We study the distributional consequences of trade in a world with two industries and two heterogeneous factors of production. Productivity in each production unit reflects the ability of the manager and the abilities of the workers, with complementarity between the two. We begin by examining the forces that govern the sorting of worker and manager types to industries and the matching of workers and managers within industries. We then consider how changes in relative output prices generated by changes in the trading environment affect sorting, matching, and the distributions of wages and salaries.