Vertical wage differences in hierarchically structured firms

In this paper, we present a cooperative model of a hierarchically structured firm to study wage differences between different levels in such a firm. We consider a class of wage functions that are based on marginal contributions to production. It turns out that the wage of a manager is always at least as high as the wage of its subordinates. On the other hand, the wage of a manager never exceeds the sum of the wages of its direct subordinates. These bounds are sharp in the sense that we can characterize for which production processes they are reached. For the class of constant elasticity of substitution (CES) production functions this implies that the wage differences are maximal for linear production functions, and they are minimal for Cobb–Douglas production functions.