The hierarchical structure of a firm: a geometric approach

This paper develops a novel, geometric approach to modelling a firm's hierarchical structure. We model the firm''s hierarchy as the sector of a circle, in which the radius represents the height of the hierarchy and the angle of the sector represents the width of the hierarchy. The firm then chooses the height and angle in order to maximise profit. We analyse the impacts of changes in economies of scale, input substitutability and labour productivity on the firm''s hierarchical structure. We find that the firm will unambiguously become more hierarchical as specialisation of its workers increases or as its output price increases. The effect of changes in scale economies is contingent on the level of task specialisation and output price.