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This article presents a tractable framework for studying frictionless matching in education and labor markets when individuals have heterogeneous communication and cognitive skills. In the model, there are gains to specialization and team production, but specialization requires communication and coordination between team members. Individuals accumulate cognitive skills in schools when young. As adults, they decide whether to work as a manager or a worker in a firm or become a teacher in a school. Individuals with more communication skills will become either managers or teachers and earn higher wages. Each manager manages several workers and each teacher teaches several students, with their span of control being determined by their communication skill. These individuals also invest discretely more in education than marginally different individuals who become workers. Equilibrium is equivalent to the solution of an utilitarian social planner solving a linear programming problem.
McCann et al. (Tue,) studied this question.