This paper examines efficient and equilibrium allocations in an economy where agents with diverse characteristics are matched through a time-consuming process to produce output. This is cast in a labour market where workers of different skills match with machines of different qualities. The efficient assignment is not always positively assortative and can be decentralized by a competitive mechanism where firms compete by posting wages and committing to the skill that their chosen machines are intended for. Implications on wage inequality are examined.
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