Search externalities with crowding-out effects

We consider a static search model with two types of workers, Nash bargaining, and free entry of firms. The matching function is specified so as cross-type congestion effects are asymmetric. Skilled workers create congestion effects for all, while unskilled workers do not affect the odds of employment 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 labor demand effect. The former (latter) effect dominates whenever the skill differential is small (large).