An Equilibrium Analysis of Wage-Productivity Gaps - Guasch, J. Luis; Weiss, Andrew (Review of Economic Studies, 1982)
We develop a model in which each firm chooses a hiring standard as well as a wage schedule and an application fee, we then characterize the set of Nash equilibria, and establish necessary and sufficient conditions for the existence of equilibrium. If the distribution of productivities within each ability type is Gaussian, workers who pass the test will be paid more than the value of their marginal product, while workers who fail the test will receive a wage, net of the application fee, below the value of their marginal product.