Search externalities with crowding-out effects
We propose a static search model with two types of workers, output sharing (Nash bargaining), and free entry of firms. The matching function is specified so as the unskilled do not create congestion effects for the skilled. An increase in the share of skilled workers has two effects on the welfare of the unskilled: a negative crowding-out effect, and a positive labour demand effect. The former (latter) effect dominates whenever the skill differential is small (large).
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