Equilibrium search with time-varying unemployment benefits

We show how time-varying unemployment benefits can generate equilibrium wage dispersion when identical firms post wages and homogeneous risk-averse workers search for jobs. We model a two-tier system similar to real-world UI programmes. The unemployed initially receive benefit b. Eventually, if a worker does not find a job, the benefit falls to s. The duration of high benefits is treated as an exponential random variable, so the model is stationary. We characterise the equilibrium and derive the comparative statics effects of changes in the two benefit levels and the expected duration of the high-benefit state on equilibrium wages and unemployment.