Optimal Wage Band for Job Matching with Signaling

We study an optimal wage band problem in which a policymaker sets a wage band prior to a competitive matching labor market, where education signals worker ability. We first prove the uniqueness of the competitive signaling equilibrium under a general class of utility and profit functions. We also show that the optimal wage band problem is isomorphic to an optimal ability threshold problem, which is more tractable than the original formulation. Building on this theoretical foundation, we construct a parametric model and analyze the mechanisms through which the policymaker's choice of a wage band leads to improved welfare outcomes compared to a no-intervention scenario. The implications and mechanisms we identify, arising from the asymmetric information, contrast sharply with those in the existing literature. Finally, the generality of our framework makes it suitable for a wide range of competitive matching applications, where agents invest in costly signals under asymmetric information.