The immobile incumbent problem in a model of short-term wage-posting

This paper takes the canonical Burdett-Mortensen model of wage-posting and relaxes the assumption that wages are set once-for-all, instead assuming they can only be committed one period at a time. It derives a closed-form solution for a steady-state Markov Rank-Preserving Equilibrium and shows how this relates to the canonical model and performs some comparative statics on it. But it is shown that a Rank-Preserving Equilibrium may fail to exist because employers have more monopsony power over existing workers than new recruits and that this non-existence can be a problem for plausible parameter values. It is shown how a Rank-Inverting Equilibrium may exist. It is argued that this problem is likely to occur in a wide range of search models.