE's composite index of all its listed common stocks fell 2.94 to 189.84. At the American Stock Exchange, the market value index was down 4.46 at 374.89. Volume on the Big Board came to 92.37 million shares at noontime, up from 76.09 million at the same point Thursday.