Atlantic Richfield Co. and Shell Oil Co. reported declines in first-quarter earnings yesterday, while Union Oil Co. of California reported a small gain.

Arco, ranked seventh among U.S. oil companies, said it earned $346.5 million ($1.39 a share), down 18.9 percent from $427.0 million ($1.72) a year earlier. Revenues climed to $7.13 billion in the last quarter from $5.46 billion.

Shell, the nation's eighth-largest oil company, said its first-quarter profits fell 3.2 percent to $361 million ($1.17) from $373 million ($1.21) in the same 1980 period. Revenues rose to $5.41 billin from $4.80 billion a year earlier.

No. 16 Union said it earned $154.5 millin (89 cents), up 1 percent from $152.9 million (88 cents) a year earlier. Revenues climbed to $2.67 billion in the lastest quarter from $2.38 billion.

The companies said their exploration and production operations benefitted from higher crude oil prices, but that their refining and marketing departments were hurt by an inability to pass on those higher prices to consumers.

A world oversupply of oil, brought on by high Saudi Arabian production and increased conservation, has resulted in tough competition in gasoline and other refined products. Several major companies reported losses on those operations last week, and most reported that overall earnings were lower.

"A free market does not quickly absorb sudden cost increases when the market is weak," said Arco Chairman Robert O. Anderson. Arco said its refining and marketing operations showed a $14 million loss before taxes, due partly to adjustments for the end of the government's crude oil entitlements program.

Arco said a decline in demand for chemicals and copper depressed the profitability of those parts of the company.

Shell reported a 20.2 percent gain, to $375 million, in profits from exploration and production, but said earnings from oil products dropped 62 1/2 percent, to $27 million, "In the face of heavy pressure on industry profit margins."

Shell President John Bookout said higher prices helped to reduce demand for oil products, but he said his company's performance was better than many in the industry.

Union President Fred L. Hartley told shareholders at the company's annual meeting in Los Angeles that profits were higher for the company's crude oil and natural gas operations, chemical division and geothermal operations.

Pan American World Airways said yesterday that it lost $114.5 million for the first quarter against $74.9 million for the year-ago period.

Its consolidated operating revenues rose 3 percent $937.3 million from $910 million and its consolidated operating expenditures increased 6 percent to $1.021.5 billion from $964 million.

The company said the first-quarter results reflected poor airline passenger traffic experienced by the industry in general and its continued difficulty in raising international passenger revenue yield -- the amount of revenue received per revenue passenger mile flown.

Its scheduled revenue passenger miles dropped 9.6 percent.

Passenger revenue yield advanced 28.3 percent on domestic routes, but the increase was only 11.7 percent in international markets, which account for almost three-fourths of Pan Am's total system traffic.

Singer Co. said yesterday that it had improved earnings and sales in the first quarter in spite of recession conditions in North America and Europe.

The improvement came from better demand for consumer sewing products and consumer durables in Latin America, Africa and the Far East, Chairman Joseph B. Flavin said. Aerospace and marine and motor product sales also improved.

Net income was $14.2 million (75 cents a share) on sales of $736.9 million, compared with $10 million (51 cents) a year ago on sales of $727.2 million. The sales gain was 9.7 percent.

A lower effective tax rate and better results on foreign currency adjustments helped the earnings, Flavin said. But the strength of the dollar against foreign currencies was a brake on sales abroad. Flavin said he considered the overseas sales good in view of this handicap. Earnings were reduced, however, by a $7.3 million rise in interest charges, caused mainly by foreign borrowings.