Eastman Kodak Co.'s profits increased 9 percent in 1981 from the previous year despite a sluggish economy and a decline in foreign sales, the company said yesterday.

Fourth-quarter earnings for Kodak, the nation's largest maker of photographic material, were down 9 percent, largely because of adverse currency translations, the company said.

Kodak said its worldwide 1981 sales totaled $10.34 billion, up 6 percent from the $9.73 billion recorded in 1980.

U.S. sales were up 12 percent to $5.93 billion, but foreign sales declined one percent to $4.4 billion. Kodak blamed the strengthening dollar for the slump in overseas sales.

Worldwide net earnings increased to $1.24 billion ($7.66 a share) from $1.15 billion ($7.15) in 1980.

Fourth-quarter earnings of $371.4 million ($2.28) were down from $404.8 million ($2.51) for the fourth quarter of 1980. Worldwide sales declined to $3.07 billion from $3.11 billion.

Firestone Tire & Rubber Co.'s fiscal first-quarter earnings plunged to $2 million from $76 million a year before, largely because of the continued auto industry slump, the nation's second-largest tire producer announced yesterday.

Firestone earned 3 cents a share on sales of $889 million during the three-month period ended Jan. 31. During last year's quarter, Firestone earned $1.32 a share on sales of $1.066 billion.

Kroger Co.'s fiscal 1981 profits rose almost 36 percent from the preceding year to $128 million.

Earnings for the nation's second-largest grocery store chain came to $4.39 a share for the year, a 28.7 percent increase from the year-earlier figure.

Sales for the year were $11.26 billion, representing a 9.2 percent increase from the previous year's sales of $10.31 billion.

In the company's fourth quarter, which ended Jan. 2, profits were $52.6 million ($1.72 a share) compared with $29.6 million ($1.07) for the year before. Sales for the quarter were $2.74 billion, an increase from the $2.71 billion in the year-earlier period.

The New York Times Co.'s profits climbed 24 percent during the final three months of 1981, largely because of increased magazine and newspaper advertising income and circulation growth, the publishing company reported yesterday. Earnings for the year also were up sharply.

Net income for the fourth quarter was $13.4 million ($1.08 a share), up from $10.7 million (89 cents) in the fourth quarter of 1980. Revenue was $234.6 million, up 16 percent from $202.4 million a year before.

For 1981, the Times--which owns The New York Times newspaper as well as 18 regional newspapers--said earnings were $50 million ($4.03) compared with $40.6 million ($3.37) in 1980. Revenue was $845.2 million, up 15 percent from $733.2 million in 1980.

The newspaper group had operating profits of $54.1 million, up 26 percent. Advertising volume for the Times was up 9 percent from 1980, and circulation rose by 11,400 copies to a daily average of 912,500. Sunday circulation was an average 1.485 million, up 27,600 copies.