Depending on workers’ application decisions, there may be more competition for some jobs than others. To capture this, we let qj be the ratio of workers who apply for jobs at firms offering wage Wj to the number firms posting that wage. We refer to this as the job’s expected queue length, an endogenous measure of the extent of competition for jobs offering Wj. We assume that a worker applying to wage wj is hired with probability //(fy), where ^ : E+ Uoo —> [0,1] is decreasing and continuously differentiable; if many workers apply for one type of job, each has a low employment probability website.

Symmetrically, the probability that firm j hires a worker is r](qj), where 77 : 1R+ U 00 —» [0,1] is increasing and continuously differentiable.2 This implies that holding constant the number of workers applying for a given wage, if more firms post that wage, each has a lower hiring probability. We impose the boundary conditions т/(0) = д(оо) == 0 and 77(00) = /x(0) = 1.

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