The Washington Post Co. yesterday joined other newspaper companies in reporting lower third-quarter profits.

The company earned $37.5 million ($3.14 a share) in the July-to-September period, a 16.2 percent decline from the $44.8 million ($3.50) profit in the same quarter a year ago. Sales increased a fraction to $348.7 million, from $346.3 million last year.

The decline in profits was driven largely by a relatively poor performance by The Washington Post newspaper, a reflection of weakening in the local economy. Ad volume at The Post fell almost 15 percent during the third quarter, continuing a yearlong falloff in which advertising is down 10.1 percent compared with the first nine months of 1989.

"As goes The Post, so goes The Post Co.," said Chuck Akre of Akre Capital Management, an Alexandria-based investment firm. Akre said the newspaper -- which contributes about half of the Post Co.'s profit and sales -- is feeling the effects of a shakeout among local retailers and slowing activity among local companies generally. The retail shakeout has cut advertising at The Post, he said, and the economic slowdown has pared help-wanted ads, typically among the most profitable forms of newspaper ads.

Richard D. Simmons, president of The Post Co., said the federal budget stalemate was also a factor in the quarter because retailers curbed their advertising out of fear of a furlough of government employees. "Once the budget impasse is resolved there will be some upturn in retail spending by advertisers, but there is nothing that leads me to be particularly ebullient" about the balance of the year, Simmons said.

Most major newspaper companies that have reported third-quarter earnings have announced a decline in profits, including Gannett Co. (down 4.5 percent), Dow Jones & Co. (off 17.3 percent) and New York Times Co. (down 95.6 percent). In response, newspaper companies have embarked on an array of cost-cutting measures. The Post plans to hold down costs by not increasing its staff or expenses and by reducing space in some weekly sections.

At The Post Co., net income has declined in each of the first three quarters of 1990. In the first nine months, The Post Co.'s profit was off 9.7 percent, from $146.8 million ($11.44) last year to $132.5 million ($10.90). Sales were up 1 percent to $1.1 billion.

In the third quarter, the company said revenue in its broadcast division was flat, while cable TV sales grew 14 percent and Newsweek magazine experienced a 7.4 percent increase.

The earnings report renewed the selling pressure on the company's publicly traded stock (a second class of non-trading stock is closely held by company Chairman Katharine Graham and her family). On the New York Stock Exchange, shares of The Post Co. closed yesterday at $184 a share, off $4.50. The close was the stock's lowest for the past 12 months and 41 percent off its all-time high of $311, reached last October.

The stock's decline since the beginning of the year, 35 percent, is roughly in line with newspaper and publishing stocks as a group, which have lost an average of 33 percent. However, the decline has been most pronounced in the past 45 days, with investors knocking almost 25 percent off the stock's market price.

Bob Coen, director of media forecasting for ad agency McCann-Erickson in New York, said he expected newspaper advertising to improve by the middle of next year. "It should get a little better by then," he said, "because how much worse could it be than it already is?"