Aluminum Company of America (Alcoa) (defendant) was the sole producer of virgin aluminum ingot in the United States, pursuant to two patents. Purchasers often distinguished between virgin ingot and secondary ingot, which was salvaged from ingot scrap. However, the price difference between the two was only between one and two cents per pound, and for many aluminum uses the two could be used interchangeably. As demand for aluminum ingot increased, Alcoa continually increased its production of virgin ingot to keep up with the demand. Aluminum Limited (Limited) (defendant) was a Canadian company formed in 1928 to take over Alcoa properties outside the United States. Limited was part of the "Alliance," which was a Swiss corporation created pursuant to an agreement between Limited and companies from France, Germany, and the United Kingdom. The Alliance members entered into agreements in 1931 and 1936 concerning aluminum manufacture and sale. The 1936 agreement set production quotas for each member that included aluminum imports into the United States. The United States Government (plaintiff) brought suit against Alcoa and Limited. The government alleged that Alcoa was monopolizing interstate and foreign commerce with respect to the manufacture and sale of aluminum ingot and that Alcoa and Limited had illegally conspired to form a monopoly and restrain domestic and foreign commerce regarding the manufacture and sale of aluminum ingot. After a trial, the district court dismissed the complaint. Among other conclusions, the district court calculated Alcoa’s market share at 33 percent by including secondary ingot in its market definition. If the market were restricted to virgin ingot, Alcoa possessed roughly 90 percent of the market share. The district court also excluded the ingot that Alcoa produced and fabricated itself. The district court also found that the Alliance's 1936 agreement did not materially affect U.S. commerce or trade because the amount of ingot imported in 1936 and 1937 was higher than in previous years. The United States appealed. The appeal was referred to the court of appeals because the United States Supreme Court was unable to attain a quorum of six justices required to hear the case. Among other issues on appeal, the appellate court considered whether Alcoa had a monopoly on the market for virgin aluminum ingot in violation of § 2 of the Sherman Act and whether the Alliance's 1936 agreement between Limited and the other foreign producers constituted an unlawful conspiracy under § 1 of the Sherman Act.