Hierarchical Assignments: Stability and Fairness

We study a simple model of the job market, where workers are assigned to employers. We specify conditions under which the market is hierarchical in a natural sense. For such hierarchies, we can state explicit values for the earnings in the worker-optimal and employer-optimal solutions. This is a discrete analogue to the Ricardian differential rent model of Sattinger (1979). We discuss the compatibility problems between fairness and stability of earnings and assignments and argue for a certain solution.