In this paper I study the assignment between machines of heterogeneous qualities and workers of heterogeneous skills in an infinite-horizon economy with matching frictions. I characterize first the efficient assignment and then the decentralizing market equilibrium. The efficient allocation assigns a unique machine quality and market tightness to each skill. This efficient allocation is saddle-path stable and the assignment along the stable path is constant over time. The efficient assignment is not positively assortative when machine qualities and skills are not sufficiently complementary with each other. Moreover, efficient wage rates are increasing functions of the skill level when the assignment is positively assortative, but not always so when the assignment is not positively assortative. Nevertheless, the social value of workers always increases in the skill level.Matching; Frictions; Efficiency; Inequality.
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