Optimal partition of a large labor force into working pairs

Kremer and Maskin (Wage inequality and segregation by skill. Working Paper 5718, National Bureau of Economic Research, , 1996) introduced an idealized model for pairing workers and managers with different skill levels into small teams selected to maximize productivity. They used it to analyze the impact of technological change and widening skill gaps on labor market segregation. The present paper extends their model to a workforce with multidimensional skill types, continuously distributed, and gives a mathematical analysis of the extension. Pure and mixed notions of optimal pairing are introduced, which play an important role in the formulation and analysis of the model. The existence and uniqueness of such pairings are established using techniques from the theory of optimal transportation and infinite-dimensional linear programming.